GRE 2025 Model Paper Set 1 Question Paper with Solutions PDF is available for download. The overall test time is about 1 hour and 58 minutes. GRE has total 5 sections:
- Analytical Writing (One "Analyze an Issue" task, Alloted time 30 minutes)
- Verbal Reasoning (Two Sections, with 12 questions and 15 questions respectively)
- Quantitative Reasoning (Two Sections, with 12 questions and 15 questions respectively)
GRE 2025 Model Paper Set 1 Question Paper with Solutions PDF
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\(5y = 15\)
\(x = 2y\)
Column A: \(x\)
Column B: 5
O is the center of the circle and the perimeter of \(\Delta AOB\) is 6. The angle \(\angle AOB\) is \(60^{\circ}\).
Column A: The circumference of the circle
Column B: 12
Ken's monthly take-home pay is \(w\) dollars. After he pays for food and rent, he has \(x\) dollars left.
Column A: \(x\)
Column B: \(w - x\)
Column A: \(\frac{13}{15} + \frac{7}{8} + \frac{3}{4}\)
Column B: 3
\((x - 2y)(x + 2y) = 4\)
Column A: \(x^2 - 4y^2\)
Column B: 8
Column A: \(\frac{0.3}{1.5}\)
Column B: \(\frac{2}{10}\)
The operation \(\diamondsuit\) is defined for all positive numbers \(r\) and \(t\) by \(r \diamondsuit t = \frac{(r-t)^2 + rt}{t}\).
Column A: \(71 \diamondsuit 37\)
Column B: \(37 \diamondsuit 71\)
Column A: \(\frac{BD}{AB}\)
Column B: \(\frac{DC}{BC}\)
Column A: \((250)(492)\)
Column B: \(\frac{492,000}{4}\)
Column A: \(x\)
Column B: \(y\)
Column A: The number of prime numbers between 70 and 76
Column B: The number of prime numbers between 30 and 36
\(6 x 7\)
\(y = 8\)
Column A: \(\frac{x}{y}\)
Column B: 0.85
KLNP is a square with a perimeter of 128.
Column A: MQ
Column B: 42
Column A: \(\frac{2 + 3x}{2}\)
Column B: \(1 + 3x\)
The median salary for professional group A is
(40,610. The median salary for professional group B is
)40,810. :
Column A: The median salary for groups A and B combined
Column B:
(40,710
The water level in a tank is lowered by 6 inches, then raised by \(8\frac{1}{2}\) inches, and then lowered by 4 inches. If the water level was x inches before the changes in level, which of the following represents the water level, in inches, after the changes?
In the figure above, M, N, and P are midpoints of the sides of an equilateral triangle whose perimeter is 18. What is the perimeter of the shaded region?
Which of the following sets of numbers has the greatest standard deviation?
If x, y, and z represent consecutive integers, and x \textless y \textless z, which of the following equals y?
I. \(x+1\)
II. \(\frac{x+z}{2}\)
III. \(\frac{x+y+z}{3}\)
When 9 students took a zoology quiz with a possible score of 0 to 10, inclusive, their average (arithmetic mean) score was 7.5. If a tenth student takes the same quiz, what will be the least possible average score on the quiz for all 10 students?
Question 21:
The two corporate sectors that increased their support for the arts from 1988 to 1991 made a total contribution in 1991 of approximately how many million dollars?
View Solution
Step 1: Understanding the Concept:
We first need to identify which sectors "increased their support". This is ambiguous and could mean an increase in percentage share or an increase in the actual dollar amount. Given the context of the bar chart showing percentages, it most likely refers to the sectors whose percentage contribution increased. We will proceed with this assumption.
Step 2: Identify the Sectors:
Let's compare the percentages for each sector from 1988 to 1991.
- Financial: 20% \(\rightarrow\) 22% (Increase)
- Services: 17% \(\rightarrow\) 8% (Decrease)
- Manufacturing: 31% \(\rightarrow\) 19% (Decrease)
- Retail: 10% \(\rightarrow\) 19% (Increase)
- Wholesale: 6% \(\rightarrow\) 4% (Decrease)
- Other: 20% \(\rightarrow\) 18% (Decrease)
The two sectors that increased their percentage support are Financial and Retail.
Step 3: Calculate the 1991 Contribution:
We need to find the total dollar contribution from these two sectors in 1991. The total support in 1991 was
(520 million.
- Financial contribution in 1991: 22% of
)520 million
\[ 0.22 \times 520 =
(114.4 million \]
- Retail contribution in 1991: 19% of
)520 million
\[ 0.19 \times 520 =
(98.8 million \]
Step 4: Find the Total:
The total contribution from these two sectors in 1991 is the sum of their individual contributions.
\[ Total =
)114.4 million +
(98.8 million =
)213.2 million \]
The question asks for an approximate value. Among typical answer choices,
(213.2 million is closest to
)200 million.
Quick Tip: In data interpretation questions, be precise about which year's total you are using for your percentage calculations. Here, the question asks for the contribution in 1991, so all percentages must be applied to the 1991 total of
(520 million.
How many of the six corporate sectors listed each contributed more than
(60 million to the arts in both 1988 and 1991?
View Solution
Step 1: Understanding the Concept:
We need to calculate the dollar contribution for each of the six sectors in both 1988 and 1991. Then, for each sector, we check if both the 1988 value and the 1991 value are greater than
)60 million.
Step 2: Calculate Dollar Contributions:
Total for 1988 =
(630 million. Total for 1991 =
)520 million.
1. Financial:
- 1988: \(0.20 \times 630 =
(126\) million (\(\textgreater60\))
- 1991: \(0.22 \times 520 =
)114.4\) million (\(\textgreater60\))
- Condition met.
2. Services:
- 1988: \(0.17 \times 630 =
(107.1\) million (\(\textgreater60\))
- 1991: \(0.08 \times 520 =
)41.6\) million (\(\textless60\))
- Condition not met.
3. Manufacturing:
- 1988: \(0.31 \times 630 =
(195.3\) million (\(\textgreater60\))
- 1991: \(0.19 \times 520 =
)98.8\) million (\(\textgreater60\))
- Condition met.
4. Retail:
- 1988: \(0.10 \times 630 =
(63\) million (\(\textgreater60\))
- 1991: \(0.19 \times 520 =
)98.8\) million (\(\textgreater60\))
- Condition met.
5. Wholesale:
- 1988: \(0.06 \times 630 =
(37.8\) million (\(\textless60\))
- Condition not met.
6. Other:
- 1988: \(0.20 \times 630 =
)126\) million (\(\textgreater60\))
- 1991: \(0.18 \times 520 =
(93.6\) million (\(\textgreater60\))
- Condition met.
Step 3: Count the Sectors:
The sectors that meet the condition (contribution \textgreater
)60 million in BOTH years) are:
- Financial
- Manufacturing
- Retail
- Other
There are a total of 4 such sectors.
Quick Tip: When a question requires checking a condition for multiple categories, create a systematic table or list to track your calculations and avoid missing a case or miscounting.
Approximately how many million dollars more did the wholesale sector contribute to the arts in 1988 than in 1991?
View Solution
Step 1: Understanding the Concept:
This question asks for the difference in the dollar amount of contributions from the wholesale sector between the two years. We need to calculate the contribution for each year and then subtract.
Step 2: Calculate Contribution for Each Year:
- Contribution in 1988: The wholesale sector contributed 6% of the total
(630 million.
\[ Amount_{1988} = 0.06 \times 630 =
)37.8 million \]
- Contribution in 1991: The wholesale sector contributed 4% of the total
(520 million.
\[ Amount_{1991} = 0.04 \times 520 =
)20.8 million \]
Step 3: Calculate the Difference:
The question asks how much more was contributed in 1988 than in 1991.
\[ Difference = Amount_{1988} - Amount_{1991} \] \[ Difference =
(37.8 -
)20.8 =
(17.0 million \]
Step 4: Final Answer:
The difference is
)17.0 million. The closest given answer choice is typically 16.5, which accounts for the word "approximately".
Quick Tip: Be careful to distinguish between a change in percentage points and a change in dollar amounts. A decrease in percentage does not automatically mean a decrease in dollars if the total amount changes, and vice-versa. Always calculate the actual values unless the question specifies otherwise.
From 1988 to 1991, which corporate sector decreased its support for the arts by the greatest dollar amount?
View Solution
Step 1: Understanding the Concept:
We need to find the dollar amount of decrease for every sector that saw a decrease, and then identify the largest of these decreases. A decrease occurs if the 1988 contribution is greater than the 1991 contribution.
Step 2: Calculate the Dollar Decrease for Each Sector:
We can reuse the dollar amounts calculated for question 22.
- Financial:
(126M (88) \(\rightarrow\)
)114.4M (91). Decrease = \(126 - 114.4 =
(11.6\)M.
- Services:
)107.1M (88) \(\rightarrow\)
(41.6M (91). Decrease = \(107.1 - 41.6 =
)65.5\)M.
- Manufacturing:
(195.3M (88) \(\rightarrow\)
)98.8M (91). Decrease = \(195.3 - 98.8 =
(96.5\)M.
- Retail:
)63M (88) \(\rightarrow\)
(98.8M (91). This is an increase, so we ignore it.
- Wholesale:
)37.8M (88) \(\rightarrow\)
(20.8M (91). Decrease = \(37.8 - 20.8 =
)17.0\)M.
- Other:
(126M (88) \(\rightarrow\)
)93.6M (91). Decrease = \(126 - 93.6 =
(32.4\)M.
Step 3: Compare the Decreases:
The calculated decreases are:
- Financial:
)11.6M
- Services:
(65.5M
- Manufacturing:
)96.5M
- Wholesale:
(17.0M
- Other:
)32.4M
The greatest value among these is
(96.5M.
Step 4: Final Answer:
The Manufacturing sector had the greatest dollar amount decrease in support.
Quick Tip: For questions asking for the "greatest" or "least" change, it's often useful to estimate before calculating. The Manufacturing sector started with the highest percentage (31%) of a large total and dropped significantly to 19% of a smaller total, making it a strong candidate for the largest drop.
Of the retail sector's 1991 contribution to the arts, \(\frac{1}{4}\) went to symphony orchestras and \(\frac{1}{2}\) of the remainder went to public television. Approximately how many million dollars more did the retail sector contribute to public television that year than to symphony orchestras?
View Solution
Step 1: Understanding the Concept:
This is a multi-step problem. We must first find the total contribution from the retail sector in 1991, then calculate the amounts for the two specific causes, and finally find the difference between them.
Step 2: Detailed Calculations:
1. Total Retail Contribution in 1991:
The retail sector contributed 19% of the 1991 total of
(520 million.
\[ Total Retail = 0.19 \times 520 =
)98.8 million \]
2. Contribution to Symphony Orchestras:
This was \(\frac{1}{4}\) of the total retail contribution.
\[ Symphony = \frac{1}{4} \times 98.8 =
(24.7 million \]
3. Calculate the Remainder:
The amount remaining after the symphony contribution is:
\[ Remainder = Total Retail - Symphony = 98.8 - 24.7 =
)74.1 million \]
Alternatively, if \(\frac{1}{4}\) was given away, \(\frac{3}{4}\) remains: \(\frac{3}{4} \times 98.8 =
(74.1\) million.
4. Contribution to Public Television:
This was \(\frac{1}{2}\) of the remainder.
\[ Public TV = \frac{1}{2} \times 74.1 =
)37.05 million \]
5. Find the Difference:
The question asks how much more was given to public television than to symphony orchestras.
\[ Difference = Public TV - Symphony \] \[ Difference = 37.05 - 24.7 =
(12.35 million \]
Step 3: Final Answer:
The difference is
)12.35 million. The closest approximate answer choice would be 13.0.
Quick Tip: Be very careful with wording like "of the remainder". This indicates a two-step calculation where the second percentage or fraction is applied to a new, smaller base amount, not the original total.
If \(x = a^3\) and \(y = a^7\), where \(a \neq 0\), which of the following is equivalent to \(a^{13}\)?
The probabilities that each of two independent experiments will have a successful outcome are \(\frac{8}{15}\) and \(\frac{2}{3}\), respectively. What is the probability that both experiments will have successful outcomes?
If x is 1, 2, or 3 and y is either 2 or 4, then the product xy can have how many different possible values?
If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?
Workers at Companies X and Y are paid the same base hourly rate. Workers at company X are paid 1.5 times the base hourly rate for each hour worked per week in excess of the first 37, while workers at Company Y are paid 1.5 times the base hourly rate for each hour worked per week in excess of the first 40. In a given week, how many hours must a Company X worker work in order to receive the same pay as a company Y worker who works 46 hours?
As businesses become aware that their advertising must ------ the everyday concerns of consumers, their commercials will be characterized by a greater degree of ------.
Because the lawyer's methods were found to be ------, the disciplinary committee ------ his privileges.
People of intelligence and achievement can nonetheless be so ------ and lacking in ------ that they gamble their reputations by breaking the law to further their own ends.
A number of scientists have published articles ------ global warming, stating ------ that there is no solid scientific evidence to support the theory that the Earth is warming because of increases in greenhouse gases.
The senator's attempt to convince the public that she is not interested in running for a second term is as ------ as her opponent's attempt to disguise his intention to run against her.
MacCrory's conversation was ------: she could never tell a story, chiefly because she always forgot it, and she was never guilty of a witticism, unless by accident.
Despite its many ------, the whole-language philosophy of teaching reading continues to gain ------ among educators.
CENSUS : POPULATION::
AUTHENTICITY : FRAUDULENT::
VARNISH : GLOSSY::
AMENITY : COMFORTABLE::
PAIN : ANALGESIC::
VOICE : SHOUT::
PONTIFICATE : SPEAK::
BIBLIOPHILE : BOOKS::
INDIGENT : WEALTH::
Eight times within the past million years, something in the Earth’s climatic equation has changed. allowing snow in the mountains and the northern Line latitudes to accumulate from one season to the next instead of melting away. Each time, the enormous ice sheets resulting from this continual buildup lasted tens of thousands of years until the end of each particular glacial cycle brought a warmer climate. Scientists speculated that these glacial cycles were ultimately driven by astronomical factors: slow, cyclic changes in the eccentricity of the Earth’s orbit and in the tilt and orientation of its spin axis. But up until around 30 years ago, the lack of an independent record of ice- age timing made the hypothesis untestable.
Then in the early 1950’s Emiliani produced the first complete record of the waxings and wanings of past glaciations. It came from a seemingly odd place. the seafloor. Single-cell marine organisms called "foraminifera" house themselves in shells made from calcium carbonate. When the foraminifera die. sink to the bottom, and become part of seafloor sedi- ments, the carbonate of their shells preserves certain characteristics of the seawater they inhabited. In particular, the ratio of a heavy, isotope of oxygen (oxygen-18) to ordinary oxygen (oxygen- 16) in the carbonate preserves the ratio of the two oxygens in water molecules.
It is now understood that the ratio of oxygen iso- topes in seawater closely reflects the proportion of the world’s water locked up in glaciers and ice sheets. A kind of meteorological distillation accounts for the link. Water molecules containing the heavier isotope tend to condense and fall as precipitation slightly sooner than molecules containing the lighter isotope. Hence, as water vapor evaporated from warm oceans moves away from its source. its oxygen -18 returns more quickly to the oceans than does its oxygen-16. What falls as snow on distant ice sheets and mountain glaciers is relatively depleted of oxygen -18. As the oxygen-18-poor ice builds up the oceans become relatively enriched in the Isotope. The larger the ice sheets grow, the higher the proportion of oxygen-18 becomes in seawater- and hence in the sediments.
Analyzing cores drilled from seafloor sediments, Emiliani found that the isotopic ratio rose and fell in rough accord with the Earth’s astronomical cycles. Since that pioneering observation, oxygen-isotope measurements have been made on hundreds of cores. A chronology for the combined record enables scientists to show that the record contains the very same periodicities as the orbital processes. Over the past 800,000 years, the global ice volume has peaked every 100,000 years, matching the period of the orbital eccentricity variation. In addition, “wrinkles” superposed on each cycle –small decreases or surges in ice volume – have come at intervals of roughly 23,000 and 41,000 years, in keeping with the pre- cession and tilt frequencies of the Earth’s spin axis.
Question 47:
Which of the following best expresses the main idea of the passage?
View Solution
Step 1: Understanding the Concept:
This question asks for the main idea, which should summarize the entire passage from the initial problem to the final conclusion.
Step 2: Detailed Explanation:
The passage begins by introducing the hypothesis that astronomical factors drive glacial cycles (lines 8-12). It notes this was initially "untestable" (line 14). It then describes how a record from "the seafloor" (line 18) provided the necessary data. Finally, it concludes that the data from this record "rose and fell in rough accord with the Earth's astronomical cycles" (lines 45-47), and a "chronology for the combined record enables scientists to show that the record contains the very same periodicities as the orbital processes" (lines 49-51).
- (A) This statement correctly summarizes the entire argument: the source of evidence (marine sediments) was used to confirm the hypothesis (astronomical cycles drive glacial cycles).
- (B) This is a crucial detail explaining how the evidence works, but it is not the overall main idea. It is the mechanism, not the final conclusion.
- (C) This is a supporting detail about the source of the data. It's an interesting fact but not the central argument of the passage.
- (D) This is true, but (A) is more complete because it mentions the specific evidence (marine sediments) and the specific impact (glacial cycles) that are the focus of the passage.
- (E) This is a specific detail mentioned in the introduction, not the main point of the entire passage.
Step 3: Final Answer:
Option (A) provides the most comprehensive summary of the passage's argument and conclusion.
Quick Tip: A good main idea answer should connect the beginning of the passage (the problem or hypothesis) with the end (the solution or conclusion). Avoid answers that focus only on a single paragraph or detail.
The passage asserts that one reason that oceans become enriched in oxygen-18 as ice sheets grow is because
View Solution
Step 1: Understanding the Concept:
This is a detail question that asks for the specific cause of a phenomenon described in the passage. We must locate the relevant lines and identify the reason given.
Step 2: Detailed Explanation:
The third paragraph explains the "meteorological distillation" that links ice volume to the ocean's oxygen isotope ratio. Lines 32-34 state: "Water molecules containing the heavier isotope tend to condense and fall as precipitation slightly sooner than molecules containing the lighter isotope." This process means that as water vapor travels from the oceans to the poles, the heavier oxygen-18 is rained out first, leaving the vapor (and the eventual snow that forms the ice sheets) poor in oxygen-18. This, in turn, leaves the ocean from which the vapor came relatively enriched in oxygen-18.
- (A) This is a direct paraphrase of the reason given in the passage (lines 32-34).
- (B) This is true, but it is the result of the process described in (A), not the root cause itself.
- (C), (D), and (E) are not mentioned in the passage as reasons for the enrichment.
Step 3: Final Answer:
The passage explicitly states that the earlier precipitation of heavier water molecules is the reason for the isotopic separation.
Quick Tip: For questions that ask "why" or "because," scan the passage for keywords from the question (like "enriched in oxygen-18") and look for causal language like "accounts for," "because," "hence," or a description of a process.
According to the passage, the large ice sheets typical of glacial cycles are most directly caused by
View Solution
Step 1: Understanding the Concept:
This is a detail question asking for the direct cause of ice sheet formation as described in the passage.
Step 2: Detailed Explanation:
The first paragraph explicitly describes the formation of ice sheets. Lines 1-6 state: "...something in the Earth's climatic equation has changed, allowing snow in the mountains and the northern latitudes to accumulate from one season to the next instead of melting away. Each time, the enormous ice sheets resulting from this continual buildup..." This clearly identifies the failure of snow to melt as the direct cause.
- (A), (B), (C), (D) describe related climatic factors, but the passage points specifically to the net accumulation of snow year after year. For example, precipitation (D) could increase, but if it all melts in the summer, no ice sheet forms. The key is that the snow doesn't melt away.
- (E) This is a direct paraphrase of the mechanism described in the first paragraph.
Step 3: Final Answer:
The passage identifies the continual accumulation of snow due to incomplete summer melting as the direct cause of ice sheet growth.
Quick Tip: Look for the most direct and specific cause mentioned in the text. While other options might be contributing factors in a broader sense, the question asks what the passage identifies as the direct cause.
It can be inferred from the passage that which of the following is true of the water locked in glaciers and ice sheets today?
The discussion of the oxygen-isotope ratios in paragraph three of the passage suggests that which of the following must be assumed if the conclusions described in lines 49-58 are to be validly drawn?
The passage suggests that the scientists who first constructed a coherent, continuous picture of past variations in marine-sediment isotope ratios did which of the following?
The passage suggests that the scientists mentioned in line 8 considered their reconstruction of past astronomical cycles to be
View Solution
Step 1: Understanding the Concept:
This question asks about the attitude of the early scientists (mentioned in line 8) towards their own theory about astronomical cycles, before the seafloor evidence was available.
Step 2: Detailed Explanation:
The passage states that scientists "speculated that these glacial cycles were ultimately driven by astronomical factors" (lines 8-10). It immediately follows this with a key statement: "But up until around 30 years ago, the lack of an independent record of ice-age timing made the hypothesis untestable" (lines 12-14). This implies a specific situation: the scientists had one part of the equation (the astronomical cycles, their "reconstruction") but were missing the other part (a detailed timeline of the ice ages). Their astronomical model was good enough to form a hypothesis, but they needed the ice-age data to test it.
- (A) The passage does not suggest their astronomical reconstruction was considered unreliable. The problem was a lack of data on ice ages.
- (B) This option accurately describes the situation. The astronomical reconstruction was considered adequate for the hypothesis, but it couldn't be tested without a record of the glacial cycles ("a record of the latter").
- (C) The passage indicates they needed an independent record of ice-age timing, not of the astronomical phenomena themselves.
- (D) The reconstruction was not "unusable"; it was the basis of a hypothesis that was simply "untestable" at the time.
- (E) This is incorrect. The passage explicitly states the hypothesis was "untestable," so it could not be considered conclusive.
Step 3: Final Answer:
The scientists had a solid theory about astronomical cycles but couldn't apply it to explain the ice ages until a reliable record of the ice ages themselves became available.
Quick Tip: Understanding the scientific method is key to many reading comprehension passages. A hypothesis is a proposed explanation that can be tested. The passage describes a situation where a hypothesis existed but was "untestable" due to a lack of data on one side of the equation.
Although Victor Turner’s writings have proved fruitful for fields beyond anthropology, his definition of ritual is overly restrictive. Ritual, he says, is “pre- list scribed formal behavior for occasions not given over to technological routine, having reference to beliefs in mystical beings or powers”, “ Technological routine” refers to the means by which a social group provides for its material needs. Turner’s differentiating ritual from technology helps us recognize that festivals and celebrations may have little purpose other than play, but it obscures the practical aims, such as making crops grow or healing patients, of other rituals.
Further, Turner’s definition implies a necessary relationship between ritual and mystical beliefs. However, not all rituals are religious; some religions have no reference to mystical beings; and individuals may be required only to participate in, not necessarily believe in, a ritual. Turner's assumption that ritual behavior follows belief thus limits the usefulness of his definition in studying ritual across cultures.
Question 54:
According to the passage, which of the following does Turner exclude from his conception of ritual?
The passage suggests that an assumption underlying Turner's definition of ritual is that
It can be inferred that the author of the passage believes each of the following concerning rituals EXCEPT:
Which of the following best describes the organization of the passage?
SLOUCH:
CLAIM:
EXPEDITE:
VALEDICTION:
FACTORABLE
CONVOKE:
REND:
CONTRAVENE:
NADIR:
ABSTRACT:
MENDACIOUS:
The painter Peter Brandon never dated his works, and their chronology is only now beginning to take shape in the critical literature. A recent dating of a Brandon self-portrait to 1930 is surely wrong. Brandon was 63 years old in 1930, yet the painting shows a young, dark-haired man-obviously Brandon, but clearly not a man of 63.
Which of the following, if justifiably assumed, allows the conclusion to be properly drawn?
Dance critic from Europe: The improved quality of ballet in the United States is the result of more Europeans' teaching ballet in the United States than ever before. I know the proportion of teachers who were born and trained in Europe has gone up among ballet teachers in the United States, because last year, on my trip to New York, more of the ballet teachers I met were from Europe-born and trained there than ever before.
Which of the following identifies a questionable assumption made by the dance critic's reasoning?
Which of the following can be a complete and accurate list of the contents of one of the packages?
If the first two packages contain exactly two games each, then the third package must contain exactly
If one of the packages contains exactly three jigsaw puzzles and none of the packages contains more than three novels, which of the following must be true?
If the first two packages contain exactly two jigsaw puzzles each, which of the following can be a complete and accurate list of the contents of the third package?
If each of the packages contains at least one game, then it must be true that one of the package contains exactly
If each of the packages contains a different number of novels from the others, which of the following can be true?
Mayor: Four years ago when we reorganized the city police department in order to save money, critics claimed that the reorganization would make the police less responsive to citizens and would thus lead to more crime. The police have compiled theft statistics from the years following the reorganization that show that the critics were wrong. There was an overall decrease in reports of thefts of all kinds, including small thefts.
Which of the following, if true, most seriously challenges the mayor's argument?
It takes a particular talent to be a successful business manager. Business courses can help people to solve management problems, but such courses can do so only for those people with managerial talent. Such people should take business courses to acquire ideas that they can subsequently use to good advantage if management problems happen to arise.
If the statements above are true, which of the following must also be true on the basis of them?
When a driver is suspected of having had too much to drink, testing the driver's ability to walk a straight line gives a more reliable indication of fitness to drive than does testing the driver's blood-alcohol level.
Which of the following, if true, best supports the claim made in the statement above?
That sales can be increased by the presence of sunlight within a store has been shown by the experience of the only Savefast department store with a large skylight. The skylight allows sunlight into half of the store, reducing the need for artificial light. The rest of the store uses only artificial light. Since the store opened two years ago, the departments on the sunlit side have had substantially higher sales than the other departments.
Which of the following, if true, most strengthens the argument?
Which of the following is an acceptable sequence of topics discussed, in order from first through sixth?
If exactly one topic is discussed between faith and love, that topic could be
View Solution
Step 1: Understanding the Concept:
This is a conditional question. We must add the new condition "F-X-L" or "L-X-F" to our existing rules and determine what X could be.
Step 2: Detailed Explanation:
1. The new condition requires a block of F-X-L or L-X-F.
2. Since F is discussed, Rule 3 must apply: we must have the MFS block.
3. In the MFS block, the topic immediately following F is S.
4. To satisfy the condition that exactly one topic is between F and L, that topic must be the one adjacent to F in the required block. In the MFS block, S is the topic adjacent to F.
5. Therefore, the sequence of topics must contain the larger block M-F-S-L. The topic (X) between F and L is S (skepticism).
6. We can confirm this is possible by constructing a full valid sequence. We have the 4-topic block M-F-S-L. We also know T must be discussed adjacent to L (Rule 2), giving us the 5-topic block M-F-S-L-T. To satisfy Rule 4, R or K must be first. A valid sequence is: R, M, F, S, L, T. In this sequence, the topic between F and L is indeed S.
Step 3: Final Answer:
Given the requirement of the MFS block, the only topic that can be immediately after F (and thus between F and L) is skepticism.
Quick Tip: In logic games, look for how new conditions interact with existing block rules (like the MFS block). The new information often forces a larger, more defined block to form, which can solve the question.
If neither faith nor madness is discussed and if revolution is discussed fourth, then skepticism must be discussed
If revolution and utopia are the first two topics discussed, the two topics not discussed could be
If knowledge is not discussed, the other topic not discussed could be
Which of the following can be the order, from position 1 through position 8, of the stones set around the bracelet?
If the turquoise is set in position 8, which of the following must be true?
Which of the following is a position in which the zircon can be set?
If the malachite is set in position 5, which of the following can be true?
If the turquoise is set in position 2, which of the following can be true?
To protect beachfront buildings from ocean storms, ocean resorts have built massive seawalls between beaches and the buildings. Not only do the seawalls block off some buildings' ocean view, but the beaches themselves become ever narrower, because sand can no longer creep inland as storms erode it at the water's edge.
If the information is correct, which of the following conclusions is most strongly supported on the basis of it?
A study found that 70 percent of children surveyed in 1970 had at one time had cavities, whereas only 50 percent of those surveyed in 1985 had ever had cavities. The researchers concluded that the level of dental disease in children had declined between 1970 and 1985.
Which of the following, if true, would most seriously undermine the researchers' conclusion presented above?
David: Since attempting to preserve every species that is currently endangered is prohibitively expensive, the endangered species whose value to humanity is the greatest should be accorded the highest priority for preservation.
Karen: Such a policy would be unsound because it is impossible to predict the future value of a species, nor is it always possible to assess the present value of species whose contributions to humanity, though significant, are indirect.
Which of the following is the main point of Karen's reply to David?
\(x=y=z\)
Column A: \(x^3\)
Column B: \(xyz\)
\(x \textless 0\)
Column A: \(3x^2\)
Column B: \(3x^3\)
PS = SR
Column A: \(x\)
Column B: \(y\)
Column A: \(\frac{24}{23} + \frac{101}{100}\)
Column B: 2
The points P(2,0), Q(0,2), R(4,2) and S(2,4) are in the rectangular coordinate system. :
Column A: The distance from P to Q
Column B: The distance from R to S
The probability that events E and F will both occur is 0.42. The probability that event E will occur is 0.58.
Column A: The probability that event F will occur
Column B: 0.58
Column A: a
Column B: b
Column A: \((1+\sqrt{2})^2\)
Column B: 3
Column A: (109)(87-14)
Column B: (109)(87)-(109)(14)
Carol's age, in years, can be expressed by reversing the digits in her father's age, in years. The sum of the digits in each age is 10.
Column A: The positive difference between Carol's age, in years, and her father's age, in years
Column B: 36
\(0 \textless p \textless 1\)
Column A: \(p^4 - p^6\)
Column B: \(p^3 - p^5\)
\(3 - 2x^2 - [-x(1+2x)] = -5\)
Column A: x
Column B: -8
a and b are positive integers.
Column A: \(\frac{a}{b}\)
Column B: \(\frac{a+3}{b+3}\)
A solid cubical block of wood has dimensions as shown in the figure (3ft side), and the block is to be cut in half as indicated by the shaded region.
Column A: The total surface area of one of the resulting halves of the block
Column B: 36 square feet
The lengths of the line segments are a, b, and ab, respectively. The line segments are drawn to scale.
Column A: a
Column B: 1
The average (arithmetic mean) number of students in 3 economics classes at a certain college is 24. If the total number of students in 2 of the classes combined is 38, how many students are in the remaining class?
If the cube of n is 180 greater than the square of n, then n =
The circular clock above shows a time of exactly 3:30. What is the value of x?
What percent of the integers between 200 and 999, inclusive, end with the digits "03"?
Which of the lines in the figure above contains only points (x,y) with x = y?
The ratio of the number of male freshmen to the number of female sophomores is approximately
View Solution
Step 1: Understanding the Concept:
This question asks for an approximate ratio between two values found in the "DISTRIBUTION OF ENROLLMENT" table.
Step 2: Detailed Explanation:
1. Find the required values from the table.
- Number of male freshmen: Look at the row for "Freshmen" and the column for "Males". The value is 303.
- Number of female sophomores: Look at the row for "Sophomores" and the column for "Females". The value is 109.
2. Form the ratio and approximate.
- The ratio is 303 to 109, or \(\frac{303}{109}\).
- To approximate this, we can round the numbers. 303 is very close to 300, and 109 is very close to 100.
- The ratio is approximately \(\frac{300}{100} = 3\).
- This corresponds to a ratio of 3 to 1.
- For a more precise check, \(303 \div 109 \approx 2.78\). This value is much closer to 3 than to 2, 1.5, 4, or 1.67.
Step 3: Final Answer:
The ratio is approximately 3 to 1.
Quick Tip: When a question asks for an "approximate" ratio, round the numbers to values that are easy to divide. This is usually sufficient to identify the correct multiple-choice option.
How many of the enrolled students are not majoring in humanities, social sciences, or physical sciences?
View Solution
Step 1: Understanding the Concept:
This question requires us to use the second table ("PERCENT OF TOTAL ENROLLMENT") to find the number of students who fall outside the listed categories. These could be students with undeclared majors or majors in other fields not listed.
Step 2: Detailed Explanation:
1. Find the total percentage of students in the listed majors.
- Humanities: 33%
- Social Sciences: 30%
- Physical Sciences: 24%
- Total percentage in these majors = \(33% + 30% + 24% = 87%\).
2. Find the percentage of students NOT in these majors.
- The total of all students is 100%.
- Percentage not in these majors = \(100% - 87% = 13%\).
3. Calculate the number of students corresponding to this percentage.
- The total enrollment is given as 1,400 students.
- Number of students not in these majors = 13% of 1,400.
\[ 0.13 \times 1400 = 13 \times \frac{1400}{100} = 13 \times 14 \]
\[ 13 \times 14 = 13 \times (10 + 4) = 130 + 52 = 182 \]
Step 3: Final Answer:
There are 182 students who are not majoring in one of the three listed academic areas.
Quick Tip: When working with percentages from a table that don't add up to 100%, the remaining percentage represents the "other" or "unlisted" category. Calculate this remaining percentage first before applying it to the total.
Which of the following can be inferred from the tables?
I. The number of males majoring in physical sciences is greater than the number of females majoring in that area.
II. Students majoring in either social sciences or physical sciences constitute more than 50 percent of the total enrollment.
III. The ratio of the number of males to the number of females in the senior class is less than 2 to 1.
How many students are either juniors or males or both?
View Solution
Step 1: Understanding the Concept:
This question asks for the total number of individuals in the union of two sets: the set of juniors and the set of males. We must be careful not to double-count the individuals who are in both sets (male juniors).
Step 2: Key Formula or Approach:
The principle of inclusion-exclusion for two sets states: \[ |A \cup B| = |A| + |B| - |A \cap B| \]
Here, Set A = Juniors, and Set B = Males.
Alternatively, we can add the total number of males to the number of juniors who are not male (i.e., female juniors).
Step 3: Detailed Explanation:
Method 1: Using Inclusion-Exclusion
1. Find the total number of juniors.
- From the table: Male Juniors = 182, Female Juniors = 88.
- Total Juniors = \(182 + 88 = 270\).
2. Find the total number of males.
- From the table's total row: Total Males = 860.
3. Find the number of students who are both male and junior (the intersection).
- From the table: Male Juniors = 182.
4. Apply the formula.
- Number of (Juniors or Males) = (Total Juniors) + (Total Males) - (Male Juniors)
- Number = \(270 + 860 - 182\)
- Number = \(1130 - 182 = 948\)
Method 2: Direct Addition
The group "juniors or males" consists of two distinct groups: (1) all males, and (2) all juniors who are not male (i.e., female juniors).
Total number of males (this includes all male freshmen, sophomores, juniors, and seniors): 860
Number of female juniors: 88
Total = \(860 + 88 = 948\)
Step 4: Final Answer:
There are 948 students who are either juniors or males or both.
Quick Tip: For "A or B or both" questions with overlapping categories, using the direct addition method (Count all of A, then add the part of B that is NOT in A) can be faster and less prone to error than the formal inclusion-exclusion formula.
If the total enrollment is 12 percent greater than it was five years ago, what was the total enrollment five years ago?
View Solution
Step 1: Understanding the Concept:
This is a reverse percentage problem. We are given the final value after a percentage increase (the current enrollment) and asked to find the original value (the enrollment five years ago).
Step 2: Key Formula or Approach:
Let \(E_0\) be the enrollment five years ago (the original value). The current enrollment, \(E_c\), is 12% greater. The relationship can be expressed with the formula: \[ E_c = E_0 + (0.12 \times E_0) = E_0 \times (1 + 0.12) = 1.12 \times E_0 \]
To find the original enrollment, we rearrange the formula: \(E_0 = E_c / 1.12\).
Step 3: Detailed Explanation:
1. Identify the given values.
- The current enrollment, \(E_c\), is 1,400 (from the information provided for the data interpretation questions).
- The percentage increase is 12%, or 0.12.
2. Set up the equation.
- Using the formula, we have: \(1400 = 1.12 \times E_0\).
3. Solve for the original enrollment, \(E_0\).
- To isolate \(E_0\), we divide both sides by 1.12.
\[ E_0 = \frac{1400}{1.12} \]
- To make the division easier, remove the decimal by multiplying the numerator and denominator by 100:
\[ E_0 = \frac{140000}{112} \]
- Simplify the fraction. We can see both are divisible by 14: \(112 = 14 \times 8\) and \(140000 = 14 \times 10000\).
\[ E_0 = \frac{10000}{8} \]
- Perform the final division:
\[ E_0 = 1250 \]
Step 4: Final Answer:
The total enrollment five years ago was 1,250.
Quick Tip: A common mistake in reverse percentage problems is to subtract 12% of the new amount (e.g., 12% of 1400). This is incorrect because the percentage increase was calculated based on the smaller, original number. Always set up the algebraic equation \( Original \times (1 + percent increase) = Final \) and solve for the "Original" value.
If the ratio of the number of English books to the number of all other books on a bookshelf is 4 to 1, what percent of the books on the bookshelf are English books?
3, 7, 9, 14, x
The numbers in the list above are ordered from least to greatest. If the average (arithmetic mean) is 2 greater than the median, what is the value of x?
A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If \(\frac{1}{9}\) of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?
If \(\frac{a}{b} = \frac{3}{2}\), which of the following must be true?
I. \(\frac{b}{a} = \frac{2}{3}\)
II. \(\frac{a-b}{a} = \frac{1}{3}\)
III. \(a+b = 5\)
What is the least integer value of n such that \(\frac{1}{2^n} \textless 0.001\)?
That she was ------ rock climbing did not diminish her ------ to join her friends on a rock-climbing expedition.
Data concerning the effects on a small population of high concentrations of a potentially hazardous chemical are frequently used to ------ the effects on a large population of lower amounts of the same chemical.
Conceptually, it is hard to reconcile a defense attorney's ------ to ensure that false testimony is not knowingly put forward with the attorney's mandate to mount the most ------ defense conceivable for the client.
The term "modern"has always been used broadly by historians, and recent reports indicate that its meaning has become more ------ than ever.
He would ------ no argument, and to this end he enjoined us to ------.
Originally, most intellectual criticism of mass culture was ------ in character, being based on the assumption that the wider the appeal, the more ------ the product.
Surprisingly, given the dearth of rain that fell on the corn crop, the yield of the harvest was ------ ; consequently, the corn reserves of the country have not been ------.
REPELLENT: ATTRACT::
ANARCHIST: GOVERNMENT::
ADMONISH: DENOUNCE::
JOKE: PUNCH LINE::
VEER: DIRECTION::
REPROBATE: MISBEHAVE::
IMPERVIOUS: PENETRATE::
CONSENSUS: FACTIONALISM::
MARTINET: DISCIPLINE::
The passage is primarily concerned with discussing which of the following?
The passage suggests that lightning bolts typically
View Solution
Step 1: Understanding the Concept:
This question asks what the passage suggests is a necessary precondition for lightning to occur. We need to find the statement that describes the state of a cloud that is ready to produce lightning.
Step 2: Detailed Explanation:
The passage states in lines 3-6: "Such transfers [lightning] require that electrically neutral clouds, with uniform charge distributions, become electrified by separation of charges into distinct regions." The next sentence adds, "The greater this separation is, the greater the voltage... of the cloud." This directly implies that lightning originates from clouds where charges have been separated and are therefore no longer uniformly distributed. A uniform distribution is characteristic of a neutral, inactive cloud. An electrified cloud, ready to produce lightning, has a non-uniform distribution.
- (A) The positive dipole is produced by the charge separation process; it is the cause of the lightning, not a product of it.
- (B), (C), and (D) describe specific details of the precipitation hypothesis, but they are not presented as universally true for all lightning. For instance, (D) is the opposite of what the hypothesis suggests (the upper regions are filled with positively charged droplets).
- (E) This is a direct restatement of the fundamental condition required for electrification mentioned at the very beginning of the passage. A non-uniform distribution is another way of saying there has been a "separation of charges into distinct regions."
Step 3: Final Answer:
The passage states that for lightning to occur, charges within a cloud must be separated, meaning they are not uniformly distributed.
Quick Tip: In science passages, distinguish between foundational principles and specific, competing theories. The correct answer to a general question is more likely to be found in the statement of the basic principle than in the details of one particular hypothesis.
According to the passage, Benjamin Franklin contributed to the scientific study of lightning by
Which of the following, if true, would most seriously undermine the precipitation hypothesis, as it is set forth in the passage?
Which of the following best expresses the main idea of the passage?
It can be inferred from the passage that the teams mentioned in line 19 were most interested in which of the following aspects of the land in the western United States?
The author of the passage claims that which of the following is the primary reason why Gilpin generally avoided extreme close-ups of natural subjects?
The passage suggests that a photographer who practiced the heroic style would be most likely to emphasize which of the following in a photographic series focusing on the Rio Grande?
It can be inferred from the passage that the first two generations of landscape photographers in the western United States had which of the following in common?
Based on the description of her works in the passage, which of the following would most likely be a subject for a photograph taken by Gilpin?
The author of the passage mentions women writers in line 50 most likely in order to
FICTITIOUS:
BRIDLED:
CAPTIVATE:
DISSIPATE:
OSTRACIZE:
LOATH:
VITIATE:
LAVISH:
VITUPERATIVE:
MORIBUND:
CATHOLIC:
Which of the following can be the schedule for the six experiments?
Any of the following experiments can be performed in August EXCEPT
If T is performed in September, which of the following must be true?
If R is performed in the same month as Z, which of the following can be the pair of experiments performed in October?
If T is performed in the month before Z is performed, which of the following is a pair of experiments that can be performed in the same month as each other?
If P is performed in the same month as Y, which of the following must be true?
If X is performed in the month before Y is performed, which of the following must be true?
Roger: Reading a lot as a child causes nearsightedness-difficulty seeing things at a distance.
Louise: I disagree. Any correlation between nearsightedness and reading results from the fact that children who have trouble seeing things at a distance are likeliest to prefer those activities, such as reading, that involve looking at things close up.
Louise disputes Roger's claim by
Years ago, consumers in Frieland began paying an energy tax in the form of two Frieland pennies for each unit of energy consumed that came from nonrenewable sources. Following the introduction of this energy tax, there was a steady reduction in the total yearly consumption of energy from nonrenewable sources.
If the statements in the passage are true, then which of the following must on the basis of them be true?
If O sits at the same table as K, which of the following must sit at the same table as each other?
Which of the following can sit at a table with L and R?
If N sits at the same table as S, which of the following can be true?
Each of the following is a pair of people who can sit at the same table as each other EXCEPT
If O and S are the only people sitting at one of the tables, which of the following can be the group of people sitting at one of the other two tables?
Despite a dramatic increase in the number of people riding bicycles for recreation in Parkville, a recent report by the Parkville Department of Transportation shows that the number of accidents involving bicycles has decreased for the third consecutive year.
Which of the following, if true during the last three years, best reconciles the apparent discrepancy in the facts above?
Do strong electric currents, by means of the electromagnetic fields that accompany them, cause cancer in people who live and work nearby? Telephone line workers, who work near such currents every day, can provide a test case. They show elevated levels of brain cancer, therefore, the hypothesis of electromagnetic causation is supported. Which of the following if true, most seriously weakens the argument?
Any of the following is an acceptable pathway for a document to be sent from S to M, listing all lines used in order from the line first used to the line last used, EXCEPT
Which of the following is a complete and accurate list of the lines any one of which could be the second line used by a document sent from T to G?
If line 3 cannot be used, a document to be sent from T to H that uses as few tube lines as possible must use line
A pathway from M to H that includes as many tube lines as possible must include lines
Which of the following could be the pairs of skaters who skate in each set, from set 1 through set 4?
If Gloria skates with Toby in set 1, which of the following must be true?
If Heidi skates in set 1 and Toby skates in set 2, which of the following must be true?
Neither the Sami nor the Kephrian delegations attended the international conference. Beforehand, the delegations of Daqua and Kephria, allies whose governments had grievances against Tessia, officially announced that one or both of the two would stay away if the Tessian delegation attended the conference. In response, the Sami delegation officially announced that it would definitely attend if both the Daquan and Kephrian delegations stayed away.
If the statements given are all true and all the delegations adhered to their official announcements, it must also be true that the
On turning 65 years old, everyone living in the town of Malton becomes eligible to receive a card that guarantees discounts. Census records for 1990 show that 2,450 inhabitants of Malton turned 64 in that year. Yet, in 1991 over 3,000 people applied for and properly received discount cards. So clearly some of Malton's population growth between 1990 and 1992 must be attributable to migration into the city by people in their mid-60's.
Which of the following is an assumption on which the argument depends?
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