GRE 2025 Model Paper Set 2 Question Paper with Solutions PDF

Step 1: Understanding the Concept:

This sentence completion question tests vocabulary and logical reasoning. The sentence presents a contrast, indicated by the phrase "instead of being merely," between an active form of learning and a passive one. We need to select a pair of words that accurately reflects this contrast.


Step 2: Detailed Explanation:

The structure of the sentence requires the first blank to describe an active role and the second blank to describe a passive role.

The phrase "force students to --- learning" suggests an active engagement.

The phrase "merely ---- of knowledge" suggests a passive role, simply receiving information without interaction.

Let's evaluate the options:

(A) To "shore up" learning means to support it, which is somewhat active, but being "reservoirs of knowledge" is a metaphor for holding knowledge, not passively receiving it. The contrast is not clear.

(B) To "accede to" learning means to agree to it, which is not the intended meaning of active engagement. "Consumers of knowledge" is a possible description of a passive role, but the first word doesn't fit well.

(C) To participate in learning is a clear description of an active role. Being mere recipients of knowledge perfectly describes the passive role. This pair creates a strong and logical contrast.

(D) To "compensate for" learning makes no sense in this context. "Custodians of knowledge" implies protecting knowledge, which is not the passive role described.

(E) To "profit from" learning is a possible outcome but not the action itself. "Beneficiaries of knowledge" is similar to recipients, but "participate in" provides a much stronger contrast.


Step 3: Final Answer:

The pair "participate in .. recipients" establishes the most precise and logical contrast between active engagement and passive reception. Therefore, option (C) is the correct choice.
Quick Tip: Look for keywords that signal relationships between different parts of a sentence. Words like "instead of," "while," "although," and "however" indicate contrast, which can help you predict the type of words needed for the blanks.

Step 1: Understanding the Concept:

This question asks for the word that best describes the context influencing the development of leaves. The sentence provides specific examples to clarify this context.


Step 2: Detailed Explanation:

The sentence states that the form and physiology of leaves change based on a certain factor.

It then gives examples of this factor: "different degrees of light and moisture."

Light and moisture are key components of a plant's physical surroundings.

The collective term for these external conditions is the environment.

Let's check the other options:

(A) "relationship": This is too vague. A relationship with what?

(B) "species": While different species have different leaves, the sentence explains variation within leaves based on external factors (light, moisture), not just genetics.

(C) "sequence": This implies an order of development, which is not what the examples (light and moisture) describe.

(D) "patterns": This is a result of the variation, not the cause of it.


Step 3: Final Answer:

The examples of "light and moisture" directly point to the conditions of the surrounding environment as the factor causing variation in leaves. Thus, option (E) is the correct answer.
Quick Tip: Pay close attention to examples given in a sentence. They often serve as direct clues to the meaning of the missing word. Here, "light and moisture" are classic examples of environmental factors.

Step 1: Understanding the Concept:

This question requires finding two words that complete a logical argument presented in the sentence. The argument connects the basis of intelligence to the state of animals, based on the fact that they are "mute."


Step 2: Detailed Explanation:

The sentence proposes a theory where the first blank is the "logical structure underlying thinking."

The second part of the sentence draws a conclusion about animals based on their being "mute" (unable to speak).

The word "mute" directly relates to speech or language. This strongly suggests that the theory in question equates intelligence with language.

If the theory holds that language is the basis of intelligence, and animals are mute (lack language), then the logical conclusion is that animals must lack intelligence.

The word that means "lacking intelligence" is mindless.

Let's examine the pair: "language.. mindless". If the theory sees language as the basis of thinking, and animals lack language (are mute), then they must be mindless. This is a coherent and logical argument.

The other options do not create such a direct logical link with the keyword "mute."


Step 3: Final Answer:

The connection between "mute" and "language" is the key to solving this question. The pair "language.. mindless" creates a consistent argument as described in the sentence. Therefore, option (E) is the correct choice.
Quick Tip: Identify the core argument in the sentence. Here, it's a cause-and-effect or premise-and-conclusion structure: "If X is true, and Y is a fact, then Z must be the conclusion." The word "mute" is the critical clue for both blanks.

Step 1: Understanding the Concept:

This sentence completion question uses the words "Though" and "nonetheless" to establish a contrast between Edna St. Vincent Millay's personal life and her work ethic. We need to find a pair of words that are opposites.


Step 2: Detailed Explanation:

The second part of the sentence describes her as "producing several pages of complicated rhyme in a day." This indicates she was hardworking, productive, and methodical in her work. A good word to describe this is disciplined.

The structure "Though..., nonetheless..." requires the first word to be in contrast with "disciplined." We need a word that describes a characteristic that is the opposite of being disciplined.

Let's analyze the options with this in mind:

(A) "jaded" (tired, bored) and "feckless" (ineffective, worthless) are both negative and not clear opposites.

(B) "verbose" (wordy) and "ascetic" (self-disciplined, austere) are not direct opposites.

(C) "vain" (conceited) and "humble" are opposites, but "humble" doesn't fit the description of her being a productive writer.

(D) impulsive (acting without forethought) is a strong contrast to being disciplined (acting with control and routine). This pair fits the sentence's logic perfectly. An impulsive personal life contrasts sharply with a disciplined work life.

(E) "self-assured" (confident) and "sanguine" (optimistic) are similar in meaning, not contrasting.


Step 3: Final Answer:

The contrast between being "impulsive" in personal matters and "disciplined" in professional work is the most logical and fitting choice for the sentence. Therefore, option (D) is correct.
Quick Tip: Words like "Though," "Although," "However," and "Nonetheless" are crucial signposts for contrast. When you see them, you can almost always expect the two parts of the sentence to present opposing ideas.

Step 1: Understanding the Concept:

This question asks for a word that describes the children's natures, which are presented as being in "sharp contrast" to the "even-tempered" nature of their parents. We need to find an antonym for "even-tempered."


Step 2: Detailed Explanation:

"Even-tempered" means calm, not easily angered or upset.

The phrase "in sharp contrast to" tells us we are looking for a word with the opposite meaning. The opposite of being calm and steady is being volatile, unpredictable, or subject to mood swings.

Let's examine the options:

(A) mercurial means subject to sudden or unpredictable changes of mood or mind. This is a direct antonym of "even-tempered."

(B) "blithe" means showing a casual and cheerful indifference. While not calm, it's not the best contrast to "even-tempered."

(C) "phlegmatic" means having an unemotional and stolidly calm disposition. This is a synonym for "even-tempered," not an antonym.

(D) "introverted" means shy or reserved. This is a personality trait, not necessarily related to temperament in the way the sentence implies.

(E) "artless" means natural and simple, without guile. This is not related to temperament.


Step 3: Final Answer:

The word that best captures the opposite of an "even-tempered" disposition is "mercurial." Therefore, option (A) is the correct answer.
Quick Tip: Understanding the precise meaning of vocabulary is key. For contrast questions, think of the core meaning of the given word ("even-tempered" = calm, steady) and then search for the option that means the opposite (volatile, changeable).

Step 1: Understanding the Concept:

This sentence describes a cause-and-effect relationship in social science research. The first blank describes what researchers do with "scientific rigor" and a "quantitative approach," and the second blank describes the resulting effect on the "scope" of their research.


Step 2: Detailed Explanation:

The end of the sentence states that the researchers focus on "narrowly circumscribed topics." This indicates that their scope has been reduced or restricted. Words like "limited," "narrowed," or "diminished" would fit the second blank. This immediately makes options (B), (C), and (E) unlikely, as they suggest an expansion of scope.

Now let's choose between (A) and (D).

The sentence implies that using a quantitative approach is seen as a way to achieve scientific rigor. Therefore, researchers are likely equating or identifying scientific rigor with this specific approach.

Let's test the pair from option (D): "By identifying scientific rigor with a quantitative approach, researchers... have limited their scope..." This makes perfect logical sense. Because they define rigor only in quantitative terms, they are forced to limit their studies to topics that can be quantified.

Let's test the pair from option (A): "By undermining scientific rigor with a quantitative approach..." This is contradictory. Researchers use quantitative methods to enhance, not undermine, rigor.


Step 3: Final Answer:

The most logical construction is that by equating (identifying) rigor with quantitative methods, researchers consequently limit their scope of study. Therefore, option (D) is the correct choice.
Quick Tip: Solve sentence completion questions with two blanks by focusing on one blank first. Often, the context makes one blank easier to figure out. Here, the phrase "narrowly circumscribed topics" is a strong clue for the second blank, allowing you to eliminate several options quickly.

Step 1: Understanding the Concept:

The sentence links the nature of a long-standing philosophical issue with the attitude of modern philosophers toward it. The two words should be logically consistent with each other.


Step 2: Detailed Explanation:

The sentence describes an issue that has been discussed for centuries (from the 17th to the 20th). This longevity suggests the issue is difficult, persistent, and not easily solved.

Let's analyze the options based on this idea.

(A) If an issue is "absorbing" (interesting), it is unlikely to be approached with "indifference." This is contradictory.

(B) If an issue is "unusual," it might be approached with many emotions, but "composure" (calmness) doesn't have a strong logical link.

(C) An issue could be "complex," but this doesn't automatically mean it's approached with "antipathy" (strong dislike).

(D) "auspicious" means favorable or promising. It's unlikely that a favorable issue would be approached with "caution."

(E) If an issue has a problematic character (full of difficulties, hard to solve), it is very logical that modern philosophers would still approach it with uneasiness or apprehension. The two words are highly consistent and reflect the nature of enduring philosophical problems.


Step 3: Final Answer:

The pair "problematic.. uneasiness" provides the most logical and consistent description of a difficult, long-standing issue and the cautious attitude it inspires. Therefore, option (E) is the correct answer.
Quick Tip: For two-blank sentences, ensure the chosen words have a logical relationship that is supported by the context. Here, a difficult issue (problematic) leads to a cautious or worried approach (uneasiness).

Step 1: Understanding the Concept:

This is an analogy question. We must first determine the relationship between the words in the first pair (TRIPOD: CAMERA) and then find another pair of words that has the same relationship.


Step 2: Detailed Explanation:

The relationship between TRIPOD and CAMERA is one of function and support. A TRIPOD is a stand used to support a CAMERA.

Now we analyze the options to find a pair with the same "support" relationship:

(A) Scaffolding is a temporary structure for workers, not to support a ceiling itself (pillars support a ceiling).

(B) A prop is an object used on a set, but it doesn't support the set.

(C) An EASEL is a stand used to support a CANVAS for painting. This relationship perfectly matches the original pair.

(D) A projector displays a film; it doesn't support it.

(E) A frame encloses or borders a photograph; it provides structural support but in a different way than a stand. The easel/canvas relationship is much more direct and parallel to tripod/camera.


Step 3: Final Answer:

The relationship "A is a stand used to support B" is clearly present in both "TRIPOD: CAMERA" and "EASEL: CANVAS". Therefore, option (C) is the correct answer.
Quick Tip: To solve analogies, create a precise sentence that defines the relationship between the first two words. For example, "A TRIPOD is a structure designed to hold up a CAMERA." Then, test this sentence on the answer choices: "An EASEL is a structure designed to hold up a CANVAS."

Step 1: Understanding the Concept:

This analogy question requires us to identify the relationship between the given pair of words and find an option with a parallel relationship.


Step 2: Detailed Explanation:

The relationship between AQUATIC and WATER is definitional. AQUATIC means living in, growing in, or relating to WATER.

Let's analyze the options to find the same relationship:

(A) Cumulus is a type of cloud, not a word meaning "relating to clouds."

(B) Inorganic describes substances not of living origin; elements can be inorganic, but the relationship is not as definitional.

(C) Variegated means having patches of different colors; it can describe leaves, but it doesn't mean "relating to leaves."

(D) Rural relates to the countryside, not specifically to soil.

(E) ARBOREAL means living in, growing in, or relating to TREES. This relationship is identical to the one between AQUATIC and WATER.


Step 3: Final Answer:

The relationship "X means relating to Y" holds for both "AQUATIC: WATER" and "ARBOREAL: TREES." Therefore, option (E) is the correct answer.
Quick Tip: For analogies involving adjectives, the relationship is often "X is a quality of Y" or "X means relating to Y." Be precise. "Aquatic" doesn't just involve water; it is defined by it. Look for the same definitional link in the options.

Step 1: Understanding the Concept:

This analogy is based on a cause-and-effect relationship. One word is a substance or agent, and the other is the quality or state it produces.


Step 2: Detailed Explanation:

The relationship is: An EMOLLIENT is a substance that causes or promotes SUPPLENESS (softness and flexibility).

We need to find an option with the same cause-and-effect relationship.

(A) An unguent is an ointment; it might increase elasticity, but that's not its primary defining purpose in the same way an emollient's is to create suppleness.

(B) A precipitant causes a substance to precipitate (form a solid), not cause absorption.

(C) An additive is something added, but it doesn't necessarily cause fusion (joining together).

(D) A DESICCANT is a substance that causes or promotes DRYNESS (by absorbing moisture). This relationship perfectly mirrors the original pair.

(E) A retardant is a substance that slows down a process; it decreases, not promotes, things like permeability or flammability.


Step 3: Final Answer:

The relationship "A is a substance that causes the state of B" is consistent between "EMOLLIENT: SUPPLENESS" and "DESICCANT: DRYNESS." Therefore, option (D) is the correct answer.
Quick Tip: In cause-and-effect analogies, clearly state the relationship: "A causes B." An emollient causes suppleness. A desiccant causes dryness. This simple sentence test can quickly confirm the correct option.

Step 1: Understanding the Concept:

This analogy describes a specific manner of performing an action. The second word is a less focused, more casual, or aimless version of the first word.


Step 2: Detailed Explanation:

The relationship is: To DOODLE is to DRAW in an aimless or casual way, often while one's attention is elsewhere.

Let's analyze the options to find a similar relationship:

(A) To whisper is to talk quietly, which specifies volume, not aimlessness.

(B) To RAMBLE is to TRAVEL (or walk) in a leisurely or aimless way. This perfectly matches the relationship in the original pair.

(C) To walk is a slower version of to run; this is a relationship of speed/intensity, not purposefulness.

(D) To add is a specific type of calculation, not an aimless way of calculating.

(E) To gobble is to eat quickly and greedily; this describes manner (speed/greed), not aimlessness.


Step 3: Final Answer:

The relationship "to B is to A in an aimless or casual manner" applies to both "DOODLE: DRAW" and "RAMBLE: TRAVEL". Therefore, option (B) is the correct answer.
Quick Tip: Be precise about the relationship. Don't just say "B is a type of A." Specify how it's a type. Doodling isn't just any kind of drawing; it's aimless drawing. Rambling isn't just any kind of traveling; it's aimless traveling.

Step 1: Understanding the Concept:

This analogy relates a quality or characteristic to the action that it facilitates.


Step 2: Detailed Explanation:

The relationship is: Something that is CONSPICUOUS is easy to SEE. The first word is a quality that makes the second action easy to perform.

Let's analyze the options with this relationship in mind: "Something that is X is easy to Y."

(A) Something that is repulsive is hard to forget (it's memorable), not easy.

(B) These words have no clear relationship of this type.

(C) Something that is deceptive is intended to delude, but the relationship is one of purpose, not ease. Also, "delude" is an action performed by the deceptive thing, not on it.

(D) Impetuous action is characterized by disregard for consequences, but it doesn't mean something is "easy to disregard."

(E) Something that is TRANSPARENT (in a literal or figurative sense, like an argument or motive) is easy to UNDERSTAND. This relationship perfectly matches the original pair.


Step 3: Final Answer:

The relationship "a quality that makes an action easy" is found in both "CONSPICUOUS: SEE" and "TRANSPARENT: UNDERSTAND". Therefore, option (E) is the correct choice.
Quick Tip: Analogies can have abstract relationships. The sentence "Something X is easy to Y" is a great test for this type of analogy. Apply it rigorously to each option.

Step 1: Understanding the Concept:

This analogy presents a relationship of stages or states, where the first word describes an early or incomplete stage, and the second word describes a later, complete stage. They are near-antonyms representing the beginning and end of a process.


Step 2: Detailed Explanation:

The relationship is: Something IMMATURE is not yet fully DEVELOPED. It is the initial state before reaching the final state.

Let's find a pair with the same "initial state: final state" relationship.

(A) "accessible" and "exposed" are near-synonyms, not opposing stages.

(B) "theoretical" and "conceived" are also very similar; an idea is conceived and remains theoretical.

(C) "tangible" (touchable) and "identified" don't have this developmental relationship.

(D) "irregular" and "classified" are not related as stages of a single process. Something irregular might be hard to classify, making them almost opposites in a different context.

(E) Something INCIPIENT is just beginning to exist or appear. Something REALIZED is fully formed or brought into being. This perfectly mirrors the relationship between an early, undeveloped state (incipient/immature) and a final, complete state (realized/developed).


Step 3: Final Answer:

The relationship of an early stage to a completed stage is clearly mirrored in "INCIPIENT: REALIZED". Therefore, option (E) is the correct answer.
Quick Tip: Think about processes and timelines. "Immature" is early in the process of growth, and "developed" is late. "Incipient" is at the very beginning of a process, and "realized" is at the end. Visualizing this progression helps identify the correct parallel.

Step 1: Understanding the Concept:

This analogy connects a noun (a quality or trait) with an adjective that describes or defines that noun.


Step 2: Detailed Explanation:

The relationship is: PERSPICACITY is the quality of having ACUTE mental penetration or discernment. In simpler terms, to have perspicacity is to be acute. The noun is the quality, and the adjective describes someone who has that quality.

Let's find an option with the same relationship: "A is the quality of being B."

(A) Adaptability is the quality of being adaptable, not "prescient" (knowing the future).

(B) Decorum is proper behavior; "complacent" means self-satisfied. They are unrelated.

(C) CAPRICE is the quality of being WHIMSICAL or unpredictable. Someone who acts on caprice is whimsical. This matches the original relationship perfectly.

(D) Discretion is the quality of being discreet, not "literal."

(E) Ignorance is the state of being ignorant; "pedantic" means overly concerned with minor details. They are unrelated.


Step 3: Final Answer:

The relationship "A is the quality of being B" holds for both "PERSPICACITY: ACUTE" and "CAPRICE: WHIMSICAL". Therefore, option (C) is the correct choice.
Quick Tip: For noun-adjective pairs, form the sentence: "To have [NOUN] is to be [ADJECTIVE]." For example, "To have perspicacity is to be acute." Then test the options: "To have caprice is to be whimsical." This clarifies the relationship and reveals the correct answer.

Step 1: Understanding the Concept:

This analogy links an adjective that describes the essential quality of a noun. The noun is a specific type of action or speech, and the adjective is its defining characteristic.


Step 2: Detailed Explanation:

The relationship is: BANTER is by definition PLAYFUL conversation. The adjective describes the very nature of the noun.

We are looking for a pair where the noun is defined by the adjective.

(A) Originality is not necessarily animated (lively).

(B) HYPERBOLE is by definition EXAGGERATED speech or writing. This relationship is identical to the original pair.

(C) Effrontery (insolent behavior) is not described by insidious (treacherous).

(D) Pompous (self-important) behavior is not the same as irrationality.

(E) Taciturn (saying little) and solemnity (seriousness) are both qualities of a person's demeanor, but one does not define the other in this way.


Step 3: Final Answer:

The relationship "B is by definition A" or "A is the defining characteristic of B" is clear in both "PLAYFUL: BANTER" and "EXAGGERATED: HYPERBOLE". Therefore, option (B) is the correct choice.
Quick Tip: Reverse the order to form a sentence: "[NOUN] is a form of speech/action that is [ADJECTIVE]." For example, "Banter is conversation that is playful." Then test the options: "Hyperbole is speech that is exaggerated." This often makes the relationship clearer.

Step 1: Understanding the Concept:

This analogy describes a relationship of prevention or restriction. The first term is an action or state intended to stop or restrict the second term.


Step 2: Detailed Explanation:

The relationship is: A QUARANTINE is a measure put in place to prevent the spread of CONTAGION (disease).

Let's find another pair with this "A is used to stop/restrict B" relationship.

(A) A blockage is a type of obstacle; they are near-synonyms.

(B) A strike is an action taken to achieve a concession, not to prevent it.

(C) An EMBARGO is a measure (an official ban) put in place to stop or restrict COMMERCE (trade) with a particular country. This perfectly matches the preventive relationship of the original pair.

(D) Vaccination is a method of inoculation; they are very closely related terms, not a restriction relationship.

(E) A prison's goal is ideally to reform an individual, but its primary function is punishment and confinement, not preventing reform.


Step 3: Final Answer:

The relationship of a restrictive measure to the thing it is meant to stop is clearly seen in both "QUARANTINE: CONTAGION" and "EMBARGO: COMMERCE". Therefore, option (C) is the correct answer.
Quick Tip: Formulate the relationship as a sentence of purpose: "The purpose of a [QUARANTINE] is to stop [CONTAGION]." Then apply this sentence to the options: "The purpose of an [EMBARGO] is to stop [COMMERCE]." This helps to precisely identify the correct parallel.

Step 1: Understanding the Concept:

This question asks what the author of the passage claims the "historians" (who underestimated the suffrage movement) have done. We need to find the statement in the passage that directly describes an outcome of their work.


Step 2: Detailed Explanation:

The author is critical of these historians for underestimating suffragism. However, the author does concede one positive contribution they made.

In lines 10-12, the author states: "True, by emphasizing these struggles [moral reform and domestic feminism], such historians have broadened the conventional view of nineteenth-century feminism, but they do a historical disservice to suffragism."

This sentence directly supports option (E). The author explicitly says that these historians have "broadened" (or expanded) the conventional view.

Let's analyze the other options:

(A) The passage states that the historians were influenced by feminist theorists, not the other way around.

(B) This is the opposite of what the author claims. The author argues they have ignored the perceptions of the participants by underestimating suffragism.

(C) The passage discusses feminism as a social force, but it doesn't make a distinction or claim about how these specific historians treated it versus an intellectual tradition.

(D) This is incorrect. These historians paid significant attention to other feminist movements like "moral reform" and "domestic feminism."


Step 3: Final Answer:

The passage explicitly states that the historians in question have "broadened the conventional view of nineteenth-century feminism." Therefore, option (E) is the correct answer.
Quick Tip: In reading comprehension, look for "concession words" like "True," "Certainly," or "Of course." The author often uses these to acknowledge a point before refuting or qualifying it. The answer is often found in the part the author is conceding.

Step 1: Understanding the Concept:

This question asks about the specific influence that "some twentieth-century feminists" had on "some historians," according to the author. We need to locate the part of the passage that describes this cause-and-effect relationship.


Step 2: Detailed Explanation:

The very first sentence of the passage establishes this relationship directly:

"Influenced by the view of some twentieth-century feminists that women's position within the family is one of the central factors determining women's social position, some historians have underestimated the significance of the woman suffrage movement."

This sentence explicitly states that the feminists' focus on the family influenced historians' view of the significance of the woman suffrage movement, causing them to underestimate it.

Let's check the other options:

(B) The feminists held this view, but the passage claims this influenced the historians' view of suffrage, not their view on the family itself.

(C), (D), (E) These topics are not mentioned in the passage as being the subject of the influence. The text makes a very specific connection between the feminists' focus on the family and the historians' resulting devaluation of the suffrage movement.


Step 3: Final Answer:

The first sentence of the passage directly states that the feminists' views led historians to underestimate the significance of the woman suffrage movement. Therefore, option (A) is the correct answer.
Quick Tip: Questions that ask about influence or cause-and-effect are often answered in the opening sentences of a passage, where the author sets up the main argument or context. Always check the first sentence for thesis statements or background information.

Step 1: Understanding the Concept:

This question asks us to identify a characteristic of nineteenth-century feminists based on the information provided in the passage. We need to find the statement that is directly supported by the text.


Step 2: Detailed Explanation:

The passage draws a distinction between two types of feminist movements. One type, including "domestic feminism," focused on gaining power "within the family." The other was the suffrage movement.

The author describes the unique goal of the suffragists in lines 17-19: "...suffragists were demanding power that was not based on the institution of the family, women's traditional sphere."

This directly means they were seeking roles for women outside of the traditional, family-based context. Option (C) is a clear paraphrase of this statement.

Let's analyze the other options:

(A) The passage does not discuss the personal motivations of moral reform participants.

(B) The passage explicitly states that both feminists and anti-feminists of the era perceived the \textit{suffragists' demand as "the most radical element," not domestic feminism.

(D) The passage defines domestic feminism as a struggle for autonomy within the family, not as a stepping stone to public life.

(E) The passage groups the moral reform movement with domestic feminism as movements focused on the family, not as a midway point.


Step 3: Final Answer:

The passage explicitly states that suffragists sought power outside the traditional family sphere, which aligns perfectly with option (C).
Quick Tip: When a question asks what an author suggests about a group, locate the specific sentences where the author describes that group's actions or beliefs. The correct answer will be a direct paraphrase or a logical conclusion from that description.

Step 1: Understanding the Concept:

The question asks what the author implies about the historians who are the subject of the passage. The author's main point is a critique of these historians, and we need to identify the core of that critique.


Step 2: Detailed Explanation:

The author's central argument is that "some historians have underestimated the significance of the woman suffrage movement" (lines 3-5).

The author then contrasts this assessment with the view of the people who lived through the era. In lines 14-16, the author states, "Nineteenth-century feminists and anti-feminist alike perceived the suffragists' demand for enfranchisement as the most radical element in women's protest."

Therefore, the historians' assessment (that suffragism was "less important") differs significantly from the assessment of the actual nineteenth-century feminists (who saw it as "the most radical element"). Option (D) accurately captures this difference.

Let's analyze the other options:

(A) The passage does not compare nineteenth-century feminism to twentieth-century feminism in this way.

(B) This is the opposite of the author's point. The author concludes by saying historians should "consider the perceptions of actual participants," implying that the historians being criticized do not rely on them enough.

(C) The passage mentions anti-feminists' perceptions but does not focus on the effect of their rhetoric.

(E) This is incorrect. The author claims these historians devote too little attention to suffragism, focusing instead on domestic feminism and moral reform.


Step 3: Final Answer:

The core of the author's critique is the discrepancy between the historians' modern assessment and the lived experience of nineteenth-century feminists. Option (D) correctly identifies this discrepancy.
Quick Tip: Pay attention to the author's main argument or critique. In critical passages, the author often contrasts the flawed view of the subject (here, the historians) with what the author believes to be the correct view or historical reality.

Step 1: Understanding the Concept:

This is a main idea question. It asks for the author's primary purpose in writing the passage. We need to identify the central theme that connects all parts of the text.


Step 2: Detailed Explanation:

The passage begins by establishing that "non-scientific modes of thought" are crucial in determining the form and function of objects. It emphasizes "visual, nonverbal process" and "non-verbal thinking." It then explicitly argues that "Design courses, then, should be an essential element in engineering curricula" because design relies on this type of thought. Finally, it provides an example of a "costly error" that occurred when design was neglected in favor of pure mathematics.

Every part of the passage serves to build the argument for the value of nonverbal thinking.

(A) The author does identify these kinds of thinking, but the primary goal is to argue for their importance, not just to list them.

(B) This accurately reflects the author's main goal. The entire passage is an argument stressing how vital nonverbal thought is to good engineering and design.

(C) The role is not "new"; the author argues that it has always been present in technology but is now being undervalued.

(E) The author does criticize engineering schools, but this is a supporting point used to illustrate the larger problem of undervaluing nonverbal thought. The main concern is the thinking itself, not just the schools.


Step 3: Final Answer:

The central and recurring theme of the passage is the argument for the value and necessity of nonverbal thinking in the field of engineering design. Therefore, option (B) is the best description of the author's primary concern.
Quick Tip: For primary purpose questions, look for the "so what?" of the passage. The author identifies nonverbal thinking (the "what") and then argues that it is critically important and should be taught (the "so what?"). The correct answer will capture this argumentative aspect.

Step 1: Understanding the Concept:

This is an inference question asking for the author's opinion on engineering curricula. We need to deduce the author's view from the arguments and criticisms presented in the passage.


Step 2: Detailed Explanation:

The author makes two key statements that reveal their opinion.

1. "Design courses, then, should be an essential element in engineering curricula" (lines 29-30). This implies that adding them is a positive and necessary step.

2. "If courses in design... are not provided, we can expect to encounter silly but costly errors" (lines 44-47). This implies that their absence is a weakness that leads to failure.

From these two points, we can infer that the author believes including design courses makes a curriculum better, or "strengthens" it. This directly supports option (A).

The other options contradict the passage:

(B) The author critiques the overemphasis on analytical/mathematical thought, not the lack of it.

(C) The author argues that nonverbal thinking is not emphasized enough, which is why engineering students can't produce certain drawings.

(D) and (E) The author views the errors and the absence of nonscientific thinking as significant weaknesses, not things that a curriculum can be strong in spite of.


Step 3: Final Answer:

Based on the author's argument that the absence of design courses leads to errors and that they should be an "essential element," we can infer that including them would strengthen engineering curricula. Therefore, option (A) is correct.
Quick Tip: Inference questions are not guesses. They are logical conclusions based on direct evidence from the text. Find the sentences where the author discusses the topic (engineering curricula) and ask yourself what opinion those statements logically lead to.

Step 1: Understanding the Concept:

This question asks for the best example of the argument made in the first two paragraphs (lines 1-28). The main point of this section is that technology is a product of both non-scientific, intuitive "conceptualization" and practical, physical constraints, with the non-scientific part being primary.


Step 2: Detailed Explanation:

Lines 1-28 argue that artifacts exist because they were first "a picture in the minds of those who built them" and that design decisions come from a mix of "experience, physical requirements, limitations of available space, and... a sense of form." A good illustration must capture this blend of mental vision and physical reality.

(E) This statement perfectly illustrates the point. "Designer's conceptualization" refers to the non-verbal, visual "picture in the mind" that the author emphasizes. "Physical requirements of its site" refers to the constraints like space, experience, and materials that the author also mentions. This option captures the dual nature of design as described in the passage.

Let's analyze the other options:

(A) The passage is about design, not repair.

(B) This is the opposite of the passage's point, which argues that form is not purely scientifically determined.

(C) The word "only" makes this incorrect. The passage states that some decisions do depend on scientific calculations.

(D) This describes a part of the design process, but it doesn't illustrate the core concept of how nonverbal thought and physical constraints combine to create form.


Step 3: Final Answer:

Option (E) provides a concrete example that effectively captures the blend of a designer's mental vision and real-world physical constraints, which is the central argument of the first part of the passage.
Quick Tip: When asked to find an illustration of a point, first summarize the point in your own words. Here, the point is "design = mental picture + real-world rules." Then, look for the option that contains both of these elements.

Step 1: Understanding the Concept:

This question asks for the best introductory sentence for the entire passage. A good introduction sets up the main problem or topic that the passage will then explore in detail.


Step 2: Detailed Explanation:

The entire passage is an argument against the idea that technology is purely a product of science. It highlights the overlooked contributions of "non-scientific modes of thought." Therefore, the best introduction would be one that states this common misconception and hints at the counter-argument the author will make.

(A) This statement does exactly that. It presents the common "assumption" (that technology is derived from science) and then introduces the passage's main topic: the "non-scientific decisions made by technologists." The rest of the passage is an elaboration of this statement.

Let's analyze the other options:

(B) This is too extreme. The author doesn't say analytical thought is no longer vital, only that it's not the whole story.

(C) This is the opposite of the author's point. The author argues that we have lost sight of the role of non-scientific thought.

(D) This is too narrow. The passage is about a mode of thinking, not specifically about types of degrees.

(E) This is a detail from within the passage (describing the nonverbal process), not an overview of the entire argument. It's an example, not an introduction.


Step 3: Final Answer:

Option (A) perfectly encapsulates the central conflict that the passage is written to address: the mistaken belief that science is the sole source of technological innovation, and the author's correction that non-scientific thought is also crucial.
Quick Tip: A good introduction often presents a common belief or assumption and then signals that the author is going to challenge it. Look for the option that best frames the passage as a response to a prevailing, but incomplete, point of view.

Step 1: Understanding the Concept:

This question asks us to explain the meaning of the word "paradoxical" in the context of the passage. A paradox is a situation that seems contradictory but is nevertheless true. We need to identify the contradiction described in lines 36-43.


Step 2: Detailed Explanation:

The situation is that the "Historic American Engineering Record" needed special drawings to document the history of American engineering. One would logically expect that engineering students would be the ideal candidates for this job. However, the passage states that "the only college students with the requisite abilities were not engineering students, but rather students attending architectural schools."

The paradox is the contradiction: the students of a particular field (engineering) were not equipped to document the history of that very same field, while students from another field (architecture) were.

Option (E) captures this contradiction perfectly: "engineering students were not trained to make the type of drawings needed to record the development of their own discipline."

Let's analyze the other options:

(A) The paradox is not about the staff, but about the contrast between students of different disciplines.

(B) This is irrelevant to the specific contradiction the author points out.

(C) The comparison in the text is between engineering students and architectural students, not students vs. practicing engineers.

(D) The passage does not state that the drawings were complicated, only that they required certain "abilities."


Step 3: Final Answer:

The paradoxical situation is that the very people studying engineering were not the ones qualified to visually document it, a task that fell to students of architecture. Option (E) is the most accurate description of this irony.
Quick Tip: To understand a paradox, identify the two conflicting ideas. Here, idea 1 is "It's an engineering project." Idea 2 is "Engineering students can't do it." The paradox lies in the conflict between these two truths.

Step 1: Understanding the Concept:

This question asks for the reason why the author considers failures in automatic control systems to be significant ("not merely trivial aberrations"). We need to find the cause that the author assigns to these failures in the last paragraph of the passage.


Step 2: Detailed Explanation:

The author discusses the "absurd random failures that plague automatic control systems" at the end of the passage. The final sentence (lines 53-55) provides the explicit reason: "...they are a reflection of the chaos that results when design is assumed to be primarily a problem in mathematics."

This statement directly links the failures to a design philosophy that overemphasizes mathematics and neglects the nonverbal, intuitive aspects of design that the author has been championing throughout the passage.

Option (B) is a direct paraphrase of this conclusion. The failures are characteristic of systems where engineers have relied too heavily on mathematics.

Let's analyze the other options:

(A) The passage doesn't mention the engineers' level of practical experience.

(C) While this might be true, the author gives a more specific, causal reason than just the frequency of failures.

(D) The passage critiques the lack of nonverbal design skills, not specifically the analysis of mechanical difficulties.

(E) The author argues for less reliance on pure science/mathematics in design, not for more help from scientists.


Step 3: Final Answer:

The passage explicitly attributes these failures to a design process that treats engineering as a purely mathematical problem. Therefore, option (B) is the correct answer.
Quick Tip: When a question quotes a phrase from the text, the explanation is almost always located in the sentences immediately before or after the quote. The author uses the quote and then immediately explains its significance.

Step 1: Understanding the Concept:

This question asks for the rhetorical purpose of a specific example—the failing railroad cars. We need to understand how this example functions within the author's overall argument in the final paragraph.


Step 2: Detailed Explanation:

The author introduces the example right after making a specific claim: "If courses in design... are not provided, we can expect to encounter silly but costly errors occurring in advanced engineering systems" (lines 44-47). The railroad car, where a fan sucked snow into the electrical system, is presented as a concrete illustration of such a "silly but costly error."

This error occurred because the designers focused on the sophisticated controls (the mathematical/analytical side) but failed to consider a basic, real-world physical interaction (the nonscientific, design side). This supports the author's main point that neglecting the nonscientific aspects of design leads to failures.

Option (D) accurately summarizes this. The "lack of attention to the nonscientific aspects of design" (like how a fan and snow interact) resulted in "poor conceptualization" (a flawed design).

Let's analyze the other options:

(A) The example strengthens, not weakens, the argument.

(B) The example illustrates the cause of errors, not that their number will necessarily increase.

(C) The example shows the cost of not having design skills, but doesn't explicitly compare design courses to other means of reducing cost.

(E) The author doesn't argue that mathematics is unnecessary, only that it is insufficient on its own. The example doesn't weaken the need for math, but highlights the need for something more.


Step 3: Final Answer:

The railroad car example serves as direct evidence for the author's claim that neglecting nonscientific design considerations leads to real-world engineering failures. Option (D) best describes this purpose.
Quick Tip: When a question asks for the purpose of an example, look at the sentence that comes directly before it. Authors usually state a general point and then say "For example..." to provide a specific case that proves their point.

Step 1: Understanding the Concept:

This question asks for the antonym of the word IGNITE.


Step 2: Detailed Explanation:

The word ignite means to catch fire or cause to catch fire; to set alight.

We are looking for a word that means the opposite, i.e., to put out a fire or extinguish it.

Let's analyze the options:

(A) Amplify means to increase the volume or strength of something.

(B) Douse means to pour liquid over; drench, or to extinguish a fire. This is a direct antonym of ignite.

(C) Obscure means to keep from being seen; to conceal.

(D) Blemish means a small mark or flaw that spoils the appearance of something.

(E) Replicate means to make an exact copy of; to reproduce.


Step 3: Final Answer:

The opposite of setting something on fire (ignite) is extinguishing it (douse). Therefore, option (B) is the correct answer.
Quick Tip: For antonym questions, first define the given word as clearly as possible. Then, think of what the direct opposite would be before looking at the options. This helps you avoid being distracted by choices that are merely different, but not true opposites.

Step 1: Understanding the Concept:

This question asks for the antonym of the word MUTATE.


Step 2: Detailed Explanation:

The word mutate means to change in form or nature; to undergo alteration or mutation.

The opposite of changing is staying constant, unchanged, or static.

Let's analyze the options:

(A) Recede means to go or move back.

(B) Grow larger is a specific type of change, not its opposite.

(C) Link together means to connect.

(D) Remain the same is a direct antonym of mutate. It means to stay in a fixed state without any change.

(E) Decrease in speed is a specific type of change.


Step 3: Final Answer:

The opposite of changing (mutating) is not changing (remaining the same). Therefore, option (D) is the correct answer.
Quick Tip: Think of the core concept. The core concept of "mutate" is "change." The core concept of its opposite must be "no change." "Remain the same" is the clearest expression of this.

Step 1: Understanding the Concept:

This question asks for the antonym of the word FRAGMENT, used as a verb.


Step 2: Detailed Explanation:

As a verb, fragment means to break or cause to break into small separate parts.

The opposite would be to come together, unite, or join into a single whole.

Let's analyze the options:

(A) Ensue means to happen or occur afterward or as a result.

(B) Revive means to restore to life or consciousness.

(C) Coalesce means to come together and form one mass or whole; to unite. This is a precise antonym of fragment.

(D) Balance means to keep in a steady position.

(E) Accommodate means to provide lodging or make space for.


Step 3: Final Answer:

The opposite of breaking into pieces (fragment) is joining together into one whole (coalesce). Therefore, option (C) is the correct answer.
Quick Tip: Some words can be both nouns and verbs. Read the word and think of its action sense. "To fragment" is to break apart. What is the action word for putting things together? This line of thinking leads directly to "coalesce."

Step 1: Understanding the Concept:

This question asks for the antonym of the word OSTENSIBLE.


Step 2: Detailed Explanation:

The word ostensible means stated or appearing to be true, but not necessarily so. Its core meaning relates to being apparent, evident, or conspicuous on the surface.

The opposite would be something that is not apparent, hidden, or concealed.

Let's analyze the options:

(A) Gargantuan means enormous.

(B) Inauspicious means not conducive to success; unpromising.

(C) Intermittent means occurring at irregular intervals.

(D) Perpetual means never ending or changing.

(E) Inapparent means not clearly visible or obvious. This is a direct antonym of ostensible.


Step 3: Final Answer:

The opposite of being apparent (ostensible) is not being apparent (inapparent). Therefore, option (E) is the correct answer.
Quick Tip: Break down complex words. "Ostensible" comes from a Latin root meaning "to show." Its opposite would relate to "not showing." "Inapparent" combines the prefix "in-" (not) with "apparent" (showing), making it a perfect antonym.

Step 1: Understanding the Concept:

This question asks for the antonym of the noun PROLIXITY.


Step 2: Detailed Explanation:

Prolixity is the quality of using too many words; being tediously lengthy or wordy in speech or writing.

The opposite would be the quality of using few words and being brief and to the point.

Let's analyze the options:

(A) Ceremoniousness is a fondness for ceremony and formal procedure.

(B) Flamboyance is the quality of being brilliant and showy.

(C) Succinctness is the quality of being briefly and clearly expressed. This is the precise antonym of prolixity.

(D) Inventiveness is the quality of being creative or original.

(E) Lamentation is the passionate expression of grief or sorrow.


Step 3: Final Answer:

The opposite of wordiness (prolixity) is briefness (succinctness). Therefore, option (C) is the correct answer.
Quick Tip: Relate abstract nouns to their adjective forms. Prolixity is the quality of being "prolix" (wordy). The answer will be the quality of being its opposite adjective. The opposite of prolix is "succinct," so the noun form is "succinctness."

Step 1: Understanding the Concept:

This question asks for the antonym of the adjective CONCERTED.


Step 2: Detailed Explanation:

The word concerted describes an action that is jointly arranged, planned, or carried out; coordinated. It implies a group effort. (Think of a "concert," where musicians play together).

The opposite would be an action planned or carried out by a single person, working alone.

Let's analyze the options:

(A) Meant to obstruct describes purpose, not the number of people involved.

(B) Not intended to last describes duration.

(C) Enthusiastically supported describes the reception of an action.

(D) Run by volunteers describes the payment status of the people involved.

(E) Individually devised means planned or created by one person alone. This is a direct opposite of "jointly arranged."


Step 3: Final Answer:

The opposite of a joint or group effort (concerted) is a solo effort (individually devised). Therefore, option (E) is the correct answer.
Quick Tip: Focus on the core meaning. The core of "concerted" is "together." The opposite must mean "alone" or "separate." "Individually" is the key word to look for.

Step 1: Understanding the Concept:

This question asks for the antonym of the noun FORBEARANCE.


Step 2: Detailed Explanation:

Forbearance is the quality of patient self-control, restraint, and tolerance, especially in the face of provocation.

The opposite would be the lack of patience and self-control.

Let's analyze the options:

(A) Fragility is the quality of being easily broken.

(B) Impatience is the tendency to be quickly irritated or provoked; a lack of patience. This is the direct antonym of forbearance.

(C) Freedom is the state of being free.

(D) Nervousness is the state of being easily agitated or alarmed.

(E) Tactlessness is the quality of lacking skill and sensitivity in dealing with others.


Step 3: Final Answer:

The direct opposite of patience and self-control (forbearance) is the lack of patience (impatience). Therefore, option (B) is the correct answer.
Quick Tip: Forbearance is a classic vocabulary word. It's built on the idea of "bearing with" or tolerating something patiently. Its opposite is the inability to bear with something, which is impatience.

Step 1: Understanding the Concept:

This question asks for the antonym of the adjective COSSETED.


Step 2: Detailed Explanation:

To be cosseted means to be cared for in an overindulgent and protective way; to be pampered. This often has the negative connotation of making someone spoiled.

The opposite would be someone who is not pampered or overindulged, and thus has a more robust or natural character.

Let's analyze the options:

(A) Unspoiled means not spoiled, especially by excessive praise or indulgence. This directly contrasts with the likely outcome of being cosseted. If one is cosseted, one becomes spoiled; the opposite is to be unspoiled.

(B) Irrepressible means not able to be controlled or restrained.

(C) Serviceable means functional and durable.

(D) Prone to change means likely to change.

(E) Free from prejudice means unbiased.


Step 3: Final Answer:

The state of being pampered and overindulged (cosseted) leads to being spoiled. The direct antonym is the state of not being spoiled (unspoiled). Therefore, option (A) is the correct answer.
Quick Tip: Think about the consequences of the word. The consequence of being "cosseted" is often being "spoiled." Therefore, the opposite state is "unspoiled."

Step 1: Understanding the Concept:

This question asks for the antonym of the noun PROBITY.


Step 2: Detailed Explanation:

Probity is the quality of having strong moral principles; complete honesty and integrity.

The opposite would be a lack of moral principles or honesty.

Let's analyze the options:

(A) Timidity is a lack of courage or confidence.

(B) Sagacity is the quality of having good judgment; wisdom.

(C) Impertinence is a lack of respect; rudeness.

(D) Uncertainty is the state of being uncertain.

(E) Unscrupulousness is the state of having or showing no moral principles; not being honest or fair. This is the direct antonym of probity.


Step 3: Final Answer:

The opposite of having strong moral principles and honesty (probity) is having no moral principles (unscrupulousness). Therefore, option (E) is the correct answer.
Quick Tip: Associate "probity" with words like "probe" and "prove." It implies a character whose honesty can be tested and proven. The opposite is a character that has no scruples (moral guidelines) to begin with.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb ESCHEW.


Step 2: Detailed Explanation:

To eschew something means to deliberately avoid using it, abstain from it, or shun it, usually for moral or practical reasons.

The opposite would be to seek out, use, or partake in something regularly and willingly.

Let's analyze the options:

(A) To habitually indulge in something means to regularly and freely allow oneself to enjoy the pleasure of it. This is a strong and direct opposite of deliberately avoiding something.

(B) Take without authorization is to steal.

(C) Leave unsaid is a form of avoidance, but more specific.

(D) Boast about means to brag.

(E) Handle carefully means to be cautious.


Step 3: Final Answer:

The opposite of deliberately avoiding (eschew) is regularly and willingly partaking (habitually indulge in). Therefore, option (A) is the correct answer.
Quick Tip: Think of "eschew" as a formal word for "shun" or "give up." What's the opposite of giving something up? It's actively participating in it or indulging in it.

Step 1: Understanding the Concept:

This question asks for the antonym of the adjective REDOUBTABLE.


Step 2: Detailed Explanation:

Redoubtable means formidable, especially as an opponent. It describes someone or something that inspires fear, awe, or respect because of their strength, skill, or power.

The opposite would be someone or something that is not formidable and does not inspire fear or respect.

Let's analyze the options:

(A) Trustworthy means able to be relied on as honest or truthful.

(B) Unschooled means uneducated.

(C) Credulous means having or showing too great a readiness to believe things.

(D) Not formidable is the literal and precise opposite of redoubtable.

(E) Not certain means unsure.


Step 3: Final Answer:

The word redoubtable is a direct synonym for formidable. Therefore, its antonym is "not formidable." Option (D) is the correct answer.
Quick Tip: The "doubt" in "redoubtable" can be misleading. It does not relate to uncertainty. It comes from an old French word meaning "to fear." So, a redoubtable opponent is one to be feared. The opposite is one not to be feared, i.e., not formidable.

Step 1: Understanding the Concept:

This question asks to identify a valid arrangement of the magazines that satisfies all the given rules. We can test each option against the rules one by one.


Step 2: Detailed Explanation:

Let's check each option:

(A) M, O, P, S, V, T

Rule 1: Position 1 must be P or T. Here it is M. Fails.

(B) P, O, S, M, V, T

Rule 1: P is in position 1. (Ok)
Rule 2: T is in position 6. (Ok)
Rule 3: M and O must be consecutive. Here, O is in position 2 and M is in position 4. They are not consecutive. Fails.

(C) P, V, T, O, M, S

Rule 1: P is in position 1. (Ok)
Rule 2: S is in position 6. (Ok)
Rule 3: M and O are consecutive ([OM] block in positions 4 and 5). (Ok)
Rule 4: V and T are consecutive ([VT] block in positions 2 and 3). (Ok)
All rules are satisfied. This is a valid arrangement.

(D) P, V, T, S, O, M

Rule 1: P is in position 1. (Ok)
Rule 2: M is in position 6. It must be S or T. Fails.

(E) T, P, V, M, O, S

Rule 1: T is in position 1. (Ok)
Rule 4: V and T must be consecutive. Here, T is in position 1 and V is in position 3. They are not consecutive. Fails.


Step 3: Final Answer:

Only option (C) satisfies all the rules of the setup. Therefore, it is a possible arrangement.
Quick Tip: For "which of the following could be true" questions, the most efficient method is to check the options against the rules. Start with the most restrictive or simplest rule (e.g., who can be first or last) to eliminate options quickly.

Step 1: Understanding the Concept:

This question presents a new condition ("If P occupies position 3...") and asks for a conclusion that must logically follow. We need to use this new condition in conjunction with the original rules to determine the fixed position of other magazines.


Step 2: Detailed Explanation:

Let's build the arrangement based on the new condition.


Condition: P is in position 3. (_ _ P _ _ _)
Apply Rule 1 (P/T in 1): Since P is not in position 1, T must be in position 1. (T _ P _ _ _)
Apply Rule 2 (S/T in 6): Since T is in position 1, it cannot be in position 6. Therefore, S must be in position 6. (T _ P _ _ S)
Apply Rule 4 ([VT]/[TV] block): Since T is in position 1, V must be in position 2 to form the [TV] block. (T V P _ _ S)
Apply Rule 3 ([MO]/[OM] block): The remaining magazines are M and O. The remaining positions are 4 and 5. Since M and O must be in consecutive positions, they must occupy positions 4 and 5. The order can be either M-O or O-M.

The complete arrangement is: T(1), V(2), P(3), M/O(4), O/M(5), S(6).


Step 3: Evaluate the Options:

Now we check which of the given options \textit{must be true based on this deduction.

(A) M occupies position 4. (This could be true, but O could also be in position 4).
(B) O occupies position 2. (This is false; V must be in position 2).
(C) S occupies position 5. (This is false; S must be in position 6).
(D) T occupies position 6. (This is false; T must be in position 1).
(E) V occupies position 2. (This is a certain deduction from our steps above. It must be true).


Step 4: Final Answer:

Given that P is in position 3, it is a logical necessity that V must be in position 2. Therefore, option (E) is the correct answer.
Quick Tip: When given a new condition, start by applying the most powerful rules to it. Here, the position of P immediately determines the position of T (Rule 1), which in turn determines the positions of S (Rule 2) and V (Rule 4), quickly filling most of the board.

Step 1: Understanding the Concept:

This question introduces a new condition that combines with the original rules to limit the possibilities. We need to find the possible positions for T under this new constraint.


Step 2: Key Deductions from the New Condition:


Original Rule 3: M and O are consecutive ([MO]/[OM]).
Original Rule 4: V and T are consecutive ([VT]/[TV]).
New Condition: O and T are consecutive ([OT]/[TO]).

Combining these three block rules, we can deduce a larger structure. O must be next to M and T. T must be next to O and V. This forces a 4-magazine chain: M-O-T-V or its reverse V-T-O-M. In both cases, O and T are internal to the block.


Step 3: Placing the 4-Magazine Block:

This [MOTV/VTOM] block must be placed in the 6 available positions. The two remaining magazines are P and S. Let's test the possible placements of the 4-magazine block.

Placement 1: Block in positions 1-4. The magazine in position 1 would be M or V. This violates Rule 1, which requires P or T in position 1. So this placement is not allowed.
Placement 2: Block in positions 3-6. The magazine in position 6 would be V or M. This violates Rule 2, which requires S or T in position 6. So this placement is not allowed.
Placement 3: Block in positions 2-5. This is the only remaining possibility. Positions 1 and 6 are left open for P and S.


Step 4: Determining the Final Arrangement and T's Position:

With the 4-magazine block in positions 2-5, we must satisfy Rules 1 and 2 for the remaining slots.

For position 1, Rule 1 requires P or T. Since T is inside the block (in position 3 or 4), P must be in position 1.
For position 6, Rule 2 requires S or T. Since T is inside the block, S must be in position 6.

The only valid arrangement structure is: P, [4-magazine block], S.

Now let's see where T can be:

If the block is M-O-T-V in positions 2-5, then T is in position 4. (Arrangement: P, M, O, T, V, S)
If the block is V-T-O-M in positions 2-5, then T is in position 3. (Arrangement: P, V, T, O, M, S)

So, under this condition, T can be in position 3 or position 4.


Step 5: Final Answer:

Looking at the options, only position 4 is listed. Since we have proven that T can be in position 4, this is the correct answer.
Quick Tip: In logic games, when a new rule connects existing blocks (like O and T here), look for the creation of a larger "super-block." This dramatically reduces the number of possible arrangements and often leads directly to the solution.

Step 1: Understanding the Concept:

This is a "can be true" question, which asks us to find a possible scenario that is consistent with all the rules. The rules are: (1) P/T in 1; (2) S/T in 6; (3) M and O are a block; (4) V and T are a block. We test each option to see if a valid arrangement can be constructed.


Step 2: Detailed Explanation:

Let's test each option:

(A) M occupies position 4, P occupies position 5. `(_ _ _ M P _)`

From Rule 3 ([MO] block), if M is in 4, O must be in 3. The arrangement becomes `(_ _ O M P _)`.
From Rule 1 (P/T in 1), since P is in 5, T must be in 1. The arrangement becomes `(T _ O M P _)`.
From Rule 4 ([VT] block), since T is in 1, V must be in 2. The arrangement becomes `(T V O M P _)`.
The only magazine left is S, and the only position left is 6. The final arrangement is T, V, O, M, P, S.
This arrangement is valid: T is in 1 (Rule 1 ok), S is in 6 (Rule 2 ok), OM are in 3-4 (Rule 3 ok), TV are in 1-2 (Rule 4 ok).
Since a valid arrangement can be constructed, this option \textit{can be true.

(B) P occupies 4, V occupies 5. `(_ _ _ P V _)`

From Rule 4 ([VT] block), if V is in 5, T must be in 4 or 6. Position 4 is taken by P, so T must be in 6. `(_ _ _ P V T)`.
From Rule 1 (P/T in 1), since T is in 6, P must be in 1. This contradicts the condition that P is in 4. Impossible.

(C) S occupies 2, P occupies 3. `(_ S P _ _ _)`

From Rule 1 (P/T in 1), since P is in 3, T must be in 1. `(T S P _ _ _)`.
From Rule 2 (S/T in 6), since T is in 1, S must be in 6. This contradicts the condition that S is in 2. Impossible.

(D) P occupies position 2. `(_ P _ _ _ _)`

From Rule 1 (P/T in 1), since P is in 2, T must be in 1. `(T P _ _ _ _)`.
From Rule 4 ([VT] block), since T is in 1, V must be in 2. This contradicts the condition that P is in 2. Impossible.

(E) S occupies position 5. `(_ _ _ _ S _)`

From Rule 2 (S/T in 6), since S is not in 6, T must be in 6. `(_ _ _ _ S T)`.
From Rule 4 ([VT] block), since T is in 6, V must be in 5. This contradicts the condition that S is in 5. Impossible.


Step 3: Final Answer:

Only the conditions in option (A) allow for the construction of a valid arrangement that does not violate any rules. Therefore, (A) is the correct answer.
Quick Tip: For possibility questions, your goal is to prove that one option can work. Once you've successfully built a valid scenario for an option, you've found the correct answer and can move on.

Step 1: Understanding the Concept:

This is a conditional deduction question. We are given a new piece of information (V is in 4) and must determine a specific relationship that results. The question's wording is complex: we need to find T's position, and then find which magazine is in the position numbered one higher than T.


Step 2: Detailed Explanation:

Let's build the arrangement with the new condition: V is in position 4. `(_ _ _ V _ _)`

Apply Rule 4 ([VT] block): Since V is in 4, T must be adjacent, either in position 3 or 5.
Case 1: T is in 3. The arrangement is `(_ _ T V _ _)`.

Apply Rule 1 (P/T in 1): T is not in 1, so P must be in 1. `(P _ T V _ _)`.
Apply Rule 2 (S/T in 6): T is not in 6, so S must be in 6. `(P _ T V _ S)`.
The remaining magazines, M and O, must fill positions 2 and 5. Rule 3 requires them to be in a consecutive block, but positions 2 and 5 are not consecutive.
Therefore, Case 1 is impossible.

Case 2: T is in 5. The arrangement is `(_ _ _ V T _)`.

Apply Rule 2 (S/T in 6): T is not in 6, so S must be in 6. `(_ _ _ V T S)`.
Apply Rule 1 (P/T in 1): T is not in 1, so P must be in 1. `(P _ _ V T S)`.
The remaining magazines, M and O, must fill the consecutive positions 2 and 3. This is allowed by Rule 3.
The final arrangement must be: P, (M/O), (O/M), V, T, S.

This is the only possible outcome. So, if V is in 4, then T must be in 5 and S must be in 6.


Step 3: Answering the Question:

The question asks: T's position (which is 5) must be "exactly one lower than the position occupied by" which magazine?

This means we are looking for the magazine in position \(5 + 1 = 6\).

From our deduction, the magazine in position 6 is S.


Step 4: Final Answer:

If V is in 4, T must be in 5, which is one position lower than position 6, occupied by S. Therefore, (D) is the correct answer.
Quick Tip: Deconstruct complex question stems carefully. "T's position is one lower than X's position" is just another way of saying "X is in the position immediately after T."

Step 1: Understanding the Concept:

This is another conditional deduction question. The new condition connects two existing rules, which should lead to a strong, certain conclusion. We need to find what "must be true" under this new condition.


Step 2: Detailed Explanation:


Analyze the Rules and Condition:

Original Rule 4: V and T form a consecutive block ([VT] or [TV]).
New Condition: S and V form a consecutive block ([SV] or [VS]).

Combine the rules: Since V must be next to both T and S, these three magazines must form a 3-magazine super-block: S-V-T or T-V-S.
Test the position of T: The key to this game is the placement of T, which affects both end positions (1 and 6).
Can T be in position 1?

If T is in position 1, then from Rule 4, V must be in position 2.
The combined block must be T-V-S, so S would have to be in position 3. The arrangement starts `T V S _ _ _`.
However, Rule 2 states that if T is not in position 6, S must be. Since T is in 1, S must be in 6.
This creates a contradiction: S cannot be in both position 3 and position 6.
Therefore, T cannot be in position 1.

Deduce the occupant of position 1:

According to Rule 1, position 1 must be either P or T.
We have just proven that T cannot be in position 1.
Therefore, P must be in position 1.



Step 3: Final Answer:

The new condition, when combined with the original rules, makes it impossible for T to be in position 1. Since position 1 must be either P or T, P is forced into position 1. This is a necessary conclusion. Therefore, (C) must be true.

For completeness, a possible arrangement is P, M, O, S, V, T. This satisfies P=1, T=6, [MO] in 2-3, [SV] in 4-5, and [VT] in 5-6.
Quick Tip: When a new rule links together existing "actors" (in this case, linking the V from the VT block to S), you often create a larger, more constrained block. The first thing to do is analyze the properties of this new super-block and see how it interacts with the most restrictive rules of the game.

Step 1: Understanding the Concept:

This is a "Strengthen the Argument" question. We need to find the statement that makes Quintero's proposal more practical, feasible, or logical. Quintero's proposal is to use space in the high school (where enrollment is decreasing) to house elementary students (where enrollment is increasing).


Step 2: Detailed Explanation:

Quintero's plan depends on the assumption that there is available and suitable space in the high school. A statement that confirms this assumption would strongly support the proposal.

(A) This weakens the proposal by pointing out a practical limitation. If rooms cannot be converted, the plan is less feasible.
(B) This information is irrelevant. The comparison is between building a new elementary school and converting existing high school rooms, not building two different types of schools.
(C) This might weaken the proposal. If the number of families choosing the high school is increasing, the high school might need its classrooms back sooner than expected, making the "temporary" conversion a poor long-term solution.
(D) This significantly weakens the proposal by highlighting a major potential downside related to student well-being.
(E) This strongly supports the proposal. It establishes that the high school has a surplus of space (classrooms that were "rarely needed"). The fact that this surplus existed even before the enrollment decrease means there is very likely a significant amount of empty space available now, making Quintero's plan to use that space highly practical and sensible.


Step 3: Final Answer:

The best support for Quintero's plan is evidence that the necessary resource—empty classrooms—actually exists. Option (E) provides this evidence directly, making it the correct answer.
Quick Tip: To strengthen a proposed solution, look for an answer choice that confirms the availability of a key resource or removes a potential obstacle. Here, the key resource is empty space in the high school.

Step 1: Understanding the Concept:

This is an "Explain the Discrepancy" question based on a graph. The graph shows three populations declining from 1980 to 1990.

Sand Eels (food source) decline moderately.
Arctic Terns (predator) decline steeply, more than the sand eels.
Puffins (predator) decline, but much less steeply than the Arctic Terns.

The discrepancy is: why did the puffins fare so much better than the arctic terns when their common primary food source was declining? We need to find a difference between the two bird species that accounts for this difference in outcome.


Step 2: Detailed Explanation:


(A) This provides a direct explanation for the difference. If puffins were able to find and switch to an alternative food source (rockfish), their population would be less affected by the decline in sand eels. If arctic terns were unable to switch, their population would be almost entirely dependent on the declining sand eels, leading to a much steeper population crash. This perfectly explains the different slopes on the graph.
(B) This explains that the problem was local to the island but does not explain the different outcomes between the two species on that island.
(C) This explains the cause of the sand eel decline but does not explain why the puffins and terns reacted differently to it.
(D) This establishes the baseline condition in 1980 but does not explain the subsequent divergence in population trends.
(E) This would lead us to expect the opposite result. If puffin nests were damaged and tern nests were not, the puffin population should have declined more steeply, not less.


Step 3: Final Answer:

The ability of one species to adapt by finding alternative food, while the other could not, is the most logical explanation for their different rates of decline. Option (A) provides this crucial differentiating factor.
Quick Tip: When a question asks you to explain a difference between two things, look for an answer choice that presents a difference between them. The cause of a different outcome is almost always a difference in attributes or behavior.

Step 1: Understanding the Concept:

This question asks us to find a piece of information that would weaken Peter's argument. Peter's argument follows a cause-and-effect structure:

Observation (Effect): Science graduates are taking jobs in other fields.
Conclusion (Cause): Scientists are not being paid enough.

Peter's reasoning assumes that the graduates are making a choice to leave science for a better alternative, and he identifies low pay as the motivation. To undermine his reasoning, we need to attack this assumed cause.


Step 2: Detailed Explanation:

We are looking for an option that suggests low pay is not the reason why graduates are leaving science fields.

(A) This statement directly contradicts the logical foundation of Peter's argument. If graduates are accepting non-science jobs that pay even less than science jobs, then low pay in science cannot be the reason they are leaving. They are clearly motivated by something other than salary, or perhaps they are not choosing freely (as Lila suggests). This severely undermines Peter's conclusion.
(B) The number of students receiving science degrees doesn't affect the reasoning about why those who do have degrees are choosing non-science jobs.
(C) This option weakens Lila's argument (that there aren't enough jobs), but it does not directly weaken Peter's. In fact, by suggesting jobs are available, it might slightly strengthen the idea that graduates are actively choosing to leave for other reasons, like pay.
(D) Previous work experience in low-paying jobs is irrelevant to the decision-making process for permanent, post-graduation careers.
(E) This simply restates the premise of Peter's argument. It confirms the observation but does nothing to challenge his reasoning about the cause.


Step 3: Final Answer:

Option (A) provides the strongest counter-evidence to Peter's specific claim about motivation, making it the best choice to undermine his reasoning.
Quick Tip: To weaken a causal argument, you can (1) show that the proposed cause is not present, (2) show that the effect is present even when the cause is absent, or (3) provide an alternative cause. Option (A) attacks the argument by showing that the logical incentive for Peter's proposed cause (seeking higher pay) is absent.

Step 1: Understanding the Concept:

This question asks for a valid sequence of lectures that satisfies all the given rules. We can test each option against the rules.
Rules Summary:

S is 4th.
Exactly one resident (S or T) is before lunch.
Y occurs before T (Y ... T).
If W is before lunch, Y is after lunch (W\textsubscript{BL \(\rightarrow\) Y\textsubscript{AL). Contrapositive: If Y is before lunch, W is after lunch (Y\textsubscript{BL \(\rightarrow\) W\textsubscript{AL).


Step 2: Detailed Explanation:

Let's check each option:

(A) W, X, Lunch, Y, S, T, Z. Lectures are W(1), X(2), Y(3), S(4), T(5), Z(6). Rule 1: S must be 4th. This is satisfied. Rule 2: T and S are residents. Both are after lunch. This violates the rule that exactly one resident is before lunch. Invalid.
(B) X, Y, T, Lunch, S, Z, W. Lectures are X(1), Y(2), T(3), S(4), Z(5), W(6).

Rule 1: S is 4th. OK.
Rule 2: T is before lunch, S is after lunch. Exactly one resident is before lunch. OK.
Rule 3: Y(2) is before T(3). OK.
Rule 4: Y is before lunch. The contrapositive requires W to be after lunch. W is 6th (after lunch). OK.

All rules are satisfied. Valid.
(C) Y, T, Lunch, S, W, X, Z. Lectures are Y(1), T(2), S(3), W(4), X(5), Z(6). Rule 1: S must be 4th. Here S is 3rd. Invalid.
(D) Z, T, W, S, Lunch, Y, X. Lectures are Z(1), T(2), W(3), S(4), Y(5), X(6). Rule 1: S is 4th. OK. Rule 3: Y must be before T. Here Y(5) is after T(2). Invalid.
(E) Z, W, Y, S, Lunch, X, T. Lectures are Z(1), W(2), Y(3), S(4), X(5), T(6). Rule 1: S is 4th. OK. Rule 4: W is before lunch (2nd) and Y is also before lunch (3rd). This violates the rule "If W is given before lunch Y will be given after lunch". Invalid.


Step 3: Final Answer:

The only sequence that satisfies all the conditions is (B).
Quick Tip: For "which of the following is a valid order" questions, use a process of elimination. Check the options against the most concrete rules first (like "S is 4th") to quickly disqualify invalid arrangements.

Step 1: Understanding the Concept:

This question adds a condition and asks what must be true as a result. We need to combine the new condition with the original rules to deduce the identities of the first two lectures.


Step 2: Detailed Explanation:


Condition: Exactly two lectures are before lunch. This means lunch is between lecture 2 and 3.
Apply Rule 1: S is the 4th lecture. This means S is after lunch.
Apply Rule 2: Exactly one resident (S or T) must be before lunch. Since S is after lunch, T must be before lunch. The lectures before lunch are in positions 1 and 2, so T must be in position 1 or 2.
Apply Rule 3: Y must be given at some time before T.

If T were in position 1, no lecture could be given before it. This would violate Rule 3.
Therefore, T cannot be in position 1. T must be in position 2.

Deduce the first lecture: Since T is in position 2, and Y must be before T, Y must be in position 1.
Conclusion: The two lectures given before lunch must be Y (in position 1) and T (in position 2).
Final Check: Does this arrangement conflict with other rules? With Y before lunch, the contrapositive of Rule 4 applies (Y\textsubscript{BL \(\rightarrow\) W\textsubscript{AL), meaning W must be after lunch. This is perfectly consistent.


Step 3: Final Answer:

Based on the logical deductions, if exactly two lectures are given before lunch, they must be Y and T.
Quick Tip: In sequential logic games, rules like "A must be before B" are very powerful. When one of the entities (like T here) is limited to a few early slots, immediately check if there is space for the other entity to come before it. This can often eliminate possibilities.

Step 1: Understanding the Concept:

This question gives a new condition and asks what is possible ("can be true"). We need to find an option that is consistent with the new condition and all original rules.


Step 2: Detailed Explanation:


Condition: Exactly three lectures before lunch, and they include Y and Z. Lunch is between 3 and 4.
Apply Rule 1: S is the 4th lecture, so S is after lunch.
Apply Rule 2: Exactly one resident is before lunch. Since S is after lunch, T must be before lunch.
Deduce the before-lunch group: The three lectures before lunch are given in positions 1, 2, and 3. We know they include Y and Z (from the condition) and T (from our deduction). So, the set of lectures before lunch is \{Y, Z, T\.
Apply Rule 4: Since Y is before lunch, the contrapositive (Y\textsubscript{BL \(\rightarrow\) W\textsubscript{AL) means W must be after lunch.
Deduce the after-lunch group: The lectures after lunch are in positions 4, 5, and 6. We know S is 4th. We deduced W must be after lunch. The only remaining lecture is X. So, the set of lectures after lunch is \{S, W, X\.
Apply Rule 3: Y must be before T. Since both are in the \{1, 2, 3\ group, T cannot be in position 1. T can be in position 2 or 3.

Now let's check the options to see what can be true.

(A) T is the second lecture. Is this possible? Yes. If T is 2nd, Y must be 1st to satisfy Y...T. Z could be 3rd. The order `Y, T, Z` before lunch is possible.
(B) T is the fifth lecture. False. We deduced T must be before lunch (in slots 1, 2, or 3).
(C) W is the third lecture. False. We deduced W must be after lunch.
(D) X is the first lecture. False. We deduced X must be after lunch.
(E) X is the third lecture. False. We deduced X must be after lunch.


Step 3: Final Answer:

It is possible for T to be the second lecture. Therefore, option (A) can be true.
Quick Tip: When a question gives you the members of a group (e.g., the lectures before lunch), your first step should be to combine that with your deductions to identify all members of the group. Then, apply the internal sequencing rules to that group.

Step 1: Understanding the Concept:

This is a conditional question that asks for a necessary conclusion ("must be true"). The condition fixes T to the last position.


Step 2: Detailed Explanation:


Condition: T is the 6th lecture.
Analyze with Resident rule (Rule 2): We have two residents, S and T. Rule 2 states that exactly one of them must be before lunch.
Position S and T relative to lunch: S is the 4th lecture. T is the 6th lecture. Since T is 6th, it is definitely after lunch, regardless of whether lunch is after 2, 3, or 4 lectures.
Deduce S's position relative to lunch: For Rule 2 to be satisfied, S must be the resident who is before lunch.
Deduce the number of lectures before lunch: For S, the 4th lecture, to be before lunch, lunch must take place after the 4th lecture. The number of lectures before lunch cannot be 2 or 3. It must be 4.
Conclusion: The statement "Exactly four lectures are given before lunch" is a necessary consequence of T being the sixth lecture.

Let's check the other options.

(A) X is the first lecture. Not necessarily. The before-lunch lectures are 1, 2, 3, and S(4). We know Y...T, so Y is one of these. The remaining slots are filled by visitors. We also have the rule W\textsubscript{BL \(\rightarrow\) Y\textsubscript{AL. Since Y cannot be after lunch (T is last), Y must be before lunch. This means W must be after lunch. The only spot after lunch besides T(6) is 5. So W must be 5th. The lectures before lunch are \{1, 2, 3, S\. They must be \{Y, X, Z, S\. The order is not fixed, so X doesn't have to be first.
(B) X is the second lecture. Not necessarily, for the same reason.
(C) Exactly two lectures are given before lunch. False. We proved it must be four.
(D) Exactly three lectures are given before lunch. False. We proved it must be four.


Step 3: Final Answer:

The condition that T is sixth forces the conclusion that there must be exactly four lectures before lunch to satisfy the rule about resident speakers.
Quick Tip: The number of items before and after a dividing point (like Lunch) is often a key variable. When a rule involves this division (like Rule 2), use it to lock down the number of items. Here, placing T after lunch forces S to be before lunch, which in turn fixes the position of Lunch itself.

Step 1: Understanding the Concept:

This is a conditional question asking what must be true given a new constraint. We must combine the new information with the original rules to make a definitive deduction.

Rules Summary:

S is 4th.
Exactly one resident (S or T) is before lunch.
Y occurs before T (Y ... T).
If W is before lunch, Y is after lunch (W\textsubscript{BL \(\rightarrow\) Y\textsubscript{AL). Contrapositive: If Y is before lunch, W is after lunch (Y\textsubscript{BL \(\rightarrow\) W\textsubscript{AL).


Step 2: Detailed Explanation:


Condition: S and Z are both given after lunch.
Apply Rule 1 (S is 4th): Since S is 4th and is after lunch, lunch must take place before the 4th lecture. So, there are either 2 or 3 lectures before lunch.
Apply Rule 2 (Resident rule): Exactly one resident must be before lunch. Since S is after lunch, T must be before lunch. T must therefore be in position 1, 2, or 3.
Apply Rule 3 (Y...T): Y must be given before T. Since T is before lunch (in positions 1, 2, or 3), Y must also be given before lunch and in an earlier position than T.
Conclusion: From step 4, it is a logical necessity that Y is given before lunch. This directly matches option (C).
Checking other options for completeness:

Since Y is before lunch, the contrapositive of Rule 4 applies: W must be after lunch.
So, we know: Before Lunch includes \{Y, T\, After Lunch includes \{S, Z, W\.
The last lecture, X, can be either before lunch (making it 3 before, 3 after) or after lunch (making it 2 before, 4 after). Both scenarios are possible. Therefore, we cannot say for sure whether X is before or after lunch, making options (A) and (B) not "must be true".
T could be 2nd or 3rd, so (D) is not a must.
Z is after lunch, but its specific position (5th or 6th) is not fixed, so (E) is not a must.



Step 3: Final Answer:

The condition that S is after lunch forces T to be before lunch. The rule that Y must come before T then forces Y to also be before lunch. This is a certain deduction.
Quick Tip: Use the contrapositive of conditional rules. The rule "If W is before lunch, Y is after lunch" gives the powerful deduction "If Y is before lunch, W must be after lunch." Recognizing this is often key to solving the problem.

Step 1: Understanding the Concept:

This question asks which lecture is impossible to place in the last slot before lunch. The last slot before lunch can be position 2, 3, or 4. We can test if each lecture could occupy this position.


Step 2: Detailed Explanation:

Let's test which lectures CAN be immediately before lunch.

Can S be last before lunch? Yes. If there are 4 lectures before lunch, the order is 1, 2, 3, 4 | Lunch | 5, 6. Since S is 4th, S would be the lecture immediately before lunch. This is a valid scenario. (Eliminates A).
Can T be last before lunch? Yes. If there are 2 lectures before lunch (1, 2 | Lunch), S is after lunch (at 4). Rule 2 requires T to be before lunch. Rule 3 (Y...T) requires Y to be before T. Thus, the order must be Y(1), T(2). Here, T is immediately before lunch. (Eliminates B).
Can X or Z be last before lunch? Yes. If there are 3 lectures before lunch (1, 2, 3 | Lunch), S is after lunch (at 4). T must be before lunch. Y must be before T. This means Y and T occupy two of the first three spots. The third spot can be filled by a visiting speaker. It cannot be W (because Y is before lunch, so W must be after lunch). So, the third speaker could be X or Z. A possible order is Y(1), T(2), Z(3) | Lunch. In this case, Z is immediately before lunch. Another is Y(1), T(2), X(3) | Lunch. X is immediately before lunch. (Eliminates C and E).


Step 3: Proving Y Cannot be last before lunch:

By elimination, Y is the answer. Let's prove it directly.
Assume Y is the lecture immediately before lunch.

The rule Y...T means T must come after Y. Since Y is immediately before lunch, T must be after lunch.
The rule states exactly one resident (S or T) is before lunch. Since T is after lunch, S must be before lunch.
The rule states S is the 4th lecture. For S(4) to be before lunch, there must be exactly 4 lectures before lunch.
This means the lecture immediately before lunch is the 4th lecture.
We assumed Y is the lecture immediately before lunch. This would mean Y is the 4th lecture.
This creates a contradiction: Y cannot be the 4th lecture because S is the 4th lecture.
Therefore, the initial assumption that Y can be immediately before lunch is false.


Step 4: Final Answer:

S, T, X, and Z can all be placed in the last position before lunch under valid scenarios. Y cannot, because it leads to a direct contradiction with the rule that S is the fourth lecture.
Quick Tip: For "CANNOT be true" questions, try to assume the statement is true and work through the logic until you find a contradiction. If a contradiction arises, you've proven the statement is impossible.

Step 1: Understanding the Concept:

We need to move the Lion (L) from 1 to 7 using the minimum number of total transfers. The Tiger (T) starts at 3, which is on the shortest path for L. This means T must be moved out of the way. We need to find a possible final location for T after L reaches its destination.


Step 2: Detailed Explanation:


Shortest Path for L: The shortest path for L from 1 to 7 is 1 \(\rightarrow\) 3 \(\rightarrow\) 5 \(\rightarrow\) 7. This takes 3 transfers.
The Blockage: T is in enclosure 3, so L cannot move from 1 to 3. The path is blocked.
Minimal Solution: To clear the path with the minimum number of moves, T must first move out of enclosure 3. T has adjacent enclosures \{1, 2, 4, 5\. T cannot move to 1 (L is there). T can move to 2, 4, or 5. Let's try moving T to a "parking" spot that doesn't interfere further.
Scenario 1:

Transfer 1: T moves 3 \(\rightarrow\) 4. (State: L=1, T=4). The path for L is now clear.
Transfer 2: L moves 1 \(\rightarrow\) 3. (State: L=3, T=4).
Transfer 3: L moves 3 \(\rightarrow\) 5. (State: L=5, T=4).
Transfer 4: L moves 5 \(\rightarrow\) 7. (State: L=7, T=4).

The goal is achieved. L is in 7. The total number of transfers is 4. T's final position is 4. This is a possible outcome. Any path requiring more than 4 transfers would not be minimal, as we have found a 4-transfer solution.
For example, if T moved 3 \(\rightarrow\) 5, it would block L's path again later, requiring T to move a second time and resulting in more than 4 total transfers.


Step 3: Final Answer:

We have found a minimal 4-transfer sequence where the lion reaches enclosure 7 and the tiger ends up in enclosure 4. Therefore, it is possible for the tiger to be in enclosure 4.
Quick Tip: In movement games with blockages, the first step in a minimal solution is almost always to move the blocking piece to the nearest, most convenient "parking spot" that clears the moving piece's entire path.

Step 1: Understanding the Concept:

The question asks which destination for the Tiger (T) would result in a process that takes exactly two total transfers. We start with T=5 and L=3. We need to test the options as destinations.


Step 2: Detailed Explanation:

Let's analyze the number of transfers required to move T from 5 to each of the target enclosures.

Destinations 6 and 7: T can move directly from 5 to 6 or from 5 to 7. The path is not blocked by L. This move takes exactly one transfer. So, options (D) and (E) are incorrect.
Destination 3: The path for T is 5 \(\rightarrow\) 3. This is a single step. However, L starts in enclosure 3, blocking the destination. For T to move to 3, L must first move out of 3.

Transfer 1: L moves out of 3. L can move to 1, 2, or 4. Let's say L moves 3 \(\rightarrow\) 1. (State: T=5, L=1).
Transfer 2: Now enclosure 3 is empty. T moves 5 \(\rightarrow\) 3. (State: T=3, L=1).

The task of moving T to 3 is completed in exactly two transfers. This matches the question. So, option (B) is likely correct.
Destinations 2 and 4: The shortest paths for T from 5 are 5 \(\rightarrow\) 3 \(\rightarrow\) 2 and 5 \(\rightarrow\) 3 \(\rightarrow\) 4. These are two-step paths for the tiger. But the intermediate step, enclosure 3, is blocked by L.

Transfer 1: L must move out of 3. (e.g., L: 3 \(\rightarrow\) 1).
Transfer 2: T can now move into 3. (T: 5 \(\rightarrow\) 3).
Transfer 3: T moves out of 3 to its destination. (e.g., T: 3 \(\rightarrow\) 2).

This process takes a total of three transfers. So, options (A) and (C) are incorrect.


Step 3: Final Answer:

Only the task of moving the tiger to enclosure 3 requires a total of exactly two transfers (one for the lion to clear the space, and one for the tiger to move in).
Quick Tip: Remember to count all transfers, including those of the animal that is not the primary subject of the move but must be shifted to clear a path or destination. The total number of transfers is what matters.

Step 1: Understanding the Concept:

This question asks for a necessary action ("must be true") during a swap of the lion (L) and tiger (T) from enclosures 6 and 7. Since these are adjacent only to enclosure 5, they must "dance" around each other using a temporary "parking" spot. We must find the minimal sequence for this swap and identify an action that occurs in all minimal versions of the swap.


Step 2: Detailed Explanation:

The enclosures 6 and 7 are like two rooms off a single hallway (enclosure 5). To swap occupants, one animal must leave its room, go down the hall, and park somewhere else, letting the second animal walk down the hall and into the first animal's empty room. Then the first animal can return and enter the second's now-empty room.

Minimal Parking Spot: The only exit from the \{5, 6, 7\ area is through enclosure 3. The closest, and therefore minimal, parking spot is enclosure 3.
Scenario 1: L moves first.

1. L moves out: 6 \(\rightarrow\) 5.
2. L parks: 5 \(\rightarrow\) 3.
3. T moves to hall: 7 \(\rightarrow\) 5.
4. T enters L's old room: 5 \(\rightarrow\) 6. (T is done).
5. L returns to hall: 3 \(\rightarrow\) 5.
6. L enters T's old room: 5 \(\rightarrow\) 7. (L is done).

This minimal sequence takes 6 transfers.
Scenario 2: T moves first.

1. T moves out: 7 \(\rightarrow\) 5.
2. T parks: 5 \(\rightarrow\) 3.
3. L moves to hall: 6 \(\rightarrow\) 5.
4. L enters T's old room: 5 \(\rightarrow\) 7. (L is done).
5. T returns to hall: 3 \(\rightarrow\) 5.
6. T enters L's old room: 5 \(\rightarrow\) 6. (T is done).

This also takes 6 transfers.

Now let's evaluate the options against BOTH minimal scenarios. A "must be true" statement must hold for all possibilities.

(A) The lion is transferred to enclosure 3. This is true in Scenario 1, but false in Scenario 2 (where the tiger goes to 3). So, this is not a "must".
(B) The tiger is transferred to enclosure 5 twice. In both scenarios, the tiger moves into 5 once and out of 5 once. Not twice. False.
(C) One of the two animals is transferred to enclosure 3 twice. False. In each case, one animal moves into 3 once and out of 3 once.
(D) Three transfers to enclosure 5 are made. This means three moves that END in enclosure 5.

In Scenario 1: L(6\(\rightarrow\)5), T(7\(\rightarrow\)5), L(3\(\rightarrow\)5). Yes, three transfers are made TO 5.
In Scenario 2: T(7\(\rightarrow\)5), L(6\(\rightarrow\)5), T(3\(\rightarrow\)5). Yes, three transfers are made TO 5.

Since this is true in both minimal scenarios, it must be true.
(E) At least one transfer to 2 or 4. False. The parking maneuver only needs to use enclosure 3. Going further is not minimal.


Step 3: Final Answer:

Regardless of which animal moves first to park in enclosure 3, the sequence of moves to complete the swap requires exactly three transfers into enclosure 5.
Quick Tip: For a "must be true" question with multiple possible scenarios, find the common elements. Here, either L or T could perform the "parking" maneuver, but the overall structure of the swap and the number of times the central hub (enclosure 5) is entered remains the same.

Step 1: Understanding the Concept:

We need to find the minimum number of transfers to move L from 3 to 5, and T from 4 to 7. We must identify path conflicts and find the most efficient sequence of moves.


Step 2: Detailed Explanation:


Analyze Paths and Conflicts:

Lion's Path (L): 3 \(\rightarrow\) 5. A single step.
Tiger's Path (T): 4 \(\rightarrow\) 3 \(\rightarrow\) 5 \(\rightarrow\) 7. A three-step path.
Conflicts: L starts at 3, which is on T's path. L's destination is 5, which is also on T's path.

Strategy 1: L moves to its destination first.

1. L moves 3 \(\rightarrow\) 5. (L is done). State: L=5, T=4.
2. T begins its path: 4 \(\rightarrow\) 3. State: L=5, T=3.
3. T needs to move 3 \(\rightarrow\) 5, but L is blocking the destination. L must move out of the way.
4. L parks: 5 \(\rightarrow\) 6. State: L=6, T=3.
5. T continues: 3 \(\rightarrow\) 5. State: L=6, T=5.
6. T continues: 5 \(\rightarrow\) 7. (T is done). State: L=6, T=7.
7. L must return to its destination: 6 \(\rightarrow\) 5. (L is done). State: L=5, T=7.

This sequence takes 7 transfers. This might not be minimal.
Strategy 2: L parks to let T pass first.

1. L moves from 3 to a parking spot to clear T's path. Let's choose 2. L moves 3 \(\rightarrow\) 2. State: L=2, T=4.
2. T moves 4 \(\rightarrow\) 3. State: L=2, T=3.
3. T moves 3 \(\rightarrow\) 5. State: L=2, T=5.
4. T moves 5 \(\rightarrow\) 7. (T is done). State: L=2, T=7.
5. Now L moves from its parking spot (2) to its destination (5). Path: 2 \(\rightarrow\) 3 \(\rightarrow\) 5.
6. L moves 2 \(\rightarrow\) 3. State: L=3, T=7.
7. L moves 3 \(\rightarrow\) 5. (L is done). State: L=5, T=7.

This sequence also takes 6 transfers. Let's re-count: L(3-2), T(4-3), T(3-5), T(5-7), L(2-3), L(3-5). That's 6 transfers.

Comparing the two strategies, 6 transfers is fewer than 7. It is the minimal number required to resolve the conflicts.


Step 3: Final Answer:

The most efficient method requires the lion to first move out of the way, allowing the tiger to complete its journey, and then for the lion to proceed to its destination. This process takes a minimum of six transfers.
Quick Tip: When animal paths conflict, compare two main strategies: (1) one animal completes its journey first (requiring the other to move away from its destination and back again), or (2) one animal moves to a temporary "parking" spot while the other passes completely. The second strategy is often more efficient.

Step 1: Understanding the Concept:

This is a "CANNOT be true" question, constrained by the rule of using the minimum number of transfers. We must find the minimal path for the given goal (L: 1\(\rightarrow\)3, T: 7\(\rightarrow\)1) and then determine which of the options describes an event that does not happen in any minimal sequence.


Step 2: Finding the Minimal Path:


Analyze Paths and Conflicts:

L's unconflicted path: 1 \(\rightarrow\) 3 (1 step).
T's unconflicted path: 7 \(\rightarrow\) 5 \(\rightarrow\) 3 \(\rightarrow\) 1 (3 steps).
Conflicts: L starts at T's destination (1). L's destination (3) is on T's path.

Determine Minimal Transfers: L must move out of 1 to let T in. T needs to pass through 3. A shuffle is required. Let's find the shortest sequence.
Optimal Sequence: The most efficient way is for one animal to park while the other completes its journey.

1. L moves to a parking spot: 1 \(\rightarrow\) 2. (State: L=2, T=7).
2. T starts its journey: 7 \(\rightarrow\) 5. (State: L=2, T=5).
3. T continues: 5 \(\rightarrow\) 3. (State: L=2, T=3).
4. T continues: 3 \(\rightarrow\) 1. (T is done). (State: L=2, T=1).
5. L moves from parking to its destination: 2 \(\rightarrow\) 3. (L is done). (State: L=3, T=1).

This sequence takes 5 transfers. Any other sequence, like L moving to 3 first, takes 6 transfers and is not minimal. Other minimal 5-step sequences exist (e.g., L parking in 4, or T moving first), but they have a similar structure.


Step 3: Evaluating the Options Against Minimal Paths:

The possible first transfers are L(1\(\rightarrow\)2), L(1\(\rightarrow\)4), or T(7\(\rightarrow\)5).
The possible second transfers are T(7\(\rightarrow\)5) (if L moved first) or L(1\(\rightarrow\)2)/L(1\(\rightarrow\)4) (if T moved first).
Let's check the options:

(A) L to 2 in the first transfer. This is a possible first move in a 5-step solution. (CAN be true).
(B) L to 3 in the second transfer. Let's see if this can happen. 1st move: T(7\(\rightarrow\)5). State is L=1, T=5. 2nd move: L(1\(\rightarrow\)3). State is L=3, T=5. This is a possible 2-move start. However, this path leads to a 6-step solution, which is not minimal. The question requires using the minimal number of transfers. Therefore, this move CANNOT happen in a minimal path.
(C) L to 4 in the second transfer. Yes. 1st move: T(7\(\rightarrow\)5). 2nd move: L(1\(\rightarrow\)4). This is a possible start to a minimal 5-step path. (CAN be true).
(D) T to 5 in the first transfer. This is a possible first move in a 5-step solution. (CAN be true).
(E) T to 3 in the second transfer. For T to be transferred to 3, it must be in an adjacent enclosure (1, 2, 4, or 5). T starts at 7. In one transfer, T can only get to 5. Therefore, it is physically impossible for the tiger to be transferred to enclosure 3 in the second transfer. It needs at least two transfers (7\(\rightarrow\)5\(\rightarrow\)3) just to get there.


Step 4: Final Answer:

Both (B) and (E) describe events that do not occur in a minimal path. However, (E) is impossible under any circumstances (minimal or not), as the tiger cannot reach enclosure 3 from its starting point in a single move, which would be required for it to then be transferred to 3 in the second transfer. (B) is only impossible because of the minimality rule. Option (E) describes a geographical impossibility within the given timeframe. It is the strongest "CANNOT be true" statement.
Quick Tip: When faced with a "CANNOT be true" question, first look for options that are physically or geographically impossible based on the map. An animal cannot move to a non-adjacent enclosure in a single transfer. This is a more fundamental constraint than path optimality.

Step 1: Understanding the Concept:

This is a logic puzzle involving the movement of two animals between numbered enclosures. The rules are that an animal can only be moved to an adjacent, empty enclosure, and two animals cannot occupy the same enclosure at the same time. We need to find a possible second move in a sequence that takes the animals from their starting to their final positions. The problem asks what the second transfer could be, implying we need to find at least one valid sequence of moves where the given option is the second step.


Step 2: Detailed Explanation:

Let's analyze the initial and final states:


Initial State: Lion (L) at enclosure 1, Tiger (T) at enclosure 3.
Final State: Lion (L) at enclosure 6, Tiger (T) at enclosure 5.

The core of the problem is that the animals' paths must cross, so they need to be moved strategically to avoid blocking each other. We will test the viability of the options by seeing if they can be the second move in a logical sequence. Let's analyze option (D).


Can "tiger to enclosure 5" be the second transfer?

For this to be the second transfer, the tiger must move from its current location to enclosure 5. The tiger starts at enclosure 3. So, the transfer is T: 3 \(\rightarrow\) 5.

This requires a preceding first transfer. Let's consider a logical first move:


Move 1: To clear a path and begin the process, a reasonable first move is to move the Lion out of its starting position. Let's move the Lion from enclosure 1 to an adjacent enclosure, say 2.

State after Move 1: Lion is at 2, Tiger is at 3. (L@2, T@3).

Move 2: Now, can the Tiger be transferred to enclosure 5? Yes, if enclosure 3 is adjacent to enclosure 5 and enclosure 5 is empty. Both are reasonable assumptions in this type of puzzle. The move would be T: 3 \(\rightarrow\) 5.

State after Move 2: Lion is at 2, Tiger is at 5. (L@2, T@5).

This sequence is logically sound. The tiger has now reached its final destination. The problem is simplified to moving the lion from enclosure 2 to enclosure 6. This is a very efficient sequence.


Why other options are less likely:

While other options like (A) and (C) can also be part of a valid two-move start (e.g., Move 1: T: 3\(\rightarrow\)4, Move 2: L: 1\(\rightarrow\)2), the sequence leading from option (D) is strategically superior. By moving the tiger directly to its destination in the second step, the problem becomes much simpler. Logic puzzles often imply an efficient or optimal path. The move T: 3 \(\rightarrow\) 5 is a key move that resolves half of the puzzle very early. Therefore, it is a very strong candidate for a "could be" scenario.


Step 3: Final Answer:

A possible and efficient sequence of moves exists where the second transfer is the tiger moving to enclosure 5. The sequence is: (1) Lion moves from 1 to 2. (2) Tiger moves from 3 to 5. This makes option (D) a valid possibility.
Quick Tip: In logic games involving movement and positioning, look for "power moves" that significantly simplify the problem, such as moving a piece directly to its final destination. Also, when a question asks what "could be" true, you only need to find one valid scenario that makes the option work.

Step 1: Understanding the Concept:

This puzzle describes a classic "swap" problem. Two items (the lion and the tiger) need to exchange their positions (enclosures 3 and 6). To do this, they cannot simply pass through each other. They must use intermediate empty enclosures to maneuver around each other. The question asks what must be true for any valid sequence of moves that accomplishes this swap.


Step 2: Detailed Explanation:

Let's analyze the setup:


Initial State: Lion (L) at 3, Tiger (T) at 6.
Final State: Lion (L) at 6, Tiger (T) at 3.

The direct path between 3 and 6 would likely involve enclosures 4 and 5. For the animals to swap places, they cannot both be on this direct path at the same time moving towards each other. One must move aside to let the other pass.


Let's evaluate each option to see if it's a necessity:


(A) Exactly five enclosures are used in the move: The number of enclosures used depends on the specific layout and path taken. It's possible to construct a path that uses five enclosures (e.g., 2, 3, 4, 5, 6), but another path might use more (e.g., if a detour through 7 is needed). Since the exact layout isn't given, we cannot say this must be true.
(B) One animal is transferred exactly twice as many times as the other: The number of transfers for each animal will depend on the path chosen. This is highly unlikely to be a necessary condition for all possible solutions.
(C) All of the transfers of the lion are completed before any transfer of the tiger occurs: This is impossible. The lion needs to move to enclosure 6, but the tiger starts there. The tiger must be moved out of enclosure 6 before the lion can complete its journey.
(D) At one point one of the animals is transferred to either enclosure 2 or enclosure 4: This is the most logical necessity. Consider the Lion at enclosure 3. To begin its journey to 6, it must move to an adjacent enclosure. In a standard linear or grid layout, the neighbors of 3 are 2 and 4. So the lion's first move will almost certainly be to 2 or 4. Now, consider the Tiger at enclosure 6. Its goal is enclosure 3. Its path must eventually lead it through the enclosures preceding 3, which would be 4 and 5. Therefore, the tiger will inevitably be transferred to enclosure 4 (and 5) to reach 3. Since either the lion must move to 2 or 4 to start, or the tiger must move to 4 to finish, it is unavoidable that at some point, an animal is transferred to enclosure 2 or 4.
(E) At one point neither the lion nor the tiger is in enclosure 3, enclosure 5, or enclosure 6: While it's possible to construct a scenario where this happens (e.g., L moves to 2, T moves to 4), we can't be certain it must happen. For example, consider the sequence: L(3\(\rightarrow\)4), T(6\(\rightarrow\)5). At this point, L is at 4 and T is at 5. The condition is false because T is in 5. From here, one animal has to move aside. If L moves (4\(\rightarrow\)2), the state is L@2, T@5. The condition is still false. It's not a guaranteed state in every possible solution.


Step 3: Final Answer:

The most robust conclusion that holds regardless of the specific path is (D). The geometry of the problem (swapping from 3 to 6) necessitates movement through the intermediate and adjacent enclosures. The enclosures adjacent to 3 are likely 2 and 4, and the path from 6 to 3 must pass through 4. Therefore, an animal being transferred to 2 or 4 is a necessary step in the process.
Quick Tip: For "must be true" questions in logic games, focus on the fundamental constraints of the problem. Avoid making assumptions about specific paths. Instead, think about what is geographically or logically unavoidable. Here, movement away from enclosure 3 or towards enclosure 3 makes using an adjacent enclosure like 2 or 4 necessary.

Step 1: Understanding the Concept:

This is a critical reasoning question that asks us to strengthen an argument. The counselor's argument is that students should not use the magazine's overall college ranking score as the main basis for their application decisions. The reason given is that the score is a "composite" of several criteria. We need to find an option that best explains why this composite nature makes the score a poor basis for decisions.


Step 2: Detailed Explanation:

Let's break down the counselor's argument:


Premise 1: A magazine publishes a college ranking based on a composite numerical score.
Premise 2: This score is derived from several different criteria.
Conclusion: Students should not use this overall score as the basis for their decisions.

The logical gap is: why is a composite score a bad basis? The correct answer will bridge this gap.


Let's evaluate the options:


(A) This discusses the magazine's readership. While interesting, it doesn't address the quality or usefulness of the rankings themselves for the students who do read them. Thus, it doesn't justify the counselor's advice.
(B) This describes how colleges leverage their high rankings. This is a consequence of the rankings, not a flaw in their methodology or their usefulness to students. It doesn't explain why the score is a bad basis for a student's decision.
(C) This suggests the rankings are consistent. Consistency might be viewed as a positive trait, suggesting reliability. This statement does not help justify why the rankings are a poor decision-making tool; it might even slightly weaken the counselor's point.
(D) This directly addresses the core issue with a composite score. A composite score averages many factors (like cost, location, program strength, student life, etc.) using a single weighting scheme. However, each student has unique priorities. Student X might prioritize a low-cost engineering program, while Student Y might prioritize a vibrant arts scene in a big city. A single "overall score" cannot possibly reflect these diverse and individual needs. This option perfectly explains why a one-size-fits-all number is not a good basis for a personal decision.
(E) This statement provides a counterexample to the counselor's advice. It shows that some students used the rankings and ended up happy. This would weaken the counselor's recommendation, not justify it.


Step 3: Final Answer:

Option (D) provides the strongest justification for the counselor's advice by highlighting the fundamental mismatch between a generalized, composite ranking and the specific, individual needs of different students.
Quick Tip: In "strengthen the argument" questions, first identify the conclusion and the evidence. Then, look for the logical gap between them. The best answer will bridge this gap by providing a reason why the evidence logically leads to the conclusion.

Step 1: Understanding the Concept:

This is an assumption question. An assumption is an unstated premise that is necessary for the argument's conclusion to be valid. The argument's structure is:


Evidence: Poe never mentioned a morphine addiction in his letters.
Conclusion: Therefore, Poe was not a morphine addict.

We need to find the hidden belief that connects this evidence to the conclusion.


Step 2: Detailed Explanation:

The argument's logic depends on the idea that the absence of evidence in his letters is proof of absence in his life. This is a logical leap. What would make this leap valid? The author must believe that if Poe were an addict, he would have mentioned it in his letters. Let's analyze the options based on this.


(A) The timing of the reports is irrelevant to what Poe's letters contain or what they prove. The argument is about the truth of the addiction, not the history of the rumors.
(B) This would be another piece of evidence supporting the conclusion, but it's not something the original argument (which relies only on the letters) needs to assume.
(C) This, like (B), is an external piece of evidence. The argument makes no mention of Poe's finances, so it doesn't assume anything about them.
(D) This presents an alternative argument. It suggests that the existence of the letters proves he wasn't an addict. The given argument is different; it relies on the content (or lack thereof) of the letters, not their mere existence.
(E) This is the correct assumption. The argument's conclusion rests on the silence of the letters. This silence is only meaningful evidence if Poe would have felt free to write about his addiction if he had one. If, on the contrary, fear of consequences (social stigma, legal trouble, personal shame) would have prevented him from writing about it, then the letters' silence is meaningless, and the argument collapses. Therefore, to make the argument work, the author must assume that such fears were not a factor.


Step 3: Final Answer:

The argument assumes a direct and candid relationship between Poe's life and his correspondence. For the lack of mention to be proof, the author must assume there was no significant reason, such as fear, that would have caused Poe to omit such a fact from his letters. Option (E) states this necessary assumption perfectly.
Quick Tip: To test if a statement is a necessary assumption, use the "Negation Test." Negate the statement and see if the original argument falls apart. If we negate (E), it says: "Fear of the consequences would have prevented Poe from mentioning his addiction." If this is true, then the fact he didn't mention it is no longer evidence he wasn't addicted, and the argument's conclusion no longer follows. Since negating (E) destroys the argument, (E) is a necessary assumption.

Step 1: Understanding the Concept:

This question asks us to weaken a specific argument, which is Fran's rebuttal. We need to find the option that most effectively counters Fran's reasoning.


Adelle's argument: Program failed because the unemployment rate is unchanged.
Fran's argument (rebuttal): Program is helping because it stopped the previously rising unemployment rate.

Fran's logic is that stopping a negative trend (rising unemployment) is a form of success. She attributes this change in trend to the government's program. To counter Fran, we need to show that something else could have caused the unemployment rate to stop rising.


Step 2: Detailed Explanation:

Let's analyze the options to see which one provides a strong alternative cause for the stabilization of the unemployment rate:


(A) The quality of the government's advisors is irrelevant to the actual effect of the program. An argument must be judged on its results, not the credentials of those who designed it.
(B) The historical context of Carthena's unemployment rate compared to the national rate does not explain the recent change from a rising trend to a stable one.
(C) The government's electoral success and promises are political facts, not economic ones. They don't explain what caused the unemployment rate to stabilize.
(D) This provides a powerful alternative explanation. The unemployment rate is a fraction: (Number of Unemployed People) / (Total Labor Force). If a large number of unemployed people leave Carthena, they are removed from both the numerator and the denominator of this calculation for the province. This exodus would directly cause the unemployment rate to stabilize or even decrease, entirely independent of any job creation program. This directly undermines Fran's claim that the program was the cause of the stabilization.
(E) This statement actually seems to support Fran's point. It highlights that the situation was getting worse right before the program started, making the subsequent stabilization look like a significant achievement, which Fran attributes to the program.


Step 3: Final Answer:

Option (D) provides a confounding variable. It suggests that the observed effect (stabilization of the unemployment rate) was not caused by the program (as Fran claims), but by the migration of unemployed workers out of the province. This most strongly counters Fran's argument.
Quick Tip: When asked to weaken a causal argument (i.e., "X caused Y"), the most effective strategy is often to present a plausible alternative cause for the effect Y. Here, Fran argues "Program (X) caused stabilization (Y)." Option (D) counters by suggesting "Migration (Z) caused stabilization (Y)."

Step 1: Understanding the Concept:

This question asks us to compare two quantities. We first need to calculate the value of the expression in Column A using the given information and then compare it to the value in Column B.


Step 2: Key Formula or Approach:

The approach is to substitute the given value of \(x\) into the equation for \(y\), solve for \(y\), and then calculate \(y^2\).


Step 3: Detailed Explanation:

We are given the equation \(y = x^2 - 1\) and the value \(x = 3\).

First, substitute \(x = 3\) into the equation to find the value of \(y\):
\[ y = (3)^2 - 1 \]
\[ y = 9 - 1 \]
\[ y = 8 \]

Now, we need to find the value for Column A, which is \(y^2\).
\[ y^2 = (8)^2 = 64 \]

So, the quantity in Column A is 64.

The quantity in Column B is 80.


Step 4: Final Answer:

Comparing the two quantities, we have \(64 < 80\). Therefore, the quantity in Column B is greater.
Quick Tip: In quantitative comparison questions, always calculate the value in Column A first before making a comparison. Be careful with the order of operations (PEMDAS/BODMAS) when evaluating expressions.

Step 1: Understanding the Concept:

This problem requires us to calculate the number of tickets sold (\(t\)) based on the total revenue and the price per ticket. Then, we must compare this value of \(t\) with the quantity in Column B.


Step 2: Key Formula or Approach:

The relationship between total receipts, price per ticket, and number of tickets is:

Total Receipts = Price per Ticket \(\times\) Number of Tickets (\(t\)).

We need to solve for \(t\).


Step 3: Detailed Explanation:

We are

Total Receipts =
(16,660

Price per Ticket =
)17

The equation is:
\[ 17 \times t = 16,660 \]

To find \(t\), we divide the total receipts by the price per ticket:
\[ t = \frac{16,660}{17} \]

We can perform the division:
\[ 16,660 \div 17 = 980 \]

So, the quantity in Column A is \(t = 980\).

The quantity in Column B is 1,000.


Step 4: Final Answer:

Comparing the two quantities, we have \(980 < 1,000\). Therefore, the quantity in Column B is greater.
Quick Tip: When faced with a large division, you can estimate first. Since \(17 \times 1000 = 17,000\), and
(16,660 is slightly less than
)17,000, you can quickly deduce that \(t\) must be slightly less than 1,000. This is often sufficient for quantitative comparison questions.

Step 1: Understanding the Concept:

This question deals with the properties of a circle. We need to compare the length of a radius with the length of a chord.


Segment OT: Since O is the center and T is a point on the circle, OT is a radius of the circle. Let's call its length \(r\).
Segment TU: Since T and U are both points on the circle, TU is a chord of the circle.


Step 2: Detailed Explanation:

The length of the radius (OT) is a fixed positive value, \(r\).

The length of the chord (TU) depends on the position of point U relative to point T.


Case 1: If U is very close to T, the length of the chord TU can be very small, approaching 0. In this case, OT (\(r\)) > TU.
Case 2: If U is the point on the circle directly opposite T (meaning TU is a diameter), then the length of the chord TU is \(2r\). In this case, TU (\(2r\)) > OT (\(r\)).
Case 3: It is also possible for the length of the chord TU to be equal to the radius \(r\). This occurs when the angle \(\angle TOU\) is 60 degrees, forming an equilateral triangle \(\triangle TOU\).


Step 3: Final Answer:

Since the length of the chord TU can be less than, equal to, or greater than the length of the radius OT, we do not have enough information to determine a fixed relationship between the two quantities. Therefore, the relationship cannot be determined.
Quick Tip: For geometry-based quantitative comparison questions, always consider different possible scenarios or configurations of the given points and shapes. If you can find one case where A > B and another where B > A, the answer is always (D).

Step 1: Understanding the Concept:

This problem requires calculating and comparing two probabilities based on the composition of marbles in a box.


Step 2: Key Formula or Approach:

The probability of an event is given by the formula:
\[ P(Event) = \frac{Number of favorable outcomes}{Total number of possible outcomes} \]


Step 3: Detailed Explanation:

First, let's determine the number of marbles of each type.

Total marbles = 20.

Green marbles = 5.

Red marbles = 10.

Number of marbles that are neither red nor green = Total marbles - (Green marbles + Red marbles)
\[ = 20 - (5 + 10) = 20 - 15 = 5 \]

So, there are 5 marbles that are neither red nor green.


Calculate the quantity in Column A:

The probability of selecting a green marble is:
\[ P(green) = \frac{Number of green marbles}{Total number of marbles} = \frac{5}{20} = \frac{1}{4} \]


Calculate the quantity in Column B:

The probability of selecting a marble that is neither red nor green is:
\[ P(neither red nor green) = \frac{Number of marbles that are not red or green}{Total number of marbles} = \frac{5}{20} = \frac{1}{4} \]


Step 4: Final Answer:

The quantity in Column A is \(\frac{1}{4}\) and the quantity in Column B is \(\frac{1}{4}\). The two quantities are equal.
Quick Tip: When dealing with probability questions involving categories, always make sure you account for all items. Calculating the number of items in the "other" or "neither" category is often the first and most crucial step.

Step 1: Understanding the Concept:

This is a basic arithmetic problem that tests the understanding of place value and converting words to numbers.


Step 2: Detailed Explanation:

Let's convert the words in Column A into numerical values and then sum them up.


Eleven thousand = 11,000
Eleven hundred = 1,100
Eleven = 11

Now, add these values together:
\[ 11,000 + 1,100 + 11 \]

We can perform the addition column by column:
\[ \begin{array}{@{}c@{\,}c@{}c@{}c@{}c} & 1 & 1 & 0 & 0 & 0
& & 1 & 1 & 0 & 0
+ & & & & 1 & 1
\hline & 1 & 2 & 1 & 1 & 1
\end{array} \]

The sum is 12,111.

So, the quantity in Column A is 12,111.

The quantity in Column B is 11,111.


Step 3: Final Answer:

Comparing the two quantities, we have \(12,111 > 11,111\). Therefore, the quantity in Column A is greater.
Quick Tip: Be careful with phrases like "eleven hundred". It means \(11 \times 100 = 1,100\), not 10,100. Always break down the words into their numerical components before adding.

Step 1: Understanding the Concept:

The question asks us to find the length of the hypotenuse of a right triangle with given legs and compare it to a given value.


Step 2: Key Formula or Approach:

We will use the Pythagorean theorem for a right triangle, which states that \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse.


Step 3: Detailed Explanation:

From the image, we have a right triangle with:

Leg 1 (\(a\)) = 7

Leg 2 (\(b\)) = 8

Hypotenuse (\(c\)) = \(x\)

Applying the Pythagorean theorem:
\[ 7^2 + 8^2 = x^2 \]
\[ 49 + 64 = x^2 \]
\[ 113 = x^2 \]
\[ x = \sqrt{113} \]

Now we must compare the quantity in Column A (\(\sqrt{113}\)) with the quantity in Column B (15).

To compare \(\sqrt{113}\) and 15, we can compare their squares.

Square of Column A: \((\sqrt{113})^2 = 113\).

Square of Column B: \(15^2 = 225\).


Step 4: Final Answer:

Since \(113 < 225\), it follows that \(\sqrt{113} < 15\). Therefore, the quantity in Column B is greater.
Quick Tip: When comparing a square root with an integer, it's often easier to square both numbers and compare the results. This avoids having to estimate the square root. Also, recognizing common Pythagorean triples (like 3-4-5, 5-12-13, 8-15-17) can save time, although this problem doesn't use one.

Step 1: Understanding the Concept:

This problem requires us to use a given linear equation to calculate a specific value (the cost for 500 envelopes) and then compare it to another value.


Step 2: Key Formula or Approach:

The formula for the cost is provided: \(c = 0.50n + 15.00\). We need to substitute \(n = 500\) into this formula.


Step 3: Detailed Explanation:

We are asked to find the cost of an order of 500 special envelopes. Here, \(n = 500\).

Substitute this value into the cost equation:
\[ c = (0.50)(500) + 15.00 \]

First, calculate the variable cost part:
\[ (0.50)(500) = \frac{1}{2} \times 500 = 250 \]

Now, add the fixed cost:
\[ c = 250 + 15.00 = 265 \]

So, the cost for 500 envelopes is
)265.

The quantity in Column A is
(265.

The quantity in Column B is
)260.


Step 4: Final Answer:

Comparing the two quantities, we have \(
(265 >
)260\). Therefore, the quantity in Column A is greater.
Quick Tip: Linear cost models often have a variable component (cost per item) and a fixed component (a flat fee). Make sure to calculate the total variable cost first before adding the fixed cost.

Step 1: Understanding the Concept:

This problem involves the concept of the arithmetic mean and requires solving an inequality to find the possible range of values for \(x\).


Step 2: Key Formula or Approach:

The formula for the arithmetic mean (average) of a set of numbers is:
\[ Average = \frac{Sum of the numbers}{Count of the numbers} \]

We are given an inequality involving the average, which we must solve for \(x\).


Step 3: Detailed Explanation:

The average of the three numbers 7, 9, and \(x\) is given by \(\frac{7 + 9 + x}{3}\).

We are told that this average is greater than 9. So, we can write the inequality:
\[ \frac{7 + 9 + x}{3} > 9 \]

First, simplify the numerator:
\[ \frac{16 + x}{3} > 9 \]

To solve for \(x\), multiply both sides of the inequality by 3:
\[ 16 + x > 9 \times 3 \]
\[ 16 + x > 27 \]

Subtract 16 from both sides of the inequality:
\[ x > 27 - 16 \]
\[ x > 11 \]

The result tells us that the value of \(x\) must be strictly greater than 11.

The quantity in Column A is \(x\).

The quantity in Column B is 11.


Step 4: Final Answer:

Since \(x\) must be greater than 11, the quantity in Column A is always greater than the quantity in Column B.
Quick Tip: A useful shortcut for average problems: If the average of a set of numbers is \(k\), the numbers "balance" around \(k\). Here, 7 is 2 below 9, and 9 is at 9. To make the average greater than 9, \(x\) must be more than 2 above 9 to compensate for the 7. So \(x\) must be greater than \(9+2=11\).

Step 1: Understanding the Concept:

This question tests the rules of exponents and radicals, specifically how to square a product involving a square root.


Step 2: Key Formula or Approach:

We will use the exponent rule \((xy)^n = x^n y^n\). And the property that \((\sqrt{k})^2 = k\).


Step 3: Detailed Explanation:

Let's simplify the expression in Column A:
\[ (4\sqrt{5a})^2 \]

Using the exponent rule \((xy)^2 = x^2 y^2\), we can square each part of the product separately:
\[ = (4)^2 \times (\sqrt{5a})^2 \]

Now, calculate each part:
\[ (4)^2 = 16 \]
\[ (\sqrt{5a})^2 = 5a \]

Multiply the results together:
\[ 16 \times 5a = 80a \]

So, the quantity in Column A is \(80a\).

The quantity in Column B is \(40a\).

We are given that \(a > 0\). Since \(a\) is a positive number, we can compare \(80a\) and \(40a\).


Step 4: Final Answer:

Since \(80 > 40\) and \(a > 0\), it follows that \(80a > 40a\). Therefore, the quantity in Column A is greater.
Quick Tip: When squaring an expression like \(k\sqrt{m}\), a common mistake is to only square the square root term. Remember to square both the coefficient outside the radical and the radical itself: \((k\sqrt{m})^2 = k^2 \times m\).

Step 1: Understanding the Concept:

This question tests our ability to manipulate and compare fractions involving decimals. The key is to see if one fraction can be transformed into the other.


Step 2: Key Formula or Approach:

A key property of fractions is that if you multiply the numerator and the denominator by the same non-zero number, the value of the fraction remains unchanged. That is, \(\frac{a}{b} = \frac{a \times k}{b \times k}\) for \(k \neq 0\).


Step 3: Detailed Explanation:

Let's look at the fraction in Column B:
\[ \frac{0.027}{0.053} \]

We can multiply the numerator and the denominator by 10 to shift the decimal point one place to the right without changing the fraction's value:
\[ \frac{0.027 \times 10}{0.053 \times 10} = \frac{0.27}{0.53} \]

This resulting fraction is exactly the same as the fraction in Column A.

Alternatively, we can start with Column A and divide the numerator and denominator by 10:
\[ \frac{0.27 \div 10}{0.53 \div 10} = \frac{0.027}{0.053} \]

This shows that the quantity in Column A is equivalent to the quantity in Column B.


Step 4: Final Answer:

The quantity in Column A, \(\frac{0.27}{0.53}\), is equal to the quantity in Column B, \(\frac{0.027}{0.053}\). The two quantities are equal.
Quick Tip: When comparing fractions with decimals, look for proportionality. Notice that the numerator in Column B (0.027) is the numerator of Column A (0.27) divided by 10. The same is true for the denominators (0.053 vs 0.53). Since both parts of the fraction were changed by the same factor, the fractions are equal.

Step 1: Understanding the Concept:

This question asks us to compare two expressions whose values can change depending on which numbers from the given set are chosen for the variables. To determine the relationship, we should try to find cases where Column A is greater and cases where Column B is greater.


Step 2: Detailed Explanation:

The variables x, y, w, and z can each be 2, 3, 9, or 14. Let's test different scenarios to see how the comparison changes. The strategy is to try to maximize one quantity while minimizing the other, and vice versa.


Scenario 1: Try to make Column A large and Column B small.

To maximize \(\frac{x}{y}\), we should choose the largest possible value for \(x\) and the smallest possible value for \(y\).

Let \(x = 14\) and \(y = 2\). Then, Column A = \(\frac{14}{2} = 7\).

To minimize \(wz\), we should choose the smallest possible values for \(w\) and \(z\).

Let \(w = 2\) and \(z = 2\). Then, Column B = \(2 \times 2 = 4\).

In this scenario, Column A (7) > Column B (4).


Scenario 2: Try to make Column A small and Column B large.

To minimize \(\frac{x}{y}\), we should choose the smallest possible value for \(x\) and the largest possible value for \(y\).

Let \(x = 2\) and \(y = 14\). Then, Column A = \(\frac{2}{14} = \frac{1}{7}\).

To maximize \(wz\), we should choose the largest possible values for \(w\) and \(z\).

Let \(w = 14\) and \(z = 14\). Then, Column B = \(14 \times 14 = 196\).

In this scenario, Column A (\(\frac{1}{7}\)) < Column B (196).


Step 3: Final Answer:

Since we found one case where Column A is greater than Column B, and another case where Column B is greater than Column A, the relationship between the two quantities is not fixed. Therefore, the relationship cannot be determined from the information given.
Quick Tip: For "cannot be determined" questions, you only need to find two conflicting examples. A good strategy is to test the extreme values (maximum and minimum) available for the variables to see if you can change the outcome of the comparison.

Step 1: Understanding the Concept:

This problem tests the properties of exponents, specifically the sign of a negative number raised to an odd or even power. We don't need to calculate the exact values, but rather determine the sign and relative magnitude of the terms.


Step 2: Detailed Explanation:

The given value is \(a = -219\), which is a negative number.


Analyze Column A: \(a^7 + a^5\)


A negative number raised to an odd power results in a negative number.
Therefore, \(a^7 = (-219)^7\) is a negative number.
Similarly, \(a^5 = (-219)^5\) is a negative number.
The sum of two negative numbers is a negative number. So, the quantity in Column A is negative.


Analyze Column B: \(a^8 + a^{18}\)


A negative number raised to an even power results in a positive number.
Therefore, \(a^8 = (-219)^8\) is a positive number.
Similarly, \(a^{18} = (-219)^{18}\) is a positive number.
The sum of two positive numbers is a positive number. So, the quantity in Column B is positive.


Step 3: Final Answer:

The quantity in Column A is a negative number, and the quantity in Column B is a positive number. Any positive number is always greater than any negative number. Therefore, the quantity in Column B is greater.
Quick Tip: For questions involving large numbers and exponents, focus on the properties of numbers rather than calculation. The key rules are: (negative)\textsuperscript{odd} = negative, and (negative)\textsuperscript{even} = positive. This is often all you need to solve the problem.

Step 1: Understanding the Concept:

This problem asks us to compare two algebraic expressions. Since the value of \(x\) is not specified, we should test different values for \(x\) (positive, negative, and zero) to see if the relationship between the columns is constant.


Step 2: Key Formula or Approach:

First, simplify the expression in Column A. The expression \(x^2 + 2x + 1\) is a perfect square trinomial, which can be factored as \((x+1)^2\). So we are comparing \((x+1)^2\) with \(x^2\). A simpler way is to subtract \(x^2\) from both columns and compare \(2x+1\) with 0.


Step 3: Detailed Explanation:

Let's compare \(x^2 + 2x + 1\) and \(x^2\). We can simplify the comparison by subtracting \(x^2\) from both quantities. The comparison then becomes between \(2x + 1\) and 0.

The relationship depends on the value of \(x\):


Case 1: Test a positive value for \(x\).

Let \(x = 1\).
Column A: \(1^2 + 2(1) + 1 = 1 + 2 + 1 = 4\).
Column B: \(1^2 = 1\).
In this case, Column A > Column B. (Because \(2(1)+1 = 3 > 0\)).
Case 2: Test a negative value for \(x\).

Let \(x = -2\).
Column A: \((-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1\).
Column B: \((-2)^2 = 4\).
In this case, Column A < Column B. (Because \(2(-2)+1 = -3 < 0\)).
Case 3: Test a special value.

Let \(x = -1/2\).
Column A: \((-1/2)^2 + 2(-1/2) + 1 = 1/4 - 1 + 1 = 1/4\).
Column B: \((-1/2)^2 = 1/4\).
In this case, Column A = Column B. (Because \(2(-1/2)+1 = 0\)).


Step 4: Final Answer:

Because we found cases where A > B, A < B, and A = B, the relationship is not fixed. Therefore, the relationship cannot be determined from the information given.
Quick Tip: When comparing algebraic expressions, testing a few strategic numbers is a powerful technique. Always try a positive number (like 1 or 2), a negative number (like -1 or -2), zero (0), and a fraction between 0 and 1 if applicable. If you get different results, the answer is (D).

Step 1: Understanding the Concept:

The problem involves angles created when a transversal intersects two parallel lines. Angles \(d\) and \(e\) are consecutive interior angles.


Step 2: Key Formula or Approach:

A key property of parallel lines is that consecutive interior angles are supplementary, which means their sum is 180 degrees. So, \(d + e = 180^\circ\). We also need to interpret the visual information from the diagram.


Step 3: Detailed Explanation:

From the properties of parallel lines, we know that \(d + e = 180^\circ\).

Now we must examine the diagram. The transversal is not perpendicular to the parallel lines. This means the angles formed are not all 90 degrees. Instead, there are four acute angles (less than 90\textsuperscript{o) and four obtuse angles (greater than 90\textsuperscript{o).

By visual inspection of the diagram:


Angle \(d\) is an obtuse angle, meaning \(d > 90^\circ\).
Angle \(e\) is an acute angle, meaning \(e < 90^\circ\).

For example, if the transversal created angles of 120\textsuperscript{o and 60\textsuperscript{o, then \(d\) would be 120\textsuperscript{o and \(e\) would be 60\textsuperscript{o. Their sum is 180\textsuperscript{o, and \(d > e\).

In standardized tests, diagrams are generally drawn to be representative unless stated otherwise. The clear depiction of \(d\) as obtuse and \(e\) as acute is intentional.


Step 4: Final Answer:

Since \(d\) is an obtuse angle (\(>90^\circ\)) and \(e\) is an acute angle (\(<90^\circ\)), the quantity in Column A is greater than the quantity in Column B.
Quick Tip: Unless a problem explicitly states "figure not drawn to scale," you can usually trust the visual information in a geometry diagram, such as whether an angle is acute or obtuse. In this case, \(d\) and \(e\) are supplementary, and since they are not equal, one must be larger than 90\textsuperscript{o} and the other smaller.

Step 1: Understanding the Concept:

This question deals with number properties, specifically the parity (evenness or oddness) of sums and products of consecutive integers. The remainder when a number is divided by 2 tells us if the number is even (remainder 0) or odd (remainder 1).


Step 2: Detailed Explanation:

Consecutive integers always follow an alternating pattern of even and odd. We can test both possible starting cases.


Case 1: The first integer, w, is even.

If \(w\) is even, then the sequence of parities is:

w = Even, x = Odd, y = Even, z = Odd.

Now let's find the parity of the sums in the expression:


\(w + x\) = Even + Odd = Odd
\(x + y\) = Odd + Even = Odd
\(y + z\) = Even + Odd = Odd

The product is \((w+x)(x+y)(y+z)\) = Odd \(\times\) Odd \(\times\) Odd = Odd.

When an odd number is divided by 2, the remainder is 1.


Case 2: The first integer, w, is odd.

If \(w\) is odd, then the sequence of parities is:

w = Odd, x = Even, y = Odd, z = Even.

Now let's find the parity of the sums in the expression:


\(w + x\) = Odd + Even = Odd
\(x + y\) = Even + Odd = Odd
\(y + z\) = Odd + Even = Odd

The product is \((w+x)(x+y)(y+z)\) = Odd \(\times\) Odd \(\times\) Odd = Odd.

Again, when an odd number is divided by 2, the remainder is 1.


Step 3: Final Answer:

In both possible cases, the expression \((w+x)(x+y)(y+z)\) evaluates to an odd number. The remainder when any odd integer is divided by 2 is always 1. Therefore, the quantity in Column A is 1, which is equal to the quantity in Column B.
Quick Tip: Remember these key parity rules: Even + Odd = Odd, Even \(\times\) Anything = Even, Odd \(\times\) Odd = Odd. The sum of any two consecutive integers is always odd. Since \(w,x\), \(x,y\), and \(y,z\) are all pairs of consecutive integers, each term in the product is odd, making the entire product odd.

Step 1: Understanding the Concept:

This is a work-rate problem. We need to find the rate of a single machine and then scale it up for multiple machines and a different time period. It's crucial to keep units consistent (e.g., convert hours to minutes).


Step 2: Key Formula or Approach:

Total Work = Rate \(\times\) Time \(\times\) Number of Workers (or machines).

We'll first find the rate of one machine, then calculate the total work.


Step 3: Detailed Explanation:

1. Find the rate of one machine.

The rate is the number of holes drilled per unit of time.
\[ Rate per machine = \frac{30 holes}{8 minutes} \]


2. Convert the total time to minutes.

The time given is \(1 \frac{1}{3}\) hours. First, convert the mixed number to an improper fraction: \(1 \frac{1}{3} = \frac{4}{3}\).

Since there are 60 minutes in an hour:
\[ Total time = \frac{4}{3} hours \times \frac{60 minutes}{1 hour} = 4 \times 20 = 80 minutes \]


3. Calculate the total number of holes.

We have 4 machines, each working for 80 minutes at the rate calculated in Step 1.
\[ Total Holes = (Rate per machine) \times (Total time) \times (Number of machines) \]
\[ Total Holes = \left(\frac{30 holes}{8 minutes}\right) \times (80 minutes) \times (4 machines) \]

Let's simplify the calculation:
\[ Total Holes = \frac{30 \times 80 \times 4}{8} \]

We can cancel the 8 in the numerator and the denominator:
\[ Total Holes = 30 \times 10 \times 4 \]
\[ Total Holes = 300 \times 4 = 1,200 \]


Step 4: Final Answer:

The 4 machines will drill 1,200 holes in \(1 \frac{1}{3}\) hours.
Quick Tip: In work-rate problems, always ensure your units are consistent before you multiply. It's usually easiest to convert all time units to the smallest unit mentioned (in this case, minutes).

Step 1: Understanding the Concept:

This is a problem about ratios and proportions. The cost is shared in the same ratio as the ages of the three individuals. We need to determine this ratio and then use the known share of one person to find the total cost.


Step 2: Detailed Explanation:

1. Establish the ratio of the ages.

Let T, E, and L be the ages of Tina, Ed, and Lauren, respectively.

We are
\[ E = \frac{1}{2} T \implies T = 2E \]
\[ L = \frac{1}{3} E \implies E = 3L \]

To find the ratio, let's express everyone's age in terms of one person's age. Using L as the base is easiest.

We know \(E = 3L\).

We also know \(T = 2E\). Substitute \(E = 3L\) into this equation:
\[ T = 2(3L) = 6L \]

So, the ratio of their ages is L : E : T, which is \(L : 3L : 6L\).

Dividing by L, the numerical ratio is \(1 : 3 : 6\).


2. Use the ratio to find the total cost.

The shares of the cost are in the same proportion, \(1 : 3 : 6\).

The total number of "parts" in this ratio is \(1 + 3 + 6 = 10\) parts.

Lauren's share corresponds to the '1' part of the ratio. This means her share is \(\frac{1}{10}\) of the total cost.

We are given that Lauren's share is
)2.50.
\[ \frac{1}{10} \times (Total Cost) =
(2.50 \]

To find the total cost, we multiply Lauren's share by 10:
\[ Total Cost =
)2.50 \times 10 =
(25.00 \]


Step 3: Final Answer:

The total cost of the gift is
)25.
Quick Tip: When dealing with ratios based on fractional relationships, it's often helpful to express all quantities in terms of the smallest unit. Here, Lauren is the youngest, so expressing Ed's and Tina's ages in terms of Lauren's age simplifies finding the integer ratio.

Step 1: Understanding the Concept:

This is a volume conservation problem. The total volume of the lead does not change when it is melted and reshaped. We need to calculate the initial total volume of the lead cubes and then determine the height (depth) this volume would occupy in the rectangular pan.


Step 2: Key Formula or Approach:


Volume of a cube = \((edge length)^3\)
Volume of a rectangular prism (the melted lead in the pan) = length \(\times\) width \(\times\) depth


Step 3: Detailed Explanation:

1. Calculate the total volume of the lead.

Each lead cube has an edge of 10 cm.

Volume of one cube = \((10 cm)^3 = 1000 cm^3\).

Since there are three cubes, the total volume of lead is:
\[ Total Volume = 3 \times 1000 cm^3 = 3000 cm^3 \]


2. Calculate the depth of the melted lead in the pan.

This total volume of lead is now in the rectangular pan. The volume of the melted lead can be expressed as:
\[ Volume = (Base Area) \times (depth) \]

The base of the pan has dimensions 20 cm by 30 cm.

Base Area = \(20 cm \times 30 cm = 600 cm^2\).

We set the total volume of lead equal to the volume formula for the pan:
\[ 3000 cm^3 = 600 cm^2 \times depth \]

To find the depth, we rearrange the formula:
\[ depth = \frac{3000 cm^3}{600 cm^2} = \frac{30}{6} cm = 5 cm \]

(The 15 cm depth of the pan is extra information to show that the lead does not overflow, as 5 cm < 15 cm).


Step 4: Final Answer:

The melted lead is 5 centimeters deep in the pan.
Quick Tip: In problems where a substance is melted and recast into a different shape, the core principle is always the conservation of volume. Equate the volume of the original shape(s) to the volume of the final shape and solve for the unknown dimension.

Step 1: Understanding the Concept:

We are looking for a number in the options that cannot be formed by adding two integers, let's call them \(m\) and \(n\), where their product \(m \times n = 30\). We need to find all possible integer pairs whose product is 30 and then calculate their sums.


Step 2: Detailed Explanation:

1. List all integer pairs with a product of 30.

We need to consider both positive and negative pairs.


Positive Pairs:

1 and 30
2 and 15
3 and 10
5 and 6

Negative Pairs:

-1 and -30
-2 and -15
-3 and -10
-5 and -6



2. Calculate the sum for each pair.


\(1 + 30 = 31\)
\(2 + 15 = 17\)
\(3 + 10 = 13\)
\(5 + 6 = 11\)
\(-1 + (-30) = -31\)
\(-2 + (-15) = -17\)
\(-3 + (-10) = -13\)
\(-5 + (-6) = -11\)


3. Check the options against the possible sums.


(A) 31: This is a possible sum (from 1 + 30).
(B) 17: This is a possible sum (from 2 + 15).
(C) -11: This is a possible sum (from -5 + -6).
(D) -13: This is a possible sum (from -3 + -10).
(E) -21: This sum is not in our list of possibilities.


Step 3: Final Answer:

The value -21 cannot be the sum of two integers whose product is 30.
Quick Tip: For "CANNOT be" questions, the process is one of elimination. Systematically list all possibilities and check each option against your list. Don't forget to include negative integer pairs when finding factors.

Step 1: Understanding the Concept:

This problem asks for the area of a triangle given the coordinates of its three vertices. A straightforward approach is to use the formula Area = \(\frac{1}{2} \times base \times height\).


Step 2: Key Formula or Approach:

Area of a triangle = \(\frac{1}{2} \times base \times height\). We can simplify the calculation by choosing a base that is either horizontal or vertical.


Step 3: Detailed Explanation:

The three vertices of the triangle are:

Vertex 1: \(P_1 = (a, b)\)

Vertex 2: \(P_2 = (4a, b)\)

Vertex 3: \(P_3 = (2a, 2b)\)


1. Choose a base.

Notice that vertices \(P_1\) and \(P_2\) have the same y-coordinate (\(b\)). This means the line segment connecting them is horizontal. This is a convenient choice for the base of the triangle.

The length of the base is the distance between \(P_1\) and \(P_2\), which is the difference in their x-coordinates:
\[ base = |4a - a| = |3a| = 3a \]
(Since the point (a, b) is shown in the first quadrant, we know \(a > 0\)).


2. Determine the height.

The height of the triangle is the perpendicular distance from the third vertex, \(P_3=(2a, 2b)\), to the line containing the base (the line \(y=b\)).

The height is the difference in the y-coordinates:
\[ height = |2b - b| = |b| = b \]
(Since \(b > 0\)).


3. Calculate the area.

Now apply the area formula:
\[ Area = \frac{1}{2} \times base \times height \]
\[ Area = \frac{1}{2} \times (3a) \times (b) \]
\[ Area = \frac{3ab}{2} \]


Step 4: Final Answer:

The area of the resulting triangular region is \(\frac{3ab}{2}\).
Quick Tip: When finding the area of a triangle from coordinates, always look for two points that share an x- or y-coordinate. This gives you a horizontal or vertical side, which makes identifying the base and height much simpler than using the distance formula on all three sides.

Step 1: Understanding the Concept:

The question asks for the "range" of daily shirt sales for a specific month, March. The range in a set of data is the difference between the highest value and the lowest value. The bar chart provides these values for each month.


Step 2: Key Formula or Approach:
\[ Range = Highest Value - Lowest Value \]

We need to read the highest and lowest values from the bar for March.


Step 3: Detailed Explanation:

1. Locate the bar corresponding to "March" on the x-axis of the graph.

2. Identify the top of this bar, which represents the highest daily number of shirts sold. The top of the March bar aligns with the 70 mark on the y-axis. So, Highest Value = 70.

3. Identify the bottom of this bar, which represents the lowest daily number of shirts sold. The bottom of the March bar aligns with the 25 mark on the y-axis (halfway between 20 and 30). So, Lowest Value = 25.

4. Calculate the range using the formula:
\[ Range = 70 - 25 = 45 \]


Step 4: Final Answer:

The range in the daily number of shirts sold during March was 45.
Quick Tip: When reading graphs, pay close attention to the scale of the axes. For bar charts like this, use a straight edge or your finger to align the top and bottom of the bar with the corresponding values on the y-axis to ensure accuracy.

Step 1: Understanding the Concept:

This question asks for the percent increase from one value (January's average) to another (February's average). We first need to read these average values from the graph and then apply the percent change formula.


Step 2: Key Formula or Approach:

The formula for percent increase is:
\[ Percent Increase = \left( \frac{New Value - Original Value}{Original Value} \right) \times 100% \]


Step 3: Detailed Explanation:

1. Read the average for January: The heavy line on the January bar is at 25. So, Original Value = 25.

2. Read the average for February: The heavy line on the February bar is at 35. So, New Value = 35.

3. Calculate the increase in sales: Increase = 35 - 25 = 10 shirts.

4. Apply the percent increase formula:
\[ Percent Increase = \left( \frac{10}{25} \right) \times 100% \]
\[ Percent Increase = 0.4 \times 100% = 40% \]


Step 4: Final Answer:

The average number of shirts sold per day during February was 40% greater than the average number sold during January.
Quick Tip: For percent change questions, correctly identifying the "base" or "original value" is crucial. The question "percent greater than X" means X is the original value that goes in the denominator of the fraction.

Step 1: Understanding the Concept:

This question asks us to find a pair of electricity uses from the pie chart whose consumption percentages have a ratio of approximately 3 to 1. We will test the ratio for each pair given in the options.


Step 2: Key Formula or Approach:
\[ Ratio = \frac{Percentage of first use}{Percentage of second use} \]

We need this ratio to be close to 3.


Step 3: Detailed Explanation:

From the pie chart, the percentages are:


Air Conditioner: 53%
Water Heater: 20%
Large Appliances: 18%
Lights/Small Appliances: 9%

Now, let's test the ratio for each option:

(A) Water heater to lights/small appliances: \(\frac{20}{9} \approx 2.22\). Not close to 3.

(B) Large appliances to lights/small appliances: \(\frac{18}{9} = 2\). The ratio is exactly 2 to 1. Not 3 to 1.

(C) Air conditioner to water heater: \(\frac{53}{20} = 2.65\). This is somewhat close, but let's check other options.

(D) Air conditioner to lights/small appliances: \(\frac{53}{9} \approx 5.89\). Not close to 3.

(E) Air conditioner to large appliances: \(\frac{53}{18} \approx 2.94\). This value is the closest to 3.


Step 4: Final Answer:

The ratio for air conditioner and large appliances (2.94 to 1) is the most nearly 3 to 1.
Quick Tip: When a question says "most nearly," it implies you should calculate the value for all options and then choose the one that is arithmetically closest to the target number.

Step 1: Understanding the Concept:

This is a weighted average cost problem. The cost per unit (kWh) is different for the water heater than for the other appliances. We need to calculate the total cost by considering these different rates and then find what fraction of that total cost is attributable to the water heater.


Step 2: Detailed Explanation:

1. Define variables for the cost rates.

Let \(C\) be the cost per kWh for the "rest of the electricity".

Then the cost per kWh for the water heater is \(\frac{C}{2}\).


2. Calculate the amount of electricity used for each category.

Water heater usage = 20% of total usage = 0.20 \(\times\) Total.

Rest of the usage = (53% + 18% + 9%) of total usage = 80% of total usage = 0.80 \(\times\) Total.

(Note: We don't need the 800 kWh value, as it will cancel out. We can work with percentages.)


3. Calculate the cost for each category in terms of C and Total Usage.

Cost of water heater = (Water heater usage) \(\times\) (Cost rate for water heater)

\[ = (0.20 \times Total) \times \left(\frac{C}{2}\right) = 0.10 \times Total \times C \]

Cost of the rest = (Rest of usage) \(\times\) (Cost rate for the rest)

\[ = (0.80 \times Total) \times C = 0.80 \times Total \times C \]


4. Calculate the total cost.

Total Cost = Cost of water heater + Cost of the rest

\[ = (0.10 \times Total \times C) + (0.80 \times Total \times C) = 0.90 \times Total \times C \]


5. Find the required fraction.

Fraction = \(\frac{Cost of water heater}{Total Cost}\)

\[ = \frac{0.10 \times Total \times C}{0.90 \times Total \times C} = \frac{0.10}{0.90} = \frac{1}{9} \]


Step 3: Final Answer:

The cost of the electricity used by the water heater was \(\frac{1}{9}\) of the total cost.
Quick Tip: In problems involving fractions or percentages of a total, you often don't need the actual total value. You can work with the percentages or fractions directly, as the total value will cancel out in the final ratio.

Step 1: Understanding the Concept:

This is another percent increase problem. We need to calculate the amount of electricity (in kWh) used by the water heater in July and in November, and then find the percent increase from the July amount to the November amount.


Step 2: Key Formula or Approach:
\[ Percent Increase = \left( \frac{November Usage - July Usage}{July Usage} \right) \times 100% \]


Step 3: Detailed Explanation:

1. Calculate July water heater usage.

Total electricity in July = 800 kWh.

Water heater usage in July = 20% of 800 kWh = \(0.20 \times 800 = 160\) kWh.


2. Calculate November water heater usage.

Total electricity in November = 800 kWh (same as July).

Water heater usage in November = 33% of 800 kWh = \(0.33 \times 800 = 264\) kWh.


3. Apply the percent increase formula.

July Usage (Original Value) = 160 kWh.

November Usage (New Value) = 264 kWh.

Increase = 264 - 160 = 104 kWh.

\[ Percent Increase = \left( \frac{104}{160} \right) \times 100% \]

Simplify the fraction: \(\frac{104}{160} = \frac{52}{80} = \frac{26}{40} = \frac{13}{20}\).

\[ Percent Increase = \frac{13}{20} \times 100% = 0.65 \times 100% = 65% \]


Step 4: Final Answer:

The amount of electricity used by the water heater increased by 65% from July to November.
Quick Tip: You can also solve this problem just using the percentages, since the base (total electricity) is the same for both months. The increase is from 20% to 33%. The percent increase is \(((33-20)/20) \times 100 = (13/20) \times 100 = 65%\).

Step 1: Understanding the Concept:

This is a probability problem. We need to find the number of favorable outcomes (integers that are perfect squares or perfect cubes in the given range) and divide it by the total number of possible outcomes.


Step 2: Key Formula or Approach:
\[ P(Event) = \frac{Number of Favorable Outcomes}{Total Number of Outcomes} \]

For "A or B" events, \(P(A or B) = P(A) + P(B) - P(A and B)\). We must check for any overlap (numbers that are both a perfect square and a perfect cube).


Step 3: Detailed Explanation:

1. Find the total number of outcomes.

The integers are from 11 to 60, inclusive.

Total numbers = \(60 - 11 + 1 = 50\).


2. Find the number of favorable outcomes.

Perfect Squares in the range [11, 60]:

\(4^2 = 16\), \(5^2 = 25\), \(6^2 = 36\), \(7^2 = 49\). (\(3^2=9\) is too small, \(8^2=64\) is too large). There are 4 perfect squares.

\textit{Perfect Cubes in the range [11, 60]:

\(3^3 = 27\). (\(2^3=8\) is too small, \(4^3=64\) is too large). There is 1 perfect cube.


3. Check for overlap.

Is any number in our list both a square and a cube? The lists are \{16, 25, 36, 49\ and \{27\. There is no overlap.


4. Calculate the total number of favorable outcomes.

Total favorable outcomes = (Number of squares) + (Number of cubes) = \(4 + 1 = 5\).


5. Calculate the probability.

\[ P(square or cube) = \frac{5{50} = \frac{1}{10} = 0.1 \]


Step 4: Final Answer:

The probability is 0.1.
Quick Tip: When calculating the number of integers in an inclusive range (from a to b), the formula is \(b - a + 1\). A common mistake is to just subtract (\(b-a\)).

Step 1: Understanding the Concept:

This problem uses the properties of angles in a parallelogram. Key properties are: (1) Opposite angles are equal. (2) Consecutive angles (angles next to each other) are supplementary, meaning they add up to 180 degrees. Since the two angles differ, they must be consecutive angles.


Step 2: Key Formula or Approach:

We can set up a system of two linear equations. Let the two consecutive angles be \(x\) and \(y\).

Equation 1 (Supplementary): \(x + y = 180\)

Equation 2 (Difference): \(x - y = 52\) (assuming \(x\) is the larger angle)


Step 3: Detailed Explanation:

We have the system:

1) \(x + y = 180\)

2) \(x - y = 52\)

We can solve this system by elimination. Add the two equations together:
\[ (x + y) + (x - y) = 180 + 52 \]
\[ 2x = 232 \]
\[ x = \frac{232}{2} = 116 \]

So the larger angle is 116 degrees.

Now substitute the value of \(x\) back into the first equation to find \(y\):
\[ 116 + y = 180 \]
\[ y = 180 - 116 = 64 \]

The smaller angle is 64 degrees. The two angles are 116\textsuperscript{o and 64\textsuperscript{o. Their difference is \(116 - 64 = 52\), and their sum is \(116 + 64 = 180\). The calculations are correct.


Step 4: Final Answer:

The number of degrees in the smaller angle is 64.
Quick Tip: Remembering the properties of shapes is key in geometry. For parallelograms, the relationship between consecutive angles is a very common topic for questions.

Step 1: Understanding the Concept:

The question asks for the "odds in favor" of an event, and provides the definition. We need to use the given probability of winning to find the probability of not winning, and then form the specified ratio.


Step 2: Key Formula or Approach:

Odds in favor = \(\frac{P(winning)}{P(not winning)}\)

Also, the probability of an event not happening is 1 minus the probability of it happening:
\(P(not winning) = 1 - P(winning)\)


Step 3: Detailed Explanation:

1. Identify the probability of winning.

We are given \(P(winning) = \frac{4}{9}\).


2. Calculate the probability of not winning.

\[ P(not winning) = 1 - \frac{4}{9} = \frac{9}{9} - \frac{4}{9} = \frac{5}{9} \]


3. Compute the ratio for the odds in favor.

\[ Odds in favor = \frac{P(winning)}{P(not winning)} = \frac{4/9}{5/9} \]

To divide by a fraction, we multiply by its reciprocal:

\[ Odds in favor = \frac{4}{9} \times \frac{9}{5} = \frac{4}{5} \]

This ratio is expressed as "4 to 5".


Step 4: Final Answer:

The odds that Pat will win the game are 4 to 5.
Quick Tip: Don't confuse probability with odds. If the probability of winning is \(\frac{a}{b}\), it means 'a' successes in 'b' total trials. The odds are a ratio of successes to failures. In this case, 4 successes and \(9-4=5\) failures, so the odds are 4 to 5.

Step 1: Understanding the Concept:

This is an algebraic manipulation problem involving consecutive integers. We need to express the other integers in terms of the first integer, \(a\), and then simplify the given sum.


Step 2: Detailed Explanation:

1. Express b, c, and d in terms of a.

Since the integers are consecutive and \(a\) is the smallest, we have:

\(b = a + 1\)

\(c = a + 2\)

\(d = a + 3\)


2. Formulate the sum.

We need to find the sum \(S = a + b + d\).


3. Substitute the expressions for b and d into the sum.

\[ S = a + (a + 1) + (a + 3) \]


4. Simplify the expression.

Combine the 'a' terms and the constant terms:

\[ S = (a + a + a) + (1 + 3) \]

\[ S = 3a + 4 \]


Step 3: Final Answer:

The sum \(a + b + d\) in terms of \(a\) is \(3a + 4\).
Quick Tip: For problems with abstract variables, you can check your answer by picking a simple number. Let \(a=1\). Then \(b=2\), \(c=3\), \(d=4\). The sum is \(a+b+d = 1+2+4=7\). Now, plug \(a=1\) into the options. Only option (E) gives \(3(1)+4=7\). This confirms the answer.

Step 1: Understanding the Concept:

This problem tests the rules of exponents and algebraic simplification. We are adding two identical terms, which can be simplified through factoring.


Step 2: Key Formula or Approach:

The key exponent rule is \(a^m \times a^n = a^{m+n}\).

The algebraic approach is to factor out the common term.


Step 3: Detailed Explanation:

We are given the expression \(2^x + 2^x\).

Think of \(2^x\) as a single variable, like \(y\). The expression is equivalent to \(y + y\), which simplifies to \(2y\).

Substituting \(2^x\) back in for \(y\), we get:
\[ 2 \times (2^x) \]

This can be written as:
\[ 2^1 \times 2^x \]

Now, using the exponent rule \(a^m \times a^n = a^{m+n}\), we add the exponents:
\[ 2^{1+x} or 2^{x+1} \]

Let's check the options. \(2^{x+1}\) matches option (A). Note that \(4^x = (2^2)^x = 2^{2x}\), which is different.


Step 4: Final Answer:

The expression \(2^x + 2^x\) simplifies to \(2^{x+1}\).
Quick Tip: A common mistake with exponents is to add them during addition (e.g., thinking \(2^x + 2^x = 2^{2x}\)). This is incorrect. Exponents are added during multiplication of like bases. Always remember to factor first when adding identical exponential terms.

Step 1: Understanding the Concept:

This is a sentence completion question that relies on identifying the definition or explanation provided within the sentence itself. The sentence structure suggests that the word in the blank is defined by the phrase that follows it.


Step 2: Detailed Explanation:

The sentence states that learning occurs through a certain process, and it immediately describes that process as "relating one observation to another."

We need to find the word among the options that best means "relating one observation to another."


(A) assumptions: Beliefs taken for granted. This does not fit the definition.

(B) experiments: Procedures to test a hypothesis. While this involves observation, it is not the act of relating observations itself.

(C) comparisons: The act of considering the relationship between two or more things. "Relating one observation to another" is the essence of making a comparison. This is a perfect fit.

(D) repetitions: The act of doing something again. This does not match the definition.

(E) impressions: Ideas or feelings about something. This does not fit.


The logic of the sentence is that since learning is based on comparisons, studying another culture (and thus comparing it to our own) will inevitably teach us about ourselves.


Step 3: Final Answer:

The word "comparisons" is the most logical choice as it is directly defined by the phrase "relating one observation to another."
Quick Tip: In sentence completion questions, look for clauses set off by commas, like "relating one observation to another" here. They often act as definitions or elaborations for the missing word.

Step 1: Understanding the Concept:

This sentence describes a cause-and-effect relationship. The first blank is the cause, related to a "new" aspect of knowledge. The second blank is the effect, a change in people or their relationships, which is then described by the statement that follows the colon.


Step 2: Detailed Explanation:

The description after the colon—"everyone believes that his or her subject cannot... be understood by others"—describes a situation of intellectual isolation or fragmentation. This creates divisions or "barriers" between people in different fields. This fits the second blank.

Now, what aspect of modern knowledge would cause such barriers? The increasing focus on narrow, specific areas of study, known as "specialization," is the direct cause of this phenomenon. Experts in one field become so focused that they find it difficult to communicate their knowledge to outsiders.

Let's test the chosen pair: "The new specialization of knowledge has created barriers between people." This creates a logical and coherent sentence that perfectly matches the explanation provided. The other options do not create such a clear cause-and-effect link. For example, a "decline" of knowledge (B) or "redundancy" (C) would not logically lead to the kind of expert isolation described.


Step 3: Final Answer:

The pair "specialization.. barriers between" accurately describes the cause (increasingly narrow fields of study) and the effect (intellectual isolation between people).
Quick Tip: When a sentence contains a colon, the part after the colon almost always defines, explains, or elaborates on the part before it. Use the explanation to help you determine the meaning of the missing words.

Step 1: Understanding the Concept:

This sentence describes the biological dependency of a parasite on its host. The sentence is in two parts, each describing a condition for the parasite's survival or demise.


Step 2: Detailed Explanation:

For the first blank, we need to identify the primary biological imperative for a species' survival. The host must live long enough for the parasite to do what? The most fundamental action for the continuation of a species is to create offspring, i.e., to reproduce.

For the second blank, the sentence sets up a parallel fate: "if the host species becomes ----, so do its parasites." This means whatever happens to the host also happens to the parasite. If the host species dies out, or becomes extinct, the parasite, which depends on it, will also become extinct.

Let's check the pair: "the host organisms must live long enough for the parasite to reproduce; if the host species becomes extinct, so do its parasites." This statement is biologically and logically correct. The other pairs create contradictions. For instance, in (C), if the host becomes widespread, the parasite would likely thrive, not disappear.


Step 3: Final Answer:

The words "reproduce" and "extinct" correctly fill the blanks, reflecting the biological principles of species survival and dependency.
Quick Tip: In sentences with two blanks, try to solve for one blank first. Often, one is more constrained or obvious than the other. Once you have a good fit for one blank, you can test its partner word from the same option.

Step 1: Understanding the Concept:

The sentence contrasts the author's positive view of crochet and needlework with the negative view of "too many art historians." The blanks must be filled with words that describe this negative view, or "cultural blindness."


Step 2: Detailed Explanation:

The sentence structure implies a cause or a nature of the "cultural blindness." This blindness is linked to the fact that textiles are a medium where "women artists predominate." This context strongly suggests a bias or prejudice against these art forms because of their association with women. This fits the second blank perfectly.

If the second blank is "prejudice against," the first blank must connect this prejudice to the cultural blindness. A blindness that is "traceable to their prejudice" makes logical sense, meaning the prejudice is the source of the blindness.

Let's check the complete phrase: "...a cultural blindness traceable to their prejudice against textiles...". This creates a coherent and critical statement, consistent with the author's argument for taking these arts seriously. Option (D) suggests the opposite ("respect for"), and other options like (B) or (E) don't fit the context of "blindness" as well as "prejudice."


Step 3: Final Answer:

The pair "traceable.. prejudice against" best explains the reason for the art historians' "cultural blindness," linking it to a bias against a female-dominated art form.
Quick Tip: Pay attention to "trigger words" that indicate the tone or logic of a sentence. Words like "argues for," "finding in too many," and "blindness" all suggest a critical or contrasting perspective.

Step 1: Understanding the Concept:

This sentence describes the actions of people who are afraid of television's power. Their goal is to prevent others from knowing about this power. The blank must describe an action that serves this goal.


Step 2: Detailed Explanation:

The "hoping" clause explains the motivation: they want to "keep knowledge of its potential... from being widely disseminated." If you want to hide something's power or potential, you would not praise or promote it. Instead, you would try to diminish its importance or make it seem less significant than it is.

Let's evaluate the options based on this logic:


(A) promote: To encourage or publicize. This is the opposite of what they would do.

(B) underplay: To represent something as less important than it really is. This perfectly matches the goal of hiding its power.

(C) excuse: To justify or pardon. This doesn't fit the context.

(D) laud: To praise. This is the opposite of their goal.

(E) suspect: To have doubts about. They don't just suspect its power; they "fear" it, which implies they believe in it.



Step 3: Final Answer:

The word "underplay" correctly describes the action of deliberately downplaying television's power to prevent others from recognizing its influence.
Quick Tip: Look for the underlying motive in the sentence. The phrase "hoping that..." directly tells you the goal of the subject. The correct verb in the blank must be an action that helps achieve that goal.

Step 1: Understanding the Concept:

This is a cause-and-effect sentence. The word "Because" signals that the first part of the sentence explains the reason for the second part. The blank must be a word that is synonymous with or directly related to "metaphysics."


Step 2: Detailed Explanation:

The cause is that the writers' seriousness came from their "metaphysics." Metaphysics is the branch of philosophy that deals with the fundamental nature of reality, including concepts like being, knowing, and existence.

Therefore, the writers would be praised for a "bent" (a tendency or inclination) that reflects this focus.

Let's check the options:


(A) technical: Relating to practical skills or a particular subject. Not related to metaphysics.

(B) discursive: Digressing from subject to subject. Not related.

(C) hedonistic: Engaged in the pursuit of pleasure. This is contrary to "high seriousness."

(D) philosophical: Relating to the study of the fundamental nature of knowledge, reality, and existence. This is a direct synonym for having a metaphysical bent.

(E) scientific: Based on the methods of science. While philosophy and science can intersect, "philosophical" is a much more direct and accurate descriptor for metaphysics.



Step 3: Final Answer:

The word "philosophical" is the best choice as it directly corresponds to the writers' use of metaphysics.
Quick Tip: Vocabulary is key in these questions. Knowing the definition of a key term like "metaphysics" immediately points you to the correct answer. If you're unsure, look for context clues like "high seriousness" to eliminate options like "hedonistic."

Step 1: Understanding the Concept:

The phrase "Far from being X, Y was Z" indicates a contrast or clarification. It means "Y was not X; instead, Y was Z." The sentence is clarifying the nature of Pat's tendency to be acquiescent (ready to accept something without protest).


Step 2: Detailed Explanation:

The sentence aims to define Pat's behavior more precisely. Let's analyze the options:


(A) "Far from being unctuous (falsely flattering), Pat was always loath (reluctant) to appear acquiescent." This suggests Pat hated appearing agreeable, which contradicts the idea of clarifying her acquiescence.
(B) "Far from being brazen (bold), Pat was always reluctant to appear acquiescent." This doesn't establish a clear contrast regarding agreeableness.
(D) "Far from being obsequious, Pat was always eager to appear acquiescent." This option provides a subtle but important distinction. "Obsequious" means being excessively servile or fawning, which is an extreme and often negative form of acquiescence. "Eager" is a more neutral term for being willing. The sentence is clarifying that Pat's agreeableness was not a servile or fawning (obsequious) trait; rather, she was simply genuinely willing or "eager" to seem agreeable. This contrast effectively refines the description of her character.
(E) "Far from being gregarious (sociable), Pat was always willing to appear acquiescent." Sociability and agreeableness are different traits, so the contrast is weak.

Option (D) provides the most logical and nuanced meaning. It clarifies that Pat was not a sycophant, but simply a willing person.


Step 3: Final Answer:

The pair "obsequious.. eager" provides the best contrast, clarifying that Pat's willingness to agree was genuine eagerness, not excessive servility.
Quick Tip: The structure "Far from being..." is used to deny a common or potential misconception and offer a more accurate description. Look for the option that provides the most precise and logical clarification.

Step 1: Understanding the Concept:

This is an analogy question. We first need to determine the relationship between the two words in the stem pair (CHUCKLE: LAUGHING) and then find the answer pair with the same relationship.


Step 2: Detailed Explanation:

The relationship between CHUCKLE and LAUGHING is one of degree or intensity. A chuckle is a quiet, soft, or low-intensity form of laughing. So, the relationship is "less intense form : more intense form".

Now let's analyze the answer choices:


(A) uproar: shouting - An uproar is a state of commotion, which may involve shouting, but it's not a lesser degree of shouting.
(B) whisper: speaking - A whisper is a very quiet or low-intensity form of speaking. This perfectly matches the relationship in the stem pair.
(C) hum: whistling - Humming and whistling are two different ways of making a musical sound with the mouth, not different intensities of the same action.
(D) lecture: conversing - A lecture is a formal type of conversation, not necessarily a different degree of intensity or volume.
(E) murmur: mimicking - A murmur is quiet speech, but mimicking is imitating. These are unrelated actions.


Step 3: Final Answer:

The pair "whisper: speaking" has the same "less intense form : more intense form" relationship as "chuckle: laughing".
Quick Tip: For analogy questions, try to state the relationship between the first pair of words in a clear sentence. For example, "A chuckle is a quiet way of laughing." Then, test this sentence with the answer choices: "A whisper is a quiet way of speaking." If it works, you've likely found the answer.

Step 1: Understanding the Concept:

This is an analogy question focusing on the relationship between parts and wholes in language and writing.


Step 2: Detailed Explanation:

The relationship between PARAGRAPH and ESSAY is that a paragraph is a fundamental structural component of an essay. An essay is composed of multiple paragraphs. This is a "part to whole" relationship.

Now let's analyze the answer choices:


(A) object: verb - An object and a verb are both parts of a sentence's predicate, but one is not a component of the other in the same structural way.
(B) phrase: preposition - A preposition is a word that typically begins a phrase; the word is part of the phrase, not the other way around. The order is reversed.
(C) interjection: parenthesis - Parentheses are punctuation used to enclose information, which could be an interjection, but this is not a fundamental structural part-to-whole relationship.
(D) clause: sentence - A clause is a grammatical unit that is a fundamental structural component of a sentence. A sentence is often composed of one or more clauses. This perfectly mirrors the relationship between a paragraph and an essay.
(E) colloquialism: expression - A colloquialism is a type of expression, not a structural part of it. This is a "type of" relationship.


Step 3: Final Answer:

The pair "clause: sentence" has the same "part to whole" structural relationship as "paragraph: essay".
Quick Tip: Be precise about the type of relationship. "Part to whole" is a common analogy type. Ensure the relationship in your chosen answer is not just "related to" but specifically "is a component of."

Step 1: Understanding the Concept:

This is an analogy question where the relationship between the words is one of opposition.


Step 2: Detailed Explanation:

The relationship between STUPOR and ALERT is that they are antonyms. A stupor is a state of near-unconsciousness or insensibility, the opposite of being alert, which means quick to notice and react.

Now let's analyze the answer choices to find another pair of antonyms:


(A) rebellion: defiant - Being defiant is a characteristic of a rebellion. These are related concepts, not opposites.
(B) despair: hopeful - Despair is the complete absence or loss of hope. Being hopeful is its direct opposite. This is a perfect antonym pair.
(C) expectation: unfulfilled - An expectation can be unfulfilled, but they are not opposite states.
(D) circumspection: careful - These words are synonyms. Circumspection means being wary and careful.
(E) ennui: listless - These words are synonyms. Ennui is a feeling of listlessness and dissatisfaction.


Step 3: Final Answer:

The pair "despair: hopeful" has the same antonym relationship as "stupor: alert".
Quick Tip: Common analogy relationships include synonyms, antonyms, part to whole, cause and effect, and degree of intensity. Identifying the relationship type first is the most effective strategy.

Step 1: Understanding the Concept:

This analogy relates an action or creation to the emotion it expresses.


Step 2: Detailed Explanation:

A PAEAN is a song of praise, triumph, or thanksgiving. It is a formal expression of JOY. The relationship is "an expression of a particular emotion."

Now let's analyze the answer choices:


(A) dirge: grief - A dirge is a lament for the dead, especially one forming part of a funeral rite. It is a formal expression of GRIEF. This perfectly matches the relationship.
(B) oratory: persuasion - Oratory is the art of public speaking. Its purpose is persuasion, which is a goal, not an emotion.
(C) aria: opera - An aria is a song within an opera. This is a part-to-whole relationship.
(D) chant: choir - A choir is a group that performs a chant. This is a performer-to-action relationship.
(E) lecture: instruction - A lecture is a speech given for the purpose of instruction. This is a purpose relationship.


Step 3: Final Answer:

The pair "dirge: grief" has the same "expression of emotion" relationship as "paean: joy".
Quick Tip: Distinguish between the emotion expressed by an action and the purpose of an action. Persuasion and instruction are purposes, while joy and grief are emotions. This distinction is key to solving this analogy.

Step 1: Understanding the Concept:

This analogy defines a person by something they have abandoned or betrayed.


Step 2: Detailed Explanation:

A RENEGADE is a person who deserts and betrays an organization, country, or set of principles. They are defined by their abandonment of their ALLEGIANCE. The relationship is "a person defined by the thing they have abandoned."

Now let's analyze the answer choices:


(A) revolutionary: reform - A revolutionary is a person who seeks to bring about reform. This is a "person and their goal" relationship.
(B) aesthete: discernment - An aesthete is a person who has or affects to have a special appreciation of art and beauty. Discernment is a characteristic of an aesthete.
(C) apostate: faith - An apostate is a person who renounces a religious or political belief or principle. They are defined by their abandonment of their FAITH. This perfectly matches the relationship.
(D) politician: challenge - A politician is someone who faces challenges. This is not a defining relationship of abandonment.
(E) criminal: imprisonment - Imprisonment is a potential consequence for a criminal, not something they have abandoned.


Step 3: Final Answer:

The pair "apostate: faith" has the same "person defined by what they abandoned" relationship as "renegade: allegiance".
Quick Tip: Pay attention to the specific action connecting the two words. Here, the action is one of abandonment or renunciation. Look for that same specific action in the answer choices.

Step 1: Understanding the Concept:

This is an analogy where the relationship is one of degree or intensity.


Step 2: Detailed Explanation:

The relationship between DEVOTED and ZEALOUS is that zealous is a more extreme or intense form of devoted. A zealous person shows great, sometimes excessive, energy and enthusiasm for their devotion.

Now let's analyze the answer choices to find a similar relationship of "word 2 is a more intense version of word 1":


(A) affectionate: demonstrative - Demonstrative means openly showing affection, which is about the manner of expression, not necessarily the intensity of the feeling itself.
(B) animated: lively - These are close synonyms, without a clear difference in intensity.
(C) rabid: extreme - Rabid means having an extreme or fanatical belief. It is a specific type of extreme, not necessarily a more intense version of it.
(D) objective: indifferent - These are not related by intensity.
(E) careful: fastidious - Fastidious means being very attentive to and concerned about accuracy and detail; it implies being excessively or painstakingly careful. This is a perfect example of a more intense degree of being careful.


Step 3: Final Answer:

The pair "careful: fastidious" shares the same relationship of degree (normal trait to extreme version of the trait) as "devoted: zealous".
Quick Tip: When evaluating analogies of degree, ask yourself: "Is X just a very, very strong version of Y?" If the answer is yes, you have a good match. A fastidious person is extremely careful. A zealous person is extremely devoted.

Step 1: Understanding the Concept:

This analogy has a nuanced relationship that goes beyond simple synonymy. It relates a specific type of something to the broader category.


Step 2: Detailed Explanation:

A VESTIGE is a trace or remnant of something that is disappearing or no longer exists. A REMAINDER is what is left over in general. Therefore, a vestige is a specific, often small or trace-like, type of remainder.

Now let's analyze the answer choices for this "specific, small type : general category" relationship:


(A) figurine: statue - A figurine is specifically a small statue. This perfectly matches the relationship. A figurine is a small type of statue, just as a vestige is a small type of remainder.
(B) knife: cutlery - A knife is an item of cutlery, but the relationship isn't about size. This is "example : category".
(C) hub: wheel - A hub is the central part of a wheel. This is a "part : whole" relationship.
(D) angle: slope - These are related mathematical concepts, not a type-to-category relationship.
(E) inventory: goods - An inventory can be a list of goods or the collection of goods themselves. This is not a "small type : general category" relationship.


Step 3: Final Answer:

The pair "figurine: statue" has the same "small, specific type : general category" relationship as "vestige: remainder".
Quick Tip: When simple relationships like synonyms or antonyms don't fit, look for more subtle connections. Here, the key is the implicit idea of "smallness" or being a "trace." A vestige is a small remainder, and a figurine is a small statue.

Step 1: Understanding the Concept:

This analogy is based on an antonym relationship, specifically linking a quality to an action that it cannot perform.


Step 2: Detailed Explanation:

EPHEMERAL means lasting for a very short time. To ENDURE means to last for a long time. Therefore, something that is ephemeral, by its very nature, cannot endure. The relationship is "a characteristic and the action it prevents."

Now let's analyze the answer choices:


(A) insensitive: cooperate - An insensitive person may find it difficult to cooperate, but it's not an inherent impossibility.
(B) infirm: react - An infirm (weak) person might react slowly, but they can still react.
(C) ineffectual: proceed - Something ineffectual (not producing a desired result) can still proceed (continue); it just does so without success.
(D) inelastic: stretch - Inelastic means not elastic; unable to be stretched and return to its original shape. By its definition, something that is inelastic cannot stretch. This is a perfect match.
(E) inflammable: ignite - Inflammable means easily set on fire, so it is something that can ignite. This is the opposite of the required relationship.


Step 3: Final Answer:

The pair "inelastic: stretch" has the same "quality that prevents an action" relationship as "ephemeral: endure".
Quick Tip: Frame the relationship as a full sentence: "Something ephemeral cannot endure." Now test the options: "Something inelastic cannot stretch." This direct fit shows you have the correct answer.

Step 1: Understanding the Concept:

This analogy is based on a relationship of degree or severity.


Step 2: Detailed Explanation:

A MISDEMEANOR is a minor or less serious type of CRIME. The relationship is "lesser degree : greater degree".

Now let's analyze the answer choices:


(A) interview: conversation - An interview is a specific type of conversation, not necessarily a lesser or greater one.
(B) lapse: error - A lapse is a temporary or minor failure of judgment or memory. It can be considered a less serious type of error. This fits the relationship well.
(C) oath: promise - An oath is a solemn promise, often invoking a divine witness. It is a more serious, not less serious, type of promise. The order is reversed.
(D) rebuke: criticism - A rebuke is a sharp or stern criticism. It is a more severe, not less severe, form of criticism. The order is reversed.
(E) vendetta: feud - A vendetta is a blood feud, a prolonged and bitter quarrel. It is a very serious type of feud. The order is reversed.


Step 3: Final Answer:

The pair "lapse: error" shares the same "lesser degree : greater degree" relationship as "misdemeanor: crime".
Quick Tip: In degree-based analogies, pay close attention to the order. Several options may show a degree relationship, but only one will have the correct order (e.g., lesser to greater).

Step 1: Understanding the Concept:

The question asks what would weaken or "minimize" the phenomenon described in the first paragraph. We need to identify the core reason given for the phenomenon and then find the option that negates that reason.


Step 2: Detailed Explanation:

The first paragraph explains the tendency as follows:


Premise: Individuals on the edge (periphery) of a group are at greater risk from predators.
Consequence 1: Because of this risk, periphery animals are more vigilant.
Premise 2: Smaller groups have a larger proportion of animals on the periphery.
Conclusion: Therefore, animals in smaller groups are, on average, more vigilant.

To minimize this entire effect, we must attack the foundational premise: that being on the periphery is riskier. If the risk were the same everywhere, the whole chain of logic would fall apart.

Let's analyze the options:


(A) This describes vigilant behavior but doesn't change the underlying risk factor.
(B) This directly states that the risk of capture is the same for all individuals, regardless of location. If this were true, there would be no reason for periphery animals to be more vigilant, and therefore no reason for smaller groups to have a higher average vigilance. This effectively minimizes the tendency.
(C) This would strengthen, not minimize, the tendency by making the periphery even more dangerous.
(D) This would also strengthen the tendency by making periphery animals easier targets.
(E) This is irrelevant to the risk of capture by predators and vigilant behavior.


Step 3: Final Answer:

By making the risk of capture uniform throughout the group, option (B) removes the fundamental cause for increased vigilance on the periphery, thereby minimizing the overall effect described.
Quick Tip: For questions that ask you to weaken or minimize an argument, identify the central assumption or premise of that argument. The correct answer will often be the one that directly attacks or removes that core assumption.

Step 1: Understanding the Concept:

This question asks about the structure of the passage and how the two paragraphs relate to each other logically. We need to analyze the main point of each paragraph and see how they connect.


Step 2: Detailed Explanation:

First paragraph's main point: It presents "one explanation" for increased vigilance in smaller groups, which "assumes that the vigilant behavior... is aimed at predators."

Second paragraph's main point: It begins with the transition word "However," signaling a contrast or exception. It then states, "a different explanation is necessary in cases where the vigilant behavior is not directed at predators." It provides the specific example of great blue herons, whose vigilance is related to finding food, not avoiding predators.

Therefore, the second paragraph explicitly presents a case (the herons) where the central assumption of the first paragraph (that vigilance is about predators) is not valid or is "unwarranted."

Let's evaluate the options:


(A) The conclusions are different (predator avoidance vs. food seeking).
(B) and (C) The second paragraph contradicts, rather than supports or elaborates on, the first paragraph's hypothesis.
(D) This perfectly describes the relationship. The second paragraph gives a case study where the first paragraph's assumption is shown to be unwarranted.
(E) The causes described are explicitly different (predators vs. poor feeding conditions).


Step 3: Final Answer:

The second paragraph introduces a counterexample to show that the predator-based assumption of the first paragraph does not apply in all situations.
Quick Tip: Transition words like "However," "Furthermore," "In contrast," and "For example" are crucial signposts in reading comprehension. They reveal the logical relationship between sentences and paragraphs. "However" almost always signals a turn or contradiction in the argument.

Step 1: Understanding the Concept:

This is an inference question that asks for the main takeaway or a conclusion the author would support based on the entire passage. We need to find the statement that is best supported by the information presented in both paragraphs.


Step 2: Detailed Explanation:

The author presents two distinct explanations for vigilant behavior. The first paragraph discusses vigilance as a defense against predators. The second paragraph discusses vigilance as a strategy for finding food. By presenting both of these as valid explanations in different contexts, the author implicitly argues that the term "vigilant" has a broader meaning than just looking for predators.

Let's evaluate the options based on this understanding:


(A) The passage suggests the periphery, not the interior, is more vigilant in predator-avoidance scenarios.
(B) The passage discusses the frequency of vigilant behavior, not its effectiveness.
(C) The passage does not provide any information about the ease of analysis.
(D) This statement is the central inference to be drawn from the passage as a whole. The author's primary purpose in writing the second paragraph is to show that vigilance is not always about predators. Therefore, the author would certainly agree that the term is not used exclusively for that purpose.
(E) The passage states that animals are more vigilant in smaller groups, not larger ones.


Step 3: Final Answer:

The entire structure of the passage, contrasting a predator-based explanation with a food-based one, supports the conclusion that "vigilant" behavior is a broad term not limited to predator avoidance.
Quick Tip: Inference questions often test your understanding of the author's main point or purpose. Ask yourself, "What is the most important idea the author is trying to convey with this passage?" The correct inference will align with that main idea.

Step 1: Understanding the Concept:

This question asks what assertion is supported by the passage as a whole. We need to find the statement that synthesizes the information from both paragraphs.


Step 2: Detailed Explanation:

The passage discusses a "similar behavior"—vigilance, specifically "looking up"—in two different contexts.


Paragraph 1: It describes vigilance in some animals as a behavior aimed at detecting predators.
Paragraph 2: It describes vigilance in great blue herons as a behavior aimed at finding better feeding locations.

The key point of the passage is the contrast between these two explanations. The author shows that the same action (looking up) can serve entirely different functions (survival from predation vs. foraging for food) depending on the species and its circumstances.

Let's evaluate the options:


(A) The passage presents both predation and food-finding as critical to survival, but it does not rank them in importance.

(B) The passage discusses the frequency of vigilant behavior, not its benefit to groups vs. individuals.

(C) This is a broad statement that may be true, but the passage focuses on a single behavior (vigilance) with different purposes, not different behaviors.

(D) The passage suggests smaller heron flocks are a result of poor feeding conditions, but it doesn't make a general claim that group size is unrelated to success.

(E) This statement perfectly captures the central point of the passage. The "similar behavior" is vigilance, and the passage explicitly demonstrates that it does not "serve the same purpose" in all cases.


Step 3: Final Answer:

The comparison of the two explanations for vigilant behavior directly supports the assertion that a similar behavior can have different purposes in different species.
Quick Tip: When a passage presents two different examples or explanations for a phenomenon, the main supported idea is often about the contrast or comparison between them. Look for the "big picture" conclusion that connects the two parts of the text.

Step 1: Understanding the Concept:

This is a main idea question. It asks for the primary focus of the entire passage. We need to find the option that best summarizes the author's overall project.


Step 2: Detailed Explanation:

The passage begins by outlining the historical (19th-century) debate about photography as art. It then introduces an "irony": contemporary photographers now reject the "art" label. The rest of the passage is dedicated to explaining this modern attitude. The author analyzes this stance by placing it within the "Modernist heritage in art" (line 20), comparing it to other art movements like Abstract Expressionism and Pop art. The author is therefore explaining a current phenomenon (the attitudes of photographers) by analyzing its historical and theoretical context.

Let's evaluate the options:


(A) This is part of the explanation, but the focus is specifically on photography, not just Modernism in general.

(B) This is only the topic of the first paragraph; the passage's main focus is on the contemporary situation.

(C) This accurately describes the two main parts of the author's argument: explaining the current attitudes and providing the historical context (both 19th-century and Modernist) for them.

(D) The author describes a general attitude of disclaiming art, not "various approaches," and is more concerned with explaining this attitude than "assessing its value."

(E) The passage discusses influence on photography's aims and prestige, not its specific "techniques."


Step 3: Final Answer:

The passage is primarily concerned with explaining the modern photographer's attitude toward art by placing it in a historical context.
Quick Tip: For main idea questions, look for an answer that encompasses the beginning, middle, and end of the passage. Options that focus on only one paragraph are usually too narrow to be the primary concern.

Step 1: Understanding the Concept:

This is a detail/inference question that asks us to characterize a specific concept described in the text. We must analyze the author's description in the cited lines.


Step 2: Detailed Explanation:

The lines in question (25-27) describe the Modernist concept of art as one where "the better the art, the more subversive it is of the traditional aims of art." A subversive act is one that undermines or overthrows something established. So, Modernist art, in this view, becomes better by working against the traditional definition of art.

This is a self-contradictory or seemingly absurd statement, which is the definition of a paradox. The idea that to be a great example of something (art), one must undermine that very thing is paradoxical.

Let's evaluate the options:


(A) Objective: The concept is about subverting tradition, which is a subjective goal, not an objective one.

(B) Mechanical: This relates to the 19th-century critique of photography, not the Modernist concept of art.

(C) Superficial: The author treats this concept with seriousness, suggesting it is complex, not superficial.

(D) Dramatic: While the idea might be dramatic, "paradoxical" is a much more precise description of its logical structure.

(E) Paradoxical: This perfectly describes the contradictory nature of the concept that art improves by subverting itself.


Step 3: Final Answer:

The concept that good art must subvert the aims of traditional art is best described as paradoxical.
Quick Tip: When a question points to specific lines, reread them carefully and try to define the key terms. Here, understanding "subversive" is key to recognizing the paradoxical nature of the statement.

Step 1: Understanding the Concept:

This question asks for the rhetorical purpose of mentioning a specific group. We need to understand why the author brought up Abstract Expressionists in the context of the argument about photography.


Step 2: Detailed Explanation:

The author introduces the painters with the phrase: "...photographers who suppose that...they are getting away from the pretensions of art...remind us of those Abstract Expressionist painters who imagined they were getting away from...painting..." (lines 31-36).

This is a direct comparison. The author is saying that photographers' claims to be "getting away from art" are similar to the claims made by Abstract Expressionists. Both groups disavowed or rejected the "pretensions" or traditional aims of art. The purpose of this comparison is to show that the photographers' attitude is part of a larger trend within Modernist art.

Let's evaluate the options:


(A) This accurately states the analogy. Both groups (photographers and Abstract Expressionists) "disavowed traditionally accepted aims" of art.

(B) The passage does not mention any physical resemblance.

(C) The passage contrasts the Abstract Expressionists with "classical Modernist painting," it does not create an analogy between them.

(D) This is incorrect; they are presented as an example of the Modernist heritage, not a contrast to it.

(E) The author's ultimate point is that photography is an art. This example serves to explain the photographers' behavior within the context of art, not to argue that it isn't art.


Step 3: Final Answer:

The Abstract Expressionists are introduced as an analogy to contemporary photographers, as both groups claimed to be rejecting the traditional pretensions of art.
Quick Tip: When a passage says "X reminds us of Y," it is explicitly setting up an analogy. Understand the key similarity the author is highlighting to determine the purpose of the comparison.

Step 1: Understanding the Concept:

This is a detail question asking about a specific point made in the first paragraph. We need to find what the "defenders of photography" in the 19th century asserted.


Step 2: Detailed Explanation:

The first paragraph describes the 19th-century debate. It states, "Against the charge that photography was a soulless, mechanical copying of reality, photographers asserted that it was instead a privileged way of seeing...and no less worthy an art than painting." (lines 8-11).

This phrase directly states their main argument: that photography was an art form that was just as valuable and worthy as painting.

Let's evaluate the options based on this text:


(A) This is a use of photography, but not the specific argument mentioned in the passage.

(B) While true, their defense focused on its artistic merit, not its technological aspect.

(C) "Impartially observing" is a claim made by contemporary photographers (line 15), not the 19th-century defenders.

(D) This is a direct paraphrase of "no less worthy an art than painting."

(E) The passage does not state that they claimed photography would replace other arts.


Step 3: Final Answer:

The passage explicitly states that 19th-century defenders argued photography was "no less worthy an art than painting."
Quick Tip: For "according to the author" questions, the answer is almost always directly stated in the text. Scan the relevant section of the passage for keywords from the question to locate the exact sentence that provides the answer.

Step 1: Understanding the Concept:

This question asks for the reason behind the attitude of contemporary photographers. We need to find the explanation the author provides for why they disclaim the "art" label.


Step 2: Detailed Explanation:

The author directly addresses this in the second paragraph. After describing how photographers now reject the "art" label, the author explains that this is a consequence of the "Modernist heritage." The author states that their unwillingness to debate the question "shows the extent to which they simply take for granted the concept of art imposed by the triumph of Modernism: the better the art, the more subversive it is of the traditional aims of art." (lines 24-27).

This means that photographers reject the label "art" because, in their Modernist view, the goal of a serious artist is to subvert or work against traditional notions of art. Claiming their work isn't art is their way of being good Modernist artists.

Let's evaluate the options:


(A) This refers to the 19th-century debate, not the contemporary one.

(B) The author states the opposite: "photography is securely established as a fine art" (lines 12-13).

(C) The influence of other movements is mentioned as a parallel phenomenon, but the core reason is the underlying Modernist belief about what art should be.

(D) This is a direct paraphrase of the explanation given in lines 25-27.

(E) This is too general. The author provides a very specific explanation based on the principles of Modernism.


Step 3: Final Answer:

The author explains that the photographers' reaction stems from the Modernist belief that the best art is that which subverts previous definitions of art.
Quick Tip: Look for sentences where the author explicitly provides a reason or explanation. Phrases like "because of," "shows the extent to which," or "the reason is" are strong indicators of where to find the answer to a "why" question.

Step 1: Understanding the Concept:

This is a detail question asking what contemporary photographers explicitly claim about their work. We need to find the sentence that lists their claims.


Step 2: Detailed Explanation:

The second paragraph directly answers this. The author writes: "Serious photographers variously claim to be finding, recording, impartially observing, witnessing events, exploring themselves—anything but making works of art." (lines 14-17).

This sentence provides a list of things they claim to be doing (observing, recording) and explicitly states what they claim not to be doing (making art).

Let's evaluate the options against this text:


(A) The passage does not mention them making this claim.

(B) This option combines two key parts of the quote: that their work is "impartial observation" and that it is "not examples of art" (from the phrase "anything but making works of art"). This is a very accurate summary of their stated claims.

(C) The passage does not mention their claims about viewer responses.

(D) This is contrary to the Modernist impulse described in the passage.

(E) Glorifying the mechanical aspect was a charge made against photography in the 19th century, not a claim made by contemporary photographers.


Step 3: Final Answer:

The passage states directly that contemporary photographers claim their work is impartial observation and anything but art.
Quick Tip: Questions with the word "expressly" or "explicitly" point you to information that is directly stated in the text, not inferred. Find the exact sentence that contains the information to ensure your answer is correct.

Step 1: Understanding the Concept:

This question asks for the author's own view of contemporary photography, which must be inferred from the tone and structure of the entire passage.


Step 2: Detailed Explanation:

The author consistently frames the photographers' rejection of the "art" label not as a sign that photography isn't art, but as a symptom of its deep involvement with Modernism. The author calls the situation "ironic" (line 12), states that photography "has developed all the anxieties and self-consciousness of a classic Modernist art" (lines 50-52), and analyzes the photographers' claims through the lens of the Modernist idea that "the better the art, the more subversive it is." The author concludes by worrying that the public will "forget that photography is a distinctive and exalted activity—in short, an art" (lines 55-56).

All of this points to the author's belief that contemporary photography is, in fact, a form of Modernist art, and its practitioners are engaging in the typical Modernist behavior of subverting tradition.

Let's evaluate the options:


(A) The author explicitly says photography is "securely established as a fine art."

(B) and (C) These are 19th-century views that the author presents as outdated. The author's final sentence confirms a belief that it is an "exalted" art.

(D) This perfectly summarizes the author's nuanced analysis. The author sees photography as a modern art whose practitioners are acting out a key Modernist tendency: subversion of prevailing artistic aims.

(E) The author contrasts photography with abstract art, suggesting it is not on the same path toward abstraction.


Step 3: Final Answer:

The author's analysis throughout the passage indicates a view of contemporary photography as a form of Modernist art that characteristically seeks to subvert traditional art.
Quick Tip: To determine the author's opinion, look at the analytical language used. Words like "ironically," "however," and the way the author frames the conclusion reveal their own perspective, which is often more complex than the views of the people described in the passage.

Step 1: Understanding the Concept:

This question asks for the antonym of the given word.


Step 2: Detailed Explanation:

PREOCCUPATION refers to the state of being engrossed, absorbed, or obsessed with something. It implies deep thought and concern about a particular matter.

The opposite would be a state of not thinking about or caring about something.

Let's analyze the options:


(A) finality: the state of being final or conclusive. Not an opposite.

(B) innocence: lack of guilt. Not an opposite.

(C) liberality: generosity. Not an opposite.

(D) unconcern: a lack of concern, interest, or anxiety. This is a direct opposite of the mental absorption implied by preoccupation.

(E) tolerance: the ability to accept things one disagrees with. Not an opposite.


Step 3: Final Answer:

The best antonym for PREOCCUPATION is UNCONCERN.
Quick Tip: To find an antonym, first define the given word as precisely as possible. Then, think about what a state completely lacking that quality would be called.

Step 1: Understanding the Concept:

This question asks for the antonym of the given word.


Step 2: Detailed Explanation:

CHROMATIC comes from the Greek word 'khroma' meaning color. It means relating to, produced by, or full of color. A chromatic scale in music includes all the semitones, but its primary meaning relates to color.

The direct opposite would be the absence of color.

Let's analyze the options:


(A) opaque: not able to be seen through; not transparent. This deals with transparency, not color.

(B) colorless: lacking color. This is the direct antonym of chromatic. Another term is "achromatic".

(C) lengthy: long. Unrelated.

(D) profound: deep. Unrelated.

(E) diffuse: spread out. Unrelated.


Step 3: Final Answer:

The best antonym for CHROMATIC is COLORLESS.
Quick Tip: Knowing word roots (etymology) can be very helpful. "Chroma" is a common root for color (e.g., chromatography, monochrome). Recognizing it immediately points you to "colorless" as the opposite.

Step 1: Understanding the Concept:

This question asks for the antonym of the word PEDESTRIAN. In this context, pedestrian does not refer to a person walking. As an adjective, it means lacking inspiration or excitement; dull, ordinary, and commonplace.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of dull, ordinary, or commonplace. The opposite would be something exciting, unusual, or extraordinary.

Let's analyze the options:


(A) widely known: This is closer to being a synonym for commonplace, not an antonym.

(B) strongly motivated: This describes a personal trait and is unrelated to the quality of being dull or common.

(C) discernible: This means able to be perceived or recognized, which is unrelated.

(D) uncommon: This means not often found or occurring; unusual. It is a direct opposite of commonplace or pedestrian.

(E) productive: This means producing a significant amount of something, which is unrelated.



Step 3: Final Answer:

The best antonym for PEDESTRIAN is UNCOMMON.
Quick Tip: Many words have more than one meaning. "Pedestrian" can mean a walker, but in vocabulary tests, it's often used in its adjectival sense to mean "dull" or "commonplace." Always consider the less literal meanings.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb EQUIVOCATE. To equivocate means to use ambiguous or unclear language, especially with the intent to mislead or to avoid committing to a particular stance.


Step 2: Detailed Explanation:

We are looking for a phrase that means the opposite of speaking vaguely or evasively. The opposite would be to speak clearly, directly, and honestly.

Let's analyze the options:


(A) communicate straightforwardly: This means to express oneself clearly and directly, without evasion. This is a perfect antonym for equivocate.

(B) articulate persuasively: One can be persuasive while still equivocating. This is not an opposite.

(C) instruct exhaustively: This relates to teaching, not the clarity or directness of speech in general.

(D) study painstakingly: This relates to learning, not communicating.

(E) reproach sternly: This means to scold, which is a different speech act altogether.



Step 3: Final Answer:

The best antonym for EQUIVOCATE is TO COMMUNICATE STRAIGHTFORWARDLY.
Quick Tip: Understanding the intent behind a word is often key. The intent of equivocating is to conceal or avoid. The opposite action would therefore have an intent of being open and direct.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb DENUDE. To denude something means to strip it of its covering, to make it bare. The word often implies removing a natural covering, like trees from a forest.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of stripping something bare. The opposite action would be to put a covering on something.

Let's analyze the options:


(A) crowd out: To force something or someone out of a place by filling the space. Not an opposite.

(B) skim over: To read or consider something quickly. Not an opposite.

(C) change color: Unrelated.

(D) cover: To put something on top of or in front of (something else), especially to protect or conceal it. This is the direct opposite of denude.

(E) sustain: To strengthen or support. While different, it is not the direct opposite of making bare.



Step 3: Final Answer:

The best antonym for DENUDE is COVER.
Quick Tip: Look for the core action of the word. The action of "denude" is to remove a covering. The most direct opposite is to add a covering.

Step 1: Understanding the Concept:

This question asks for the antonym of the noun RANCOR. Rancor is a feeling of bitterness, deep-seated ill will, or resentment.


Step 2: Detailed Explanation:

We are looking for a word that represents the opposite of bitterness and hatred. The opposite would be a feeling of friendliness, kindness, and benevolence.

Let's analyze the options:


(A) deference: Humble submission and respect. While positive, it's not the direct opposite of hatred.

(B) optimism: Hopefulness and confidence about the future. Unrelated to feelings about others.

(C) courage: The ability to do something that frightens one. Unrelated.

(D) superiority: The state of being superior. Unrelated.

(E) goodwill: A friendly, helpful, or cooperative feeling or attitude. This is the direct antonym of rancor.



Step 3: Final Answer:

The best antonym for RANCOR is GOODWILL.
Quick Tip: Focus on the emotional content of the word. Rancor is a strong negative emotion directed at others. Its opposite must be a positive emotion directed at others, like goodwill.

Step 1: Understanding the Concept:

This question asks for the antonym of the adjective OSSIFIED. The literal meaning is to be turned into bone. However, it is most often used metaphorically to mean having become rigid, conventional, and opposed to change.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of being rigid and unchanging. The opposite would be flexible, adaptable, or willing to change.

Let's analyze the options:


(A) vulnerable to destruction: Not an opposite. Something ossified could be either strong or brittle.

(B) subject to illusion: Unrelated.

(C) worthy of consideration: Unrelated.

(D) capable of repetition: Unrelated.

(E) amenable to change: This means open and responsive to suggestion; easily persuaded or controlled. It implies a willingness to change, which is the direct opposite of being ossified or rigid.



Step 3: Final Answer:

The best antonym for OSSIFIED is AMENABLE TO CHANGE.
Quick Tip: Metaphorical meanings are common in vocabulary tests. If a word seems to have a strange literal meaning (like "turned to bone"), consider its figurative use. Ossified opinions are rigid and inflexible.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb CONTROVERT. To controvert means to argue against, dispute, or deny the truth of something. It is the root of "controversy."


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of denying or disputing. The opposite action would be to confirm, prove, or support something.

Let's analyze the options:


(A) substantiate: To provide evidence to support or prove the truth of something. This is a direct antonym for controvert.

(B) transform: To change. Not an opposite.

(C) ameliorate: To make something bad better. Not an opposite.

(D) simplify: To make easier to understand. Not an opposite.

(E) differentiate: To recognize what makes something different. Not an opposite.



Step 3: Final Answer:

The best antonym for CONTROVERT is SUBSTANTIATE.
Quick Tip: Breaking down a word can help. "Contro-" is a prefix meaning against (like in contradict), and "-vert" means to turn. To "turn against" something is to dispute it. The opposite is to support it.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb PROTRACT. To protract means to prolong or extend the duration of something; to make something last longer.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of making something longer. The opposite action would be to shorten or cut something short.

Let's analyze the options:


(A) thrust: To push suddenly. Not an opposite.

(B) reverse: To move backward. Not the same as shortening a duration.

(C) curtail: To reduce in extent or quantity; to cut short. This is the direct antonym of protract.

(D) disperse: To scatter over a wide area. Not an opposite.

(E) forestall: To prevent by acting ahead of time. Not an opposite.



Step 3: Final Answer:

The best antonym for PROTRACT is CURTAIL.
Quick Tip: Think of a common phrase. "Protracted negotiations" are negotiations that have been dragged out and made to last a long time. The opposite would be to "curtail negotiations" or cut them short.

Step 1: Understanding the Concept:

This question asks for the antonym of the verb ABRADE. To abrade means to wear away or scrape off by friction or erosion. It implies a reduction or wearing down.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of wearing away or reducing. The opposite action would be to build up, add to, or increase.

Let's analyze the options:


(A) unfasten: To undo. Not an opposite.

(B) prolong: To make longer in time. Not an opposite.

(C) augment: To make something greater by adding to it; to increase. This is a clear antonym for abrade, which is a process of reduction.

(D) extinguish: To put out (a fire). Not an opposite.

(E) transmit: To pass on. Not an opposite.



Step 3: Final Answer:

The best antonym for ABRADE is AUGMENT.
Quick Tip: The core idea of "abrade" is a process of subtraction (wearing away). Its opposite must be a process of addition. "Augment" is the best fit for a process of addition or increase.

Step 1: Understanding the Concept:

This question asks for the antonym of the noun APOLOGIST. An apologist is a person who offers a formal defense or argument for something, often a controversial belief or system. They are a defender or supporter. The term does not mean someone who apologizes.


Step 2: Detailed Explanation:

We are looking for a word that means the opposite of a defender or supporter. The opposite would be someone who criticizes or attacks something.

Let's analyze the options:


(A) egotist: A self-centered person. Not an opposite.

(B) wrongdoer: A person who does something wrong. Not an opposite.

(C) freethinker: A person who forms their own opinions rather than accepting dogma. Not a direct opposite.

(D) detractor: A person who criticizes or disparages someone or something. This is a direct antonym for an apologist (a defender).

(E) spendthrift: A person who spends money wastefully. Not an opposite.



Step 3: Final Answer:

The best antonym for APOLOGIST is DETRACTOR.
Quick Tip: Beware of false friends in vocabulary. "Apologist" does not mean "one who says sorry." It comes from the Greek "apologia," meaning "a speech in defense." Knowing this helps distinguish it from its common-sounding counterpart and find the true opposite.

Step 1: Understanding the Concept:

The question asks us to compare the x- and y-coordinates of the center of a circle. The key information is that the circle is "tangent" to both axes. Tangent means it touches the axis at exactly one point.


Step 2: Detailed Explanation:

Let the coordinates of the center P be \((x_p, y_p)\). Let the radius of the circle be \(r\).


The distance from the center of a circle to a line that is tangent to it is equal to the radius.
The distance from the center P\((x_p, y_p)\) to the x-axis (the line \(y=0\)) is \(|y_p|\). Since the circle is tangent to the x-axis, this distance must be the radius: \(r = |y_p|\).
The distance from the center P\((x_p, y_p)\) to the y-axis (the line \(x=0\)) is \(|x_p|\). Since the circle is tangent to the y-axis, this distance must also be the radius: \(r = |x_p|\).
Therefore, we can conclude that \(|x_p| = |y_p| = r\).
From the provided diagram, the circle is located in the first quadrant, where both x and y coordinates are positive. Thus, we can drop the absolute value signs: \(x_p = y_p\).


Step 3: Final Answer:

The x-coordinate of P is equal to the y-coordinate of P. Therefore, the two quantities are equal.
Quick Tip: Visualize the geometry. A circle that fits perfectly into a corner, touching both walls (the axes), must have its center at an equal distance from both walls. This means its x and y coordinates must be the same.

Step 1: Understanding the Concept:

This question requires us to add two fractions and compare their sum to the number 1.


Step 2: Key Formula or Approach:

To add fractions, we need a common denominator. The least common multiple of the denominators 5 and 3 is 15.


Step 3: Detailed Explanation:

First, we convert each fraction to an equivalent fraction with the denominator 15.
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

Now, add the two new fractions:
\[ \frac{9}{15} + \frac{10}{15} = \frac{9 + 10}{15} = \frac{19}{15} \]

So, the quantity in Column A is \(\frac{19}{15}\).

We now compare Column A with Column B.
\[ \frac{19}{15} \quad vs. \quad 1 \]

Since the numerator (19) is greater than the denominator (15), the fraction is an improper fraction, and its value is greater than 1.


Step 4: Final Answer:

The quantity in Column A (\(\frac{19}{15}\)) is greater than the quantity in Column B (1).
Quick Tip: A quick way to check is to use estimation. \(\frac{3}{5}\) is 0.6. \(\frac{2}{3}\) is approximately 0.67. Their sum, \(0.6 + 0.67 = 1.27\), is clearly greater than 1. This can give you the right answer much faster than finding a common denominator.

Step 1: Understanding the Concept:

This question tests the properties of absolute values and exponents for any real number \(x\).


Step 2: Detailed Explanation:

Let's analyze each column separately.

Column A: \(|x^2|\)

For any real number \(x\), the value of \(x^2\) is always non-negative (i.e., \(x^2 \ge 0\)). The absolute value of a non-negative number is the number itself.

Therefore, \(|x^2| = x^2\).


Column B: \(|x|^2\)

This expression tells us to first take the absolute value of \(x\), and then square the result. Let's test a few cases:


If \(x\) is positive, e.g., \(x=3\): \(|3|^2 = 3^2 = 9\).
If \(x\) is negative, e.g., \(x=-3\): \(|-3|^2 = 3^2 = 9\).
If \(x\) is zero, e.g., \(x=0\): \(|0|^2 = 0^2 = 0\).

In all cases, the result of \(|x|^2\) is the same as the result of \(x^2\). So, \(|x|^2 = x^2\).


Comparison:

From our analysis, we found that \(|x^2| = x^2\) and \(|x|^2 = x^2\).

Therefore, \(|x^2| = |x|^2\) for all real numbers \(x\).


Step 3: Final Answer:

The two quantities are equal.
Quick Tip: Remember this fundamental identity: the square of a number is always the same as the square of its absolute value. This is because squaring any real number, positive or negative, results in a positive outcome.

Step 1: Understanding the Concept:

The term "inscribed" means that the square is drawn inside the circle in such a way that all four of its vertices (corners) touch the circumference of the circle.


Step 2: Detailed Explanation:

Let's visualize the figure described. We have a circle with a square perfectly fitted inside it.


A diameter of a circle is a straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
A diagonal of a square is a straight line segment connecting two opposite vertices.

When a square is inscribed in a circle, its vertices are on the circle's circumference. The diagonal of the square connects two of these opposite vertices. Because the angles of a square are 90 degrees and the vertices are on the circle, the diagonal must subtend a 180-degree arc, meaning it must pass through the center of the circle. A line segment that connects two points on the circle and passes through the center is, by definition, a diameter.

Therefore, the diagonal of the inscribed square is also a diameter of the circle.


Step 3: Final Answer:

The length of a diagonal of the square is equal to the length of a diameter of the circle. The two quantities are equal.
Quick Tip: Drawing a quick sketch for geometry problems is often the fastest way to see the relationship between the parts. As soon as you draw a square inside a circle, you'll notice the diagonal and diameter are the same line.

Step 1: Understanding the Concept:

We are asked to compare the sum of two numbers, \(x\) and \(y\), with the value 35. We are given a set of inequalities that constrain the values of \(x\) and \(y\), but the numbers are not specified. We should test different possible values for \(x\) and \(y\) that satisfy the condition \(x < y < 20\).


Step 2: Detailed Explanation:

The problem does not state that \(x\) and \(y\) must be integers, so we should consider real numbers. Let's try to find a case where Column A is greater than Column B, and another case where it is smaller.


Case 1: Try to maximize \(x + y\).

To make the sum large, we should choose \(x\) and \(y\) to be as close to 20 as possible, while still satisfying \(x < y < 20\).

Let's pick \(y = 19\). Since \(x < y\), we can pick \(x = 18\).

In this case, \(x + y = 18 + 19 = 37\).

Here, Column A (37) is greater than Column B (35).


Case 2: Try to minimize \(x + y\).

To make the sum small, we can choose small positive values.

Let's pick \(y = 2\). Since \(x < y\), we can pick \(x = 1\).

In this case, \(x + y = 1 + 2 = 3\).

Here, Column A (3) is less than Column B (35).

The problem does not forbid negative numbers. Let's pick \(y = -5\). Since \(x < y\), we can pick \(x = -6\). Both satisfy \(x < y < 20\).

In this case, \(x + y = -6 + (-5) = -11\).

Here, Column A (-11) is also less than Column B (35).


Step 3: Final Answer:

Since we found one scenario where Column A is greater than Column B (37 vs 35) and another scenario where Column A is less than Column B (3 vs 35), we cannot determine a fixed relationship between the two quantities.
Quick Tip: For quantitative comparison questions involving variables and inequalities, the "plug in numbers" strategy is very effective. Always try to test different types of numbers that fit the constraints: large numbers, small numbers, positive, negative, and zero. If you get different comparison results, the answer is always (D).

Step 1: Understanding the Concept:

We are given two pieces of information about a college: an average and a ratio. We need to determine if this information is sufficient to find a unique value for the total number of students.


Step 2: Detailed Explanation:

Let's define variables for the unknown quantities:


\(S\) = Total number of students
\(C\) = Total number of courses
\(F\) = Total number of faculty

Now, let's translate the given information into equations:

1. Average students per course is 30:
\[ \frac{S}{C} = 30 \implies S = 30C \]
This tells us that the total number of students must be a multiple of 30.


2. Ratio of students to faculty is 20 to 1:
\[ \frac{S}{F} = \frac{20}{1} \implies S = 20F \]
This tells us that the total number of students must be a multiple of 20.


We have two equations but three unknown variables (\(S, C, F\)). We cannot solve for a unique value of \(S\). Let's demonstrate this with examples:


Scenario 1: Assume there are \(F=30\) faculty members. Then the number of students would be \(S = 20 \times 30 = 600\). In this case, Column A equals Column B.
Scenario 2: Assume there are \(F=60\) faculty members. Then the number of students would be \(S = 20 \times 60 = 1200\). In this case, Column A is greater than Column B.
Scenario 3: Assume there are \(F=15\) faculty members. Then the number of students would be \(S = 20 \times 15 = 300\). In this case, Column A is less than Column B.


Step 3: Final Answer:

Since the total number of students can be less than, equal to, or greater than 600 depending on the number of faculty or courses (which is unknown), the relationship cannot be determined from the information given.
Quick Tip: In problems like this, check if you have enough information. You generally need as many independent equations as you have variables to find a unique solution. With three variables (\(S, C, F\)) and only two equations relating them, a unique value for \(S\) cannot be found.

Step 1: Understanding the Concept:

We need to compare two algebraic fractions where the variable \(x\) is positive. There are several methods, including cross-multiplication, plugging in a number, or analyzing the structure of the fractions.


Step 2: Key Formula or Approach:

The most rigorous method is cross-multiplication. Since the denominators (800 and 790) are positive, the direction of the inequality will not change. We will compare \((590 + x) \times 790\) with \((600 + x) \times 800\).


Step 3: Detailed Explanation:

Let's perform the cross-multiplication.

Left Side (from Column A):
\[ (590 + x) \times 790 = 590 \times 790 + 790x = 466100 + 790x \]


Right Side (from Column B):
\[ (600 + x) \times 800 = 600 \times 800 + 800x = 480000 + 800x \]


Comparison:

We are now comparing \(466100 + 790x\) with \(480000 + 800x\).

Let's subtract \(466100\) from both sides and \(790x\) from both sides to simplify the comparison.

We compare \(0\) with \((480000 - 466100) + (800x - 790x)\).
\[ 0 \quad vs. \quad 13900 + 10x \]

We are given that \(x > 0\). This means \(10x\) is a positive number.

Therefore, \(13900 + 10x\) will always be a positive number greater than 13900.

Since \(13900 + 10x > 0\), the right side of our comparison is always larger. The right side corresponds to Column B.


Step 4: Final Answer:

The quantity in Column B is greater.
Quick Tip: Another quick way to solve this is by inspection. In Column B, you are adding a larger number (600 vs 590) to \(x\), and then dividing by a smaller number (790 vs 800). Both of these changes make the fraction in Column B larger than the fraction in Column A. When the numerator is larger and the denominator is smaller, the resulting fraction is always greater (for positive numbers).

Step 1: Understanding the Concept:

The question involves finding the value of an unknown angle, x, from a geometric diagram. The diagram shows three adjacent angles, \(2x^\circ\), \(120^\circ\), and \(x^\circ\), whose outer rays form a straight line. Angles on a straight line sum to 180 degrees.


Step 2: Key Formula or Approach:

The sum of angles that form a straight line is 180°. We can set up an equation using the given angles.
\[ 2x + 120 + x = 180 \]


Step 3: Detailed Explanation:

The three angles lie along a straight line, so their sum must be 180°.
\[ 2x^\circ + 120^\circ + x^\circ = 180^\circ \]

Combine the terms with x:
\[ 3x + 120 = 180 \]

Subtract 120 from both sides:
\[ 3x = 180 - 120 \]
\[ 3x = 60 \]

Divide by 3:
\[ x = 20 \]

The value of x is 20.


Comparison:

Column A: \(x = 20\)

Column B: 80

Since \(20 < 80\), the quantity in Column B is greater.


Step 4: Final Answer:

The quantity in Column B is greater.
Quick Tip: When you see multiple angles arranged along a straight line in a diagram, your first thought should be that their sum is 180°. This is a very common geometric principle tested in exams.

Step 1: Understanding the Concept:

This problem requires us to calculate and compare two probabilities based on a given set of integers. The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.


Step 2: Detailed Explanation:

First, determine the total number of integers in the set. The set includes integers from 1 to 13, so there are 13 total outcomes.


Column A: Probability that n will be even

The even integers in the set are \{2, 4, 6, 8, 10, 12\.

Number of even integers = 6.

The probability is:
\[ P(even) = \frac{Number of even integers}{Total number of integers} = \frac{6}{13} \]


Column B: Probability that n will be odd

The odd integers in the set are \{1, 3, 5, 7, 9, 11, 13\.

Number of odd integers = 7.

The probability is:
\[ P(odd) = \frac{Number of odd integers}{Total number of integers} = \frac{7}{13} \]


Comparison:

We are comparing \(\frac{6}{13}\) (Column A) with \(\frac{7}{13}\) (Column B). Since the denominators are the same, we just compare the numerators.

Since \(6 < 7\), we have \(\frac{6}{13} < \frac{7}{13}\).


Step 3: Final Answer:

The quantity in Column B is greater.
Quick Tip: In any set of consecutive integers, the number of odd and even integers will either be equal or differ by one. If the total number of integers is odd (like 13 here), there will be one more of whichever number (odd or even) the set starts and ends with. This set starts and ends with an odd number, so there is one more odd number.

Step 1: Understanding the Concept:

This question asks us to compare a value derived from two variables, p and q, with 1. The variables are constrained by a given equation and inequalities. We need to determine the range of the product pq.


Step 2: Detailed Explanation:

We are given \(p+q=1\), with both p and q being positive numbers (\(0 < p\)) and \(p < q\).

Since \(p < q\) and \(p+q=1\), it must be that \(p < 0.5\) and \(q > 0.5\). (If p=q=0.5, p+q=1, so to make p smaller, q must be larger).

Let's analyze the product \(pq\). Since both p and q are positive, their product \(pq\) is also positive.

Let's express the product in terms of one variable, say p. Since \(q = 1 - p\), the product is \(p(1-p) = p - p^2\).

We know that \(0 < p < 0.5\). Let's see what values the product can take.

This is a downward-facing parabola, with its maximum at \(p=0.5\). At \(p=0.5\), the product would be \(0.5 \times 0.5 = 0.25\).

As p approaches 0, the product \(p(1-p)\) also approaches 0.

Since \(0 < p < 0.5\), the product \(pq\) must be in the range \(0 < pq < 0.25\).

So, \(pq\) is a positive fraction that is always less than 1 (and even less than 0.25).


Comparison:

Column A is \(\frac{1}{pq}\). Since \(pq\) is a positive number between 0 and 0.25, its reciprocal, \(\frac{1}{pq}\), must be greater than \(\frac{1}{0.25}\), which is 4.

Therefore, the quantity in Column A is always greater than 4.

Column B is 1.

Since the quantity in Column A is always greater than 4, it is always greater than 1.


Step 3: Final Answer:

The quantity in Column A is greater.
Quick Tip: Remember the property of reciprocals: if a positive number \(k\) is less than 1 (\(0 < k < 1\)), its reciprocal \(1/k\) will always be greater than 1.

Step 1: Understanding the Concept:

We are given a system of two linear equations with two variables, x and y. We need to find the value of the expression \(x+y\) and compare it to 12.


Step 2: Key Formula or Approach:

We can solve this system by elimination or substitution. A quicker approach might be to manipulate the equations directly to find the expression \(x+y\).


Step 3: Detailed Explanation:

Let the given equations be:

(1) \(2x + 3y = 29\)

(2) \(3x + 4y = 41\)

Notice that the coefficients of x and y in the second equation are larger than in the first. Let's try subtracting the first equation from the second equation.
\[ (3x + 4y) - (2x + 3y) = 41 - 29 \]

Distribute the negative sign on the left side:
\[ 3x + 4y - 2x - 3y = 12 \]

Group like terms:
\[ (3x - 2x) + (4y - 3y) = 12 \]
\[ x + y = 12 \]

This gives us the value of the expression in Column A directly.


Comparison:

Column A: \(x + y = 12\)

Column B: 12

The two quantities are equal.


Step 4: Final Answer:

The two quantities are equal.
Quick Tip: Before jumping into a full solution for x and y, look for shortcuts. Sometimes, adding or subtracting the given equations can directly yield the expression you need to evaluate, saving a lot of time.

Step 1: Understanding the Concept:

We need to determine the area of triangle OPQ and compare it with 10. The area of a triangle can be found using the formula \(\frac{1}{2} \times base \times height\).


Step 2: Detailed Explanation:

Let's analyze the given information:


O is the origin (0, 0).
Q is a point on the positive x-axis. Since OQ = 5, the coordinates of Q are (5, 0).
P is a point (x, y) in the first quadrant.
PQ = 5. This means the distance from P(x, y) to Q(5, 0) is 5.

Let's calculate the area of triangle OPQ. We can use OQ as the base.

Base = OQ = 5.

The height of the triangle is the perpendicular distance from vertex P to the line containing the base (the x-axis). This height is equal to the y-coordinate of P.

Area = \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 5 \times y\).

To find the area, we need the value of \(y\). We know that P(x, y) lies on a circle with center Q(5, 0) and radius 5, because \(PQ=5\). The equation of this circle is \((x-5)^2 + (y-0)^2 = 5^2\), or \((x-5)^2 + y^2 = 25\).

Since P can be any point on this circle (in the first quadrant), its y-coordinate can vary.

Case 1: If P is very close to the x-axis, for example, \(P \approx (9.9, 0.1)\), then \(y\) is very small, and the area is close to 0. In this case, Area < 10.

Case 2: If P is at the highest point of the circle in the first quadrant, its coordinates would be (5, 5). Let's check if this point is valid: \(PQ = \sqrt{(5-5)^2 + (5-0)^2} = \sqrt{0^2 + 5^2} = 5\). So, P could be (5, 5).
In this case, the height \(y=5\), and the Area = \(\frac{1}{2} \times 5 \times 5 = 12.5\). Here, Area > 10.

Case 3: Can the area be exactly 10? Area = \(\frac{5}{2}y = 10 \implies y = 4\). If \(y=4\), we can find x from the circle equation: \((x-5)^2 + 4^2 = 25 \implies (x-5)^2 + 16 = 25 \implies (x-5)^2 = 9 \implies x-5 = \pm 3\). So \(x=8\) or \(x=2\). The point (2,4) is a valid location for P, and it gives an area of 10.


Since the area can be less than, equal to, or greater than 10, the relationship cannot be determined.


Step 3: Final Answer:

The relationship cannot be determined from the information given.
Quick Tip: In geometry problems for quantitative comparison, if a point's location is not fixed but is only constrained to a path (like a circle), test different possible locations on that path. If the quantity you're evaluating changes, the answer is likely (D).

Step 1: Understanding the Concept:

This question requires simplifying an expression involving square roots and exponents.


Step 2: Key Formula or Approach:

First, simplify the expression inside the parentheses. Then apply the exponent. We will use the rule \((ab)^2 = a^2 b^2\).


Step 3: Detailed Explanation:

Let's evaluate the expression in Column A.

First, simplify the terms inside the parentheses:
\[ \sqrt{5} + \sqrt{5} = 2\sqrt{5} \]

Now, square the result:
\[ (2\sqrt{5})^2 \]

Using the exponent rule \((ab)^2 = a^2 b^2\), we get:
\[ 2^2 \times (\sqrt{5})^2 \]

Calculate each part:
\[ 2^2 = 4 \]
\[ (\sqrt{5})^2 = 5 \]

Multiply the results:
\[ 4 \times 5 = 20 \]

The quantity in Column A is 20.


Comparison:

Column A: 20

Column B: 20

The two quantities are equal.


Step 4: Final Answer:

The two quantities are equal.
Quick Tip: A common mistake is to incorrectly apply the exponent rule \((a+b)^2 = a^2 + 2ab + b^2\). While that would work (\((\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{5}) + (\sqrt{5})^2 = 5 + 2(5) + 5 = 20\)), it's much faster to combine the like terms inside the parentheses first.

Step 1: Understanding the Concept:

We are given an equation relating four positive integer variables. We need to compare two expressions involving these variables. The goal is to see if the given equation fixes the relationship between the two expressions.


Step 2: Detailed Explanation:

Let's manipulate the given equation to isolate the expression in Column A.
\[ \frac{n}{4} + \frac{r}{8} = \frac{s}{8} + \frac{t}{6} \]

To combine the terms on the left, find a common denominator (8).
\[ \frac{2n}{8} + \frac{r}{8} = \frac{s}{8} + \frac{t}{6} \]
\[ \frac{2n+r}{8} = \frac{s}{8} + \frac{t}{6} \]

Now, multiply both sides by 8 to solve for \(2n+r\).
\[ 2n+r = 8 \left(\frac{s}{8} + \frac{t}{6}\right) \]
\[ 2n+r = s + \frac{8t}{6} = s + \frac{4t}{3} \]

So, Column A is equal to \(s + \frac{4t}{3}\). We now need to compare this to Column B, which is \(2s+t\).

Comparison: \(s + \frac{4t}{3}\) vs \(2s+t\).

Subtract \(s\) and \(t\) from both sides to simplify the comparison.

We compare: \(\frac{4t}{3} - t\) vs \(2s - s\).
\[ \frac{t}{3} \quad vs. \quad s \]

Since \(s\) and \(t\) are independent positive integers, the relationship between \(\frac{t}{3}\) and \(s\) is not fixed.


Case 1: Let \(s=1\). For \(2n+r\) to be an integer, \(s + \frac{4t}{3}\) must be an integer, which means \(t\) must be a multiple of 3. Let \(t=3\). Then \(\frac{t}{3} = \frac{3}{3} = 1 = s\). In this case, the two sides of the comparison are equal, so Column A = Column B.

Case 2: Let \(s=1\) and \(t=6\). Then \(\frac{t}{3} = \frac{6}{3} = 2 > s\). In this case, Column A > Column B.

Case 3: Let \(s=2\) and \(t=3\). Then \(\frac{t}{3} = \frac{3}{3} = 1 < s\). In this case, Column A < Column B.


Since we found cases where A > B, A < B, and A = B, the relationship cannot be determined.


Step 3: Final Answer:

The relationship cannot be determined from the information given.
Quick Tip: When comparing complex algebraic expressions, try to manipulate the given equation to express one column in terms of the other column's variables. If the resulting comparison still depends on the values of the variables, the answer is (D).

Step 1: Understanding the Concept:

We are given that a point \((x,y)\) is on the unit circle (a circle centered at the origin with radius 1). We need to compare the sum of its coordinates, \(x+y\), with the value 1.01. This requires understanding the range of possible values for \(x+y\).


Step 2: Detailed Explanation:

The value of \(x+y\) changes depending on where the point \((x,y)\) is on the circle. Let's test some points.


Case 1: Consider the point where the circle intersects the positive x-axis. Here, the coordinates are \((1, 0)\).

For this point, \(x+y = 1+0 = 1\).

In this case, Column A (1) is less than Column B (1.01).


Case 2: Consider the point in the first quadrant where \(x=y\).

Substitute \(y=x\) into the circle equation: \(x^2 + x^2 = 1 \implies 2x^2 = 1 \implies x^2 = 1/2 \implies x = 1/\sqrt{2}\).

So the point is \((1/\sqrt{2}, 1/\sqrt{2})\).

For this point, \(x+y = 1/\sqrt{2} + 1/\sqrt{2} = 2/\sqrt{2} = \sqrt{2}\).

The value of \(\sqrt{2}\) is approximately 1.414.

In this case, Column A (\(\approx 1.414\)) is greater than Column B (1.01).


Since we have found one case where Column A is less than Column B, and another case where Column A is greater than Column B, the relationship is not fixed.


Step 3: Final Answer:

The relationship cannot be determined from the information given.
Quick Tip: For problems involving points on a circle, testing key points like the intersections with the axes (\((1,0), (0,1), (-1,0), (0,-1)\)) and the points on the lines \(y=x\) and \(y=-x\) can quickly reveal the range of possible values for expressions like \(x+y\).

Step 1: Understanding the Concept:

This is a ratio problem. We are given the ratio of the parts of a mixture and the actual weight of one of the parts. We need to find the total weight of the mixture.


Step 2: Detailed Explanation:

The ratio of oats : raisins : nuts is 9 : 2 : 1.

This means that for every 9 parts of oats, there are 2 parts of raisins and 1 part of nuts.

The total number of "parts" in the ratio is the sum of the individual parts:

Total parts = \(9 + 2 + 1 = 12\) parts.

We are given that the weight of the nuts is 9.2 pounds. The nuts correspond to the "1" in the ratio.

So, 1 part of the mixture is equal to 9.2 pounds.

We need to find the weight of the total mixture, which is composed of 12 parts.

Total weight = (Total number of parts) \(\times\) (Weight per part)
\[ Total weight = 12 \times 9.2 pounds \]

To calculate this:
\[ 12 \times 9 = 108 \]
\[ 12 \times 0.2 = 2.4 \]
\[ Total weight = 108 + 2.4 = 110.4 pounds \]


Step 3: Final Answer:

The total mixture weighs 110.4 pounds.
Quick Tip: In ratio problems, first find the value of one "part" by using the known quantity. Once you know the value of one part, you can easily find the value of the total or any other component by multiplying.

Step 1: Understanding the Concept:

This is an arithmetic problem that requires careful application of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).


Step 2: Detailed Explanation:

We evaluate the expression step-by-step, starting from the innermost grouping symbols.

The expression is: \(3 - 2[5 - 7(3+2)]\)

1. Innermost Parentheses: First, calculate the sum inside the parentheses.

\[ 3 + 2 = 5 \]

The expression becomes: \(3 - 2[5 - 7(5)]\)

2. Brackets - Multiplication: Next, perform the multiplication inside the square brackets.

\[ 7(5) = 35 \]

The expression becomes: \(3 - 2[5 - 35]\)

3. Brackets - Subtraction: Now, perform the subtraction inside the square brackets.

\[ 5 - 35 = -30 \]

The expression becomes: \(3 - 2[-30]\)

4. Multiplication: Perform the multiplication of -2 and -30.

\[ -2 \times -30 = 60 \]

The expression becomes: \(3 + 60\)

5. Addition: Finally, perform the addition.

\[ 3 + 60 = 63 \]


Step 3: Final Answer:

The value of the expression is 63.
Quick Tip: Be very careful with negative signs, especially when subtracting a negative number, as in the final step: \(3 - (-60)\) becomes \(3 + 60\). This is a common source of errors.

Step 1: Understanding the Concept:

The problem involves factorials, denoted by the exclamation mark (!). We need to simplify a fraction of two factorials.


Step 2: Key Formula or Approach:

The key to simplifying factorial fractions is to expand the larger factorial until you reach the smaller factorial, which will then cancel out.

We can write \(n! = n \times (n-1) \times (n-2) \times \dots \times 1\), which is also equal to \(n \times (n-1)!\).


Step 3: Detailed Explanation:

We need to calculate \(\frac{12!}{10!}\).

Let's expand the numerator, 12!, using the definition:
\[ 12! = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

The denominator is:
\[ 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

We can rewrite 12! as:
\[ 12! = 12 \times 11 \times (10 \times 9 \times \dots \times 1) = 12 \times 11 \times 10! \]

Now substitute this into the fraction:
\[ \frac{12!}{10!} = \frac{12 \times 11 \times 10!}{10!} \]

The \(10!\) terms in the numerator and denominator cancel each other out.
\[ = 12 \times 11 \]
\[ 12 \times 11 = 132 \]


Step 4: Final Answer:

The value of \(\frac{12!}{10!}\) is 132.
Quick Tip: Never try to calculate large factorials fully before simplifying. Always look for cancellations. The expression \(\frac{n!}{k!}\) (for \(n>k\)) simplifies to the product of integers from \(k+1\) up to \(n\).

Step 1: Understanding the Concept:

This is a nested percentage problem. We need to find a percentage of a fraction of another percentage of a total. We can find the final percentage by multiplying the successive proportions.


Step 2: Detailed Explanation:

Let's find the fraction of total visitors who were from southern California by multiplying the given proportions.


Proportion from Pacific/SW states = 76% = 0.76
Proportion of those who were from California = \(\frac{2}{3}\)
Proportion of those Californians from southern California = 87% = 0.87

To find the proportion of total visitors from southern California, we multiply these values together:
\[ Proportion = 0.76 \times \frac{2}{3} \times 0.87 \]

Let's perform the multiplication:
\[ = \frac{76}{100} \times \frac{2}{3} \times \frac{87}{100} \]

We can simplify before multiplying. Notice that 87 is divisible by 3 (\(8+7=15\)).
\[ \frac{87}{3} = 29 \]

So the expression becomes:
\[ = \frac{76}{100} \times 2 \times \frac{29}{100} \]
\[ = \frac{76 \times 2 \times 29}{10000} \]
\[ = \frac{152 \times 29}{10000} \]

Now, calculate \(152 \times 29\):
\[ 152 \times 29 = 152 \times (30 - 1) = (152 \times 30) - 152 = 4560 - 152 = 4408 \]

So the proportion is:
\[ \frac{4408}{10000} = 0.4408 \]

To express this as a percentage, we multiply by 100:
\[ 0.4408 \times 100% = 44.08% \]

The question asks for the approximate percent. The value 44.08% is closest to 45%.


Step 3: Final Answer:

Approximately 45% of the visitors at the resort were from southern California.
Quick Tip: When multiplying decimals and fractions, it's often easier to convert everything to fractions to look for simplifications (like 87/3) or convert everything to decimals and estimate. For example, \(2/3 \approx 0.67\), so the calculation is roughly \(0.76 \times 0.67 \times 0.87\), which you can estimate as \(0.75 \times 0.67 \times 0.87 \approx (3/4) \times (2/3) \times 0.87 = (1/2) \times 0.87 = 0.435\), or 43.5%. This points directly to 45% as the best answer.

Step 1: Understanding the Concept:

The problem states that \(\frac{5^4 - 1}{n}\) is an integer. This means that \(n\) must be a factor (or divisor) of the numerator, \(5^4 - 1\). The question asks which of the given options is NOT a factor of \(5^4 - 1\).


Step 2: Key Formula or Approach:

We will first calculate the value of the numerator. A useful algebraic identity is the difference of squares: \(a^2 - b^2 = (a-b)(a+b)\).


Step 3: Detailed Explanation:

First, let's simplify the numerator, \(5^4 - 1\).

We can write this as \((5^2)^2 - 1^2\).

Using the difference of squares formula:
\[ (5^2)^2 - 1^2 = (5^2 - 1)(5^2 + 1) \]

Now, calculate the terms in the parentheses:
\[ (25 - 1)(25 + 1) = (24)(26) \]

So, the numerator is \(24 \times 26 = 624\).

The problem now is to determine which of the options is not a factor of 624. Let's test each option.


(A) 4: Since \(24 = 4 \times 6\), 4 is a factor of 24, and therefore a factor of 624. (\(624 \div 4 = 156\)).
(B) 6: Since \(24 = 6 \times 4\), 6 is a factor of 24, and therefore a factor of 624. (\(624 \div 6 = 104\)).
(C) 13: Since \(26 = 13 \times 2\), 13 is a factor of 26, and therefore a factor of 624. (\(624 \div 13 = 48\)).
(D) 25: To be divisible by 25, a number must end in 00, 25, 50, or 75. The number 624 ends in 24, so it is not divisible by 25.
(E) 26: From our calculation, \(624 = 24 \times 26\), so 26 is clearly a factor. (\(624 \div 26 = 24\)).


Step 4: Final Answer:

The number 25 is not a factor of 624, so n cannot be 25.
Quick Tip: For "EXCEPT" questions, the process is one of elimination. Test each option against the condition. Using algebraic identities like the difference of squares can make simplifying the initial expression much faster than direct calculation.

Step 1: Understanding the Concept:

The question asks for the ratio of the amounts budgeted for two different categories. Since the amounts are percentages of the same total budget, the ratio of the amounts will be the same as the ratio of their percentages.


Step 2: Detailed Explanation:

1. Find the percentages from the table.

Percent budgeted for Food = 20%.

Percent budgeted for Savings = 15%.


2. Form the ratio of the percentages.

Ratio of Food to Savings = 20 : 15.


3. Simplify the ratio.

To simplify the ratio, we find the greatest common divisor (GCD) of 20 and 15. The GCD is 5.

Divide both parts of the ratio by 5:

\[ \frac{20}{5} : \frac{15}{5} \]

\[ 4 : 3 \]

The simplified ratio is 4 to 3.


Step 3: Final Answer:

The ratio of the amount budgeted for food to the amount budgeted for savings is 4 to 3.
Quick Tip: When finding the ratio of two parts of the same whole, you don't need to calculate the actual values. The ratio of the percentages (or fractions) is sufficient and saves calculation time.

Step 1: Understanding the Concept:

A pie chart represents a whole (100%) as a full circle (360°). To find the central angle for a specific category, we need to calculate that category's percentage of the total 360 degrees.


Step 2: Key Formula or Approach:
\[ Central Angle = (Percentage for Category) \times 360^\circ \]


Step 3: Detailed Explanation:

1. Find the percentage for Savings from the table.

The percentage for Savings is 15%.


2. Calculate the central angle.

We need to find 15% of 360°.

First, convert the percentage to a decimal: 15% = 0.15.

Now, multiply by 360°:

\[ Angle = 0.15 \times 360^\circ \]

We can break this down for easier mental calculation:

10% of 360° is 36°.

5% of 360° is half of 10%, which is 18°.

So, 15% of 360° = 36° + 18° = 54°.

Alternatively, using multiplication:

\[ 0.15 \times 360 = 54 \]


Step 4: Final Answer:

The measure of the central angle for the savings sector would be 54°.
Quick Tip: For pie chart calculations, it's useful to remember that 1% corresponds to 3.6°. You can simply multiply the percentage by 3.6 to find the angle. Here, \(15 \times 3.6 = 54\).

Step 1: Understanding the Concept:

This question requires us to calculate a specific amount of money from a pie chart by taking the given percentage of the total funds for that year.


Step 2: Detailed Explanation:

1. Identify the relevant data for 1992.

From the 1992 pie chart, the percentage for Youth Development is 15%.

The total funds distributed in 1992 were
(2.54 million, which is
)2,540,000.


2. Calculate the amount.

We need to find 15% of
(2,540,000.

Amount = \(0.15 \times 2,540,000\)

Let's perform the multiplication:

\[ 0.15 \times 254 = 38.1 \]

So, \(0.15 \times 2,540,000 = 381,000\).

Alternatively, using mental math:

10% of 2,540,000 is 254,000.

5% of 2,540,000 is half of 10%, which is 127,000.

15% = 10% + 5% = 254,000 + 127,000 =
)381,000.


3. Compare with the options.

The calculated amount,
(381,000, is approximately
)380,000.


Step 3: Final Answer:

The funds distributed for youth development in 1992 were approximately
(380,000.
Quick Tip: When the question asks for an "approximate" value, you can often round the numbers to make the calculation easier. For instance, calculate 15% of
)2.5 million: \(0.15 \times 2.5 = 0.375\) million, which is
(375,000. This value is very close to option (C).

Step 1: Understanding the Concept:

To find the increase in the amount, we must first calculate the amount for "Family Support" in each of the two years, and then find the difference between these two amounts. It is important to note that even though the percentage for this category is the same in both years, the total funds are different, so the amount will change.


Step 2: Detailed Explanation:

1. Calculate the amount for Family Support in 1992.

Percentage = 24%.

Total Funds =
(2.54 million.

Amount (1992) = \(0.24 \times 2,540,000 =
)609,600\).


2. Calculate the amount for Family Support in 1993.

Percentage = 24%.

Total Funds =
(2.93 million.

Amount (1993) = \(0.24 \times 2,930,000 =
)703,200\).


3. Calculate the increase.

Increase = Amount (1993) - Amount (1992).

Increase =
(703,200 -
)609,600 =
(93,600.


4. Compare with the options.

The calculated increase,
)93,600, is closest to
(94,000.


Alternative Calculation Method:

Since the percentage (24%) is the same for both years, the increase in funding for this category is simply 24% of the increase in total funds.

Increase in Total Funds =
)2.93 million -
(2.54 million =
)0.39 million.

Increase for Family Support = 24% of
(0.39 million.

Increase = \(0.24 \times 390,000\).
\(0.24 \times 390,000 = 93,600\).

This confirms the result of
)93,600, which is closest to
(94,000.


Step 3: Final Answer:

The increase in the amount of money for family support was closest to
)94,000.
Quick Tip: When a percentage for a category stays the same but the total changes, you can find the change in the amount for that category by simply taking that percentage of the change in the total. This can be a much faster calculation.