GRE 2025 Model Paper Set 3 Question Paper with Solutions PDF

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Updated on, Oct 14, 2025

byShivam Yadav

GRE 2025 Model Paper Set 3 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 3 Question Paper with Solutions PDF

GRE 2025 Model Paper Set 3 Question Paper with Solutions PDF download iconDownload Check Solutions
GRE 2025 Model Paper Set 3 Question Paper with Solutions PDF

Question 1:


Column A & Column B
\(2(8-7)\) & \(2(7-8)\)

 


Question 2:

\(x+y=2\).

Column A & Column B
\(x\) & \(y\)

 


Question 3:


Column A & Column B
\(\frac{3}{7} + \frac{2}{7}\) & \(1\)


 


Question 4:




Column A & Column B
\(x\) & \(5\)

 


Question 5:


On Elm Street, there are 6 houses on one side of the street and 4 houses on the other. Each pair of houses on Elm Street is connected by exactly one telephone line.


Column A & Column B

The total number of such lines that connect houses on opposite sides of Elm Street & 12


 


Question 6:




Column A} & Column B

The area of triangular region OPQ & The area of triangular region ORS


 


Question 7:

Column A} & Column B
\((0.01)(0.07)(70)\) & \(0.49\)


 


Question 8:

\(x < y < z\)

Column A & Column B
\(\frac{x+y+z}{3}\) & \(z\)


 


Question 9:




The three small rectangles have the same dimensions
Column A} & Column B
\(\frac{PS}{RS}\) & \(\frac{1}{2}\)


 


Question 10:


In a certain city, 20\(^\circ\)F was the average (arithmetic mean) of the low temperatures of \(x^\circ\)F, 25\(^\circ\)F, and 37\(^\circ\)F on three consecutive days.

Column A} & Column B
\(x\) & \(0\)

 


Question 11:

\(m = 4x+4y\) , \(x \neq -y\)

Column A} & Column B}
\(\frac{2m}{x+y}\) & \(8\)


 


Question 12:




ABCD is a rectangle with diagonals AC and DB.

Column A} & Column B}
\(r+u+v\) & \(r+u+w\)

 


Question 13:

\(n\) is a positive integer.

Column A} & Column B}
\(n^{100}\) & \(100^n\)

 


Question 14:

\(f(t) = kt\) for all \(t\), where \(k\) is a constant, and \(f(3) = \frac{1}{2}\).

Column A} & Column B}
\(k\) & \(f(1)\)

 


Question 15:

\(100x < y\)
\(1000x < 2y\)

Column A} & Column B}
\(1,100x\) & \(y\)


 


Question 16:

Mr. Gifford wishes to put 372 eggs into cartons that can hold 12 eggs each. If he has 50 empty cartons and completely fills as many of them as possible with the 327 eggs, how many of the cartons will remain empty?

  • (A) 12
  • (B) 15
  • (C) 19
  • (D) 28
  • (E) 31

Question 17:

Which of the following numbers is greatest?

  • (A) -0.225
  • (B) -0.0225
  • (C) -0.323
  • (D) -0.0325
  • (E) -0.3205

Question 18:

If a certain automobile gets between 20 and 24 miles per gallon of gasoline, inclusive, what would be the maximum amount of gasoline, in gallons, this automobile would consume on a trip of 360 miles?

  • (A) 20.0
  • (B) 18.0
  • (C) 16.4
  • (D) 16.0
  • (E) 15.0

Question 19:

If \(y - x = 2\) and \(y - z = 3\), which of the following best represents the relative positions of x, y, and z on the number line? (Note: The figures are drawn to scale.)



Question 20:

Two beads are to be independently and randomly selected, one from each of two bags. If \(\frac{2}{7}\) of the beads in one bag and \(\frac{3}{7}\) of the beads in the other bag are yellow, what is the probability that both beads selected will be yellow?

  • (A) \(\frac{2}{3}\)
  • (B) \(\frac{5}{7}\)
  • (C) \(\frac{6}{7}\)
  • (D) \(\frac{5}{49}\)
  • (E) \(\frac{6}{49}\)

Question 21:

By what percent did the number of personal computers sold by Compaq increase from 1992 to 1993?

  • (A) 50%
  • (B) 65%
  • (C) 75%
  • (D) 100%
  • (E) 110%

Question 22:

In 1992, Packard Bell accounted for what percent of the computers sold by the four companies listed?

  • (A) 6%
  • (B) 9%
  • (C) 10%
  • (D) 12%
  • (E) 14%

Question 23:

If the ratio of the number of personal computers sold by IBM, Compaq, and Tandy (not shown) in 1993 was 6 to 4 to 1, respectively, approximately how many personal computers were sold by Tandy in 1993?

  • (A) 350,000
  • (B) 400,000
  • (C) 450,000
  • (D) 500,000
  • (E) 550,000

Question 24:

For the categories given, which category accounts for approximately \(\frac{1}{4}\) of the total number of graduates expected for each of the years shown?

  • (A) High school diploma
  • (B) Associate degree
  • (C) Bachelor's degree
  • (D) Master's degree
  • (E) Doctoral degree

Question 25:

The number of associate degrees expected to be granted in 2001 is most nearly what percent greater than the number of associate degrees expected to be granted in 1995?

  • (A) 2%
  • (B) 3%
  • (C) 5%
  • (D) 7%
  • (E) 9%

Question 26:




If the area of the shaded region of the square above is 20, what is the perimeter of the square?

  • (A) \(4\sqrt{5}\)
  • (B) \(8\sqrt{5}\)
  • (C) \(16\sqrt{5}\)
  • (D) 80
  • (E) 400

Question 27:

If \(x = \frac{1}{y}\) and \(y = \frac{1}{1-x}\), then y=

  • (A) 2
  • (B) \(\frac{1}{2}\)
  • (C) \(-\frac{1}{2}\)
  • (D) -1
  • (E) -2

Question 28:

If 720 is the product of the consecutive integers beginning with 2 and ending with n, what is the value of n-1?

  • (A) 5
  • (B) 6
  • (C) 8
  • (D) 11
  • (E) 23

Question 29:

When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium. It was decided to have two performances. if the total number of tickets sold was equal to the total number who attended and if the auditorium was \(\frac{2}{3}\) full for each of the two performances, what is the seating capacity of the auditorium?

  • (A) 100
  • (B) 200
  • (C) 225
  • (D) 300
  • (E) 450

Question 30:

If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including 1 and n?

  • (A) 3
  • (B) 5
  • (C) 6
  • (D) 7
  • (E) 8

Question 31:

Though ---- to some degree, telling a small lie sometimes enables one to avoid --- another's feelings.

  • (A) necessary.. mollifying
  • (B) regrettable.. harming
  • (C) unfortunate.. exaggerating
  • (D) attractive.. considering
  • (E) difficult.. resisting

Question 32:

Perhaps because scientists have been so intrigued by dogs' superior senses of smell and hearing, researchers have long --- their eyesight, assuming that they inhabit a drab, black-and-white world, devoid of color.

  • (A) studied
  • (B) coveted
  • (C) appreciated
  • (D) resented
  • (E) underestimated

Question 33:

Despite a string of dismal earnings reports, the two-year-old strategy to return the company to profitability is beginning to ----.

  • (A) falter
  • (B) disappoint
  • (C) compete
  • (D) work
  • (E) circulate

Question 34:

The President reached a decision only after lengthy ----, painstakingly weighing the ---- opinions expressed by cabinet members.

  • (A) deliberation.. divergent
  • (B) confrontation.. unanimous
  • (C) relegation.. consistent
  • (D) speculation.. conciliatory
  • (E) canvassing.. arbitrary

Question 35:

Although just barely ---- as a writer of lucid prose, Jones was an extremely ---- editor who worked superbly with other writers in helping them improve the clarity of their writing.

  • (A) deficient.. muddling
  • (B) proficient.. contentious
  • (C) adequate.. capable
  • (D) appalling.. competent
  • (E) engaging.. inept

Question 36:

The accusations we bring against others should be ---- ourselves; they should not ---- complacency and easy judgments on our part concerning our own moral conduct.

  • (A) definitions of.. produce
  • (B) instructions to.. equate
  • (C) denigrations of.. exclude
  • (D) warnings to.. justify
  • (E) parodies of.. satirize

Question 37:

Although the meanings of words may necessarily be liable to change, it does not follow that the lexicographer is therefore unable to render spelling, in a great measure, ----.

  • (A) arbitrary
  • (B) superfluous
  • (C) interesting
  • (D) flexible
  • (E) constant

Question 38:

ELEGIAC: SORROW::

  • (A) polemical: resolution
  • (B) fictional: humor
  • (C) devotional: reverence
  • (D) didactic: inspiration
  • (E) literary: emotion

Question 39:

ROSTRUM: ORATOR::

  • (A) stage: audience
  • (B) bench: judge
  • (C) shelf: clerk
  • (D) municipality: citizen
    (E) crosswalk: pedestrian

Question 40:

MISUNDERSTOOD: CLARIFY::

  • (A) fanatical: espouse
  • (B) popular: renounce
  • (C) fantastic: shock
  • (D) erroneous: retract
  • (E) conspicuous: flaunt

Question 41:

REFINERY: PETROLEUM::

  • (A) mill: grain
  • (B) mine: ore
  • (C) warehouse: merchandise
  • (D) generator: electricity
    (E) forest: lumber

Question 42:

TEDIOUS: ENERGY::

  • (A) avaricious: satisfaction
  • (B) fractious: irritation
  • (C) disturbing: composure
  • (D) improbable: ambition
    (E) informed: intelligence

Question 43:

GRACEFUL: MOVEMENT::

  • (A) euphonious: sound
  • (B) forbidding: countenance
  • (C) ephemeral: duration
  • (D) melodramatic: emotion
    (E) vibrant: color

Question 44:

BRAVURA: PERFORMANCE::

  • (A) extravagant: expenditure
  • (B) elaborate: oration
  • (C) foreseeable: outcome
  • (D) thorough: analysis
    (E) resplendent: appearance

Question 45:

BADGER: BOTHER::

  • (A) persecute: injure
  • (B) haunt: remember
  • (C) belabor: mention
  • (D) quibble: argue
    (E) censure: evaluate

Question 46:

CONGRUENT: DIMENSIONS::

  • (A) convenient: time
  • (B) coordinate: axis
  • (C) conglomerate: parts
  • (D) coincident: chance
    (E) coeval: age

Question 47:

The author of the passage is primarily concerned with

  • (A) revealing a commonly ignored deficiency
  • (B) proposing a return to traditional terminology
  • (C) describing an attempt to correct a shortcoming
  • (D) assessing the success of a new pedagogical approach
  • (E) predicting a change in a traditional teaching strategy

Question 48:

It can be inferred that the author of the passage expects that the experience of the student mentioned as having studied Wife in the Right would have which of the following effects?

  • (A) It would lead the student to disregard information found in the Bibliotheca Britannica.
  • (B) It would teach the student to question the accuracy of certain kinds of information sources when studying neglected authors.
  • (C) It would teach the student to avoid the use of reference sources in studying neglected authors.
  • (D) It would help the student to understand the importance of first editions in establishing the authorship of plays.
  • (E) It would enhance the student's appreciation of the works of authors not included in the canon.

Question 49:

The author of the passage suggests that which of the following is a disadvantage of the strategy employed in the experimental scholarly methods course?

  • (A) Students were not given an opportunity to study women writers outside the canon.
  • (B) Students' original work would not be appreciated by recognized scholars.
  • (C) Little scholarly work has been done on the work of Elizabeth Griffith.
    (D) Most of the students in the course had had little opportunity to study eighteenth-century literature.
    (E) Students were not given an opportunity to encounter certain sources of information that could prove useful in their future studies.

Question 50:

Which of the following best states the "particular pedagogical purpose" mentioned in line 28?

  • (A) To assist scholars in revising the canon of authors
  • (B) To minimize the trivial aspects of the traditional scholarly methods course
  • (C) To provide students with information about Griffith's work
    (D) To encourage scholarly rigor in students' own research
    (E) To reestablish Griffith's reputation as an author

Question 51:

Which of the following best describes the function of the last paragraph in relation to the passage as a whole?

  • (A) It summarizes the benefits that students can derive from the experimental scholarly methods course.
  • (B) It provides additional reasons why Griffith's work raises issues having to do with the canon of authors.
  • (C) It provides an illustration of the immediate nature of the experiences students can derive from the experimental scholarly methods course.
  • (D) It contrasts the experience of a student in the experimental scholarly methods course with the experience of a student in the traditional course
  • (E) It provides information that emphasizes the suitability of Griffith's work for inclusion in the canon of authors.

Question 52:

It can be inferred that which of the following is most likely to be among the "issues" mentioned in line 38?

  • (A) Why has the work of Griffith, a woman writer who was popular in her own century, been excluded from the canon?
  • (B) In what ways did Griffith's work reflect the political climate of the eighteenth century?
  • (C) How was Griffith's work received by literary critics during the eighteenth century?
  • (D) How did the error in the title of Griffith's play come to be made?
  • (E) How did critical reception of Griffith's work affect the quantity and quality of that work?

Question 53:

It can be inferred that the author of the passage considers traditional scholarly methods courses to be

  • (A) irrelevant to the work of most students
  • (B) inconsequential because of their narrow focus
  • (C) unconcerned about the accuracy of reference sources
  • (D) too superficial to establish important facts about authors
  • (E) too wide-ranging to approximate genuine scholarly activity

Question 54:

According to the passage, the size of a male cycad cone directly influences which of the following?

  • (A) The arrangement of the male cone's structural elements
  • (B) The mechanism by which pollen is released from the male cone.
  • (C) The degree to which the ovules of female cycads are accessible to airborne pollen
  • (D) The male cone's attractiveness to potential insect pollinators
  • (E) The amount of pollen produced by the male cone

Question 55:

The passage suggests that which of the following is true of the structure of cycad cones?

  • (A) The structure of cycad cones provides conclusive evidence in favor of one particular explanation of cycad pollination.
  • (B) The structure of cycad cones provides evidence concerning what triggers the first step in the pollination process.
  • (C) An irresolvable discrepancy exists between what the structure of most male cycad cones suggests about cycad pollination and what the structure of most female cones suggests about that process.
  • (D) The structure of male cycad cones rules out a possible mechanism for cycad pollination that is suggested by the structure of most female cycad cones.
  • (E) The structure of male cycad cones is consistent with a certain means of cycad pollination, but that means is inconsistent with the structure of most female cycad cones.

Question 56:

The evidence in favor of insect pollination of cycads presented in lines 2-4 would be more convincing if which of the following were also true?

  • (A) Only a small variety of cycad species can be successfully transplanted.
  • (B) Cycads can sometimes be pollinated by means other than wind or insects.
  • (C) Insects indigenous to regions to which cycads are transplanted sometimes feed on cycads.
  • (D) Winds in the areas to which cycads are usually transplanted are similar to winds in cycads' native habitats.
  • (E) The transplantation of cycads from one region to another usually involves the accidental removal and introduction of insects as well.

Question 57:

The passage suggests that which of the following is true of scientific investigations of cycad pollination?

  • (A) They have not yet produced any systematic evidence of wind pollination in cycads.
  • (B) They have so far confirmed anecdotal reports concerning the wind pollination of cycads.
  • (C) They have, until recently, produced little evidence in favor of insect pollination in cycads.
  • (D) They have primarily been carried out using cycads transplanted from their native habitats.
    (E) They have usually concentrated on describing the physical characteristics of the cycad reproductive system.

Question 58:

PROCRASTINATION:

  • (A) diligence
  • (B) complacence
  • (C) reasonableness
  • (D) allegiance
  • (E) rehabilitation

Question 59:

CIRCUITY:

  • (A) straightforwardness
  • (B) inventiveness
  • (C) authenticity
  • (D) insightfulness
  • (E) practicality

Question 60:

CONCLUDE:

  • (A) foster
  • (B) frequent
  • (C) emanate from
  • (D) empower to
    (E) embark on

Question 61:

RITE:

  • (A) coherent interpretation
  • (B) improvised act
  • (C) deductive approach
  • (D) casual observation
    (E) unnecessary addition

Question 62:

BLATANT:

  • (A) indecisive
  • (B) perceptive
  • (C) unobtrusive
  • (D) involuntary
    (E) spontaneous

Question 63:

PONTIFICATE:

  • (A) request rudely
  • (B) glance furtively
  • (C) behave predictably
  • (D) work efficiently
    (E) speak modestly

Question 64:

POSIT:

  • (A) deceive
  • (B) begrudge
  • (C) deny
  • (D) consent
    (E) reinforce

Question 65:

FETTER:

  • (A) justify
  • (B) comfort
  • (C) intrude
  • (D) liberate
  • (E) optimize

Question 66:

SYNERGIC:

  • (A) natural in origin
  • (B) fragile in structure
  • (C) untainted
  • (D) inessential
  • (E) antagonistic

Question 67:

DEPRIVATION:

  • (A) sanity
  • (B) awareness
  • (C) surfeit
  • (D) fecundity
  • (E) health

Question 68:

CORPOREAL:

  • (A) unreliable
  • (B) unscientific
  • (C) indistinguishable
  • (D) inanimate
  • (E) immaterial

Question 69:

Armtech, a temporary-employment agency, previously gave its employees 2.5 paid vacation days after each 700 hours worked. Armtech's new policy is to give its employees 5.0 paid vacation days after each 1,200 hours worked. Therefore, this new policy is more generous to Armtech employees in giving them more vacation days per hour worked than the old policy did.

Which of the following is an assumption on which the argument depends?

  • (A) Most current Armtech employees approve of the company's new vacation policy.
  • (B) A few Armtech employees leave the company before having worked 700 hours.
  • (C) Most Armtech employees were not aware that the company planned to change its vacation policy until after it had already done so.
  • (D) A significant portion of Armtech employees stay with the company long enough to work for 1,200 hours.
  • (E) Armtech's new vacation policy closely matches the vacation policies of competing temporary employment agencies.

Question 70:

The global population of frogs has declined in recent years while the amount of ultraviolet radiation reaching the Earth has increased. Since the genetic material in frog eggs is harmed when exposed to ultraviolet radiation, and since the eggs themselves are not protected by shells or leathery coverings but are gelatinous, the frog population decline is probably due, at least in part, to the ultraviolet radiation increase.

Which of the following, if true, provides the strongest support for the argument?

  • (A) Even in those regions where there has been no significant increase in ultraviolet radiation, only a small proportion of the frog eggs that are laid ever hatch.
  • (B) In areas where there has been the least decline in frog populations, populations of species of insects that frogs eat have decreased.
  • (C) The eggs of frog species whose populations are declining tend to have higher concentrations of damaging pesticides than do the eggs of frog species whose populations have not declined.
  • (D) In many places where turtles, which lay eggs with tough, leathery coverings, share habitats with frogs, turtle populations are also in decline.
  • (E) Populations of frog species that hide their eggs beneath rocks or under sand have declined considerably less than have populations of frog species that do not cover their eggs.

Question 71:

Which of the following lists the patients in an order in which their scheduled appointments can occur, from appointment 1 through appointment 5 ?

  • (A) J, K, N, L, M
  • (B) J, M, N, K, L
  • (C) K, J, N, M, L
  • (D) L, J, K, N, M
  • (E) L, J, N, M, K

Question 72:

If J is scheduled for appointment 2, which of the following can be true?

  • (A) K is scheduled for appointment 3.
  • (B) K is scheduled for appointment 4.
  • (C) L is scheduled for appointment 4.
  • (D) L is scheduled for appointment 5.
  • (E) M is scheduled for appointment 1.

Question 73:

If L is scheduled for appointment 5, which of the following must be true?

  • (A) J is scheduled for appointment 1.
  • (B) J is scheduled for appointment 2.
  • (C) J is scheduled for appointment 4.
  • (D) K is scheduled for appointment 4.
  • (E) N is scheduled for appointment 5.

Question 74:

Which of the following is a complete and accurate list of patients any one of whom can be the patient scheduled for appointment 2?

  • (A) K
  • (B) J, K
  • (C) J, M
  • (D) J, K, L
  • (E) K, L, M

Question 75:

If M is scheduled for appointment 5, which of the following can be true of the scheduling?

  • (A) J's appointment is appointment 1.
  • (B) N's appointment is appointment 1.
  • (C) J's appointment is earlier than K's appointment.
  • (D) K's appointment is earlier than L's appointment.
  • (E) N's appointment is earlier than L's appointment.

Question 76:

If K's appointment is scheduled for a time later than N's appointment, which of the following must be true?

  • (A) J is scheduled for appointment 4.
  • (B) K is scheduled for appointment 5.
  • (C) L is scheduled for appointment 1.
  • (D) M is scheduled for appointment 4.
  • (E) N is scheduled for appointment 2.

Question 77:

Which of the following, if true about the years 1990 through 1992, most helps to explain the data illustrated in the graph?

  • (A) Most of the people arrested for and convicted of drunken driving were repeat offenders.
  • (B) Many of the people arrested for and convicted of drunken driving participated in alcohol-education programs in order to reduce their jail sentences.
  • (C) Juries in drunken driving cases became increasingly reluctant to convict people on whom mandatory jail sentences would be imposed.
  • (D) Since the law was enacted, the number of deaths attributed to drunken driving has declined significantly.
  • (E) The majority of the residents of the country supported the strict law to deter people from drunken driving.

Question 78:

Which of the following, if true, strengthens the claim that the changes in the ratio of arrests to convictions since the beginning of 1990 are due to an increase in the number of people arrested for drunken driving who were not drunk?

  • (A) Before 1990 only people driving erratically were stopped by the police on suspicion of drunken driving, but since the beginning of 1990 police have been allowed to stop drivers randomly and to arrest any driver whom they suspect of having drunk any alcohol.
  • (B) Since the beginning of 1990 new technology has enabled police who stop a driver to establish immediately whether the driver is drunk, whereas before 1990 police had to rely on observations of a driver's behavior to make a judgment about that driver's drunkenness.
  • (C) After 1990 the number of police officers assigned to patrol for drunken drivers increased only very slightly compared to the number of police officers assigned to patrol for drunken drivers in the years 1985 through 1989.
  • (D) In 1990 a greater number of drivers were ignorant of the laws concerning drunken driving than were ignorant of the drunken driving laws in 1989.
  • (E) After 1990 teenagers and young adults constituted a greater proportion of those arrested for drunken driving than in the years 1985 through 1989.

Question 79:

To improve productivity, manufacturing companies have recently begun restructuring work to produce more goods with fewer assembly-line workers, and the companies have laid off many workers as a consequence. The workers laid off have been those with the least seniority (time on the job), generally the younger workers.

The statements above, if true, most strongly support which of the following as a conclusion?

  • (A) The products manufactured by the companies are not undergoing design changes while the manufacturing jobs are being restructured.
  • (B) When assembly-line workers have made suggestions for improvements in manufacturing processes, some suggestions have been implemented, but many have not.
  • (C) Assembly-line workers now need increased reading and mathematical skills to do their jobs.
  • (D) Some of the innovations in assembly-line processes and procedures that were made to increase productivity have instead proved to be counterproductive.
  • (E) The manufacturing companies are increasing the average age of their assembly-line workforce while still seeking to increase production.

Question 80:

During the nineteenth century, Britain's urban population increased as its rural population diminished. A historian theorizes that, rather than industrialization's being the cause, this change resulted from a series of migrations to urban areas, each occasioned by a depression in the agrarian economy. To test this hypothesis, the historian will compare economic data with population census data.

The historian's hypothesis would be most strongly supported if which of the following were found to be true?

  • (A) The periods of greatest growth in the industrial economy were associated with a relatively rapid decline in the rural population.
  • (B) The periods of greatest weakness in the agrarian economy were associated with relatively slow growth in the population as a whole.
  • (C) Periods when the agrarian economy was comparatively strong and the industrial economy comparatively weak were associated with a particularly rapid decline in the rural population.
  • (D) Periods when the agrarian and industrial economies were both strong were associated with particularly rapid growth in the urban population.
  • (E) The periods of greatest strength in the agrarian economy were associated with relatively slow growth in the urban population.

Question 81:

Which of the following can be the schedule of employees staffing the booth on the three days?

Monday | Tuesday | Wednesday

  • (A) Feng,Gómez | Feng,Gómez | Feng,Hull
  • (B) Feng,Gómez | Feng,Hull | Gómez,Hull
  • (C) Feng,Hull | Feng,Gómez | Gómez,Hull
  • (D) Gómez,Hull | Feng,Gómez | Gómez,Hull
  • (E) Gómez,Hull | Feng,Gómez | Feng,Hull

Question 82:

If Gómez staffs the booth on Monday and Tuesday, which of the following must be true?

  • (A) Feng staffs the booth on Monday.
  • (B) Feng staffs the booth on Tuesday.
  • (C) Feng staffs the booth on Wednesday.
  • (D) Hull staffs the booth on Monday.
  • (E) Hull staffs the booth on Tuesday.

Question 83:

If Hull staffs the booth on Monday and Wednesday, which of the following must be true?

  • (A) Feng and Gómez staff the booth on Tuesday.
  • (B) Feng and Hull staff the booth on Monday.
  • (C) Feng and Hull staff the booth on Tuesday.
  • (D) Gómez and Hull staff the booth on Tuesday.
  • (E) Gómez and Hull staff the booth on Wednesday.

Question 84:

If Hull staffs the booth on only one of the days, which of the following can be true?

  • (A) Feng and Hull staff the booth on Monday.
  • (B) Feng and Hull staff the booth on Wednesday.
  • (C) Gómez and Hull staff the booth on Monday.
  • (D) Gómez and Hull staff the booth on Tuesday.
  • (E) Gómez and Hull staff the booth on Wednesday.

Question 85:

Which of the following could be the projects assigned to the two classes?

\begin{tabular}{l l} Class 1 & Class 2 \end{tabular}

  • (A) R, V, X, Y & S, T, Z
  • (B) S, T, V, Z & R, X, Y
  • (C) S, T, X, Y & R, V, Z
  • (D) S, T, X, Z & R, V, Y
  • (E) S, V, X, Y & R, T, Z

Question 86:

If X is assigned to Class 2, which of the following must be true?

  • (A) R is assigned to Class 1.
  • (B) S is assigned to Class 2.
  • (C) T is assigned to Class 2.
  • (D) Y is assigned to Class 1.
  • (E) Z is assigned to Class 2.

Question 87:

If Z is assigned to Class 2, which of the following must be true?

  • (A) S is assigned to Class 2.
  • (B) T is assigned to Class 2.
  • (C) V is assigned to Class 1.
  • (D) X is assigned to Class 1.
  • (E) Y is assigned to Class 2.

Question 88:

If Y is assigned to Class 2, any of the following could be assigned together to one of the classes EXCEPT

  • (A) R and T
  • (B) S and T
  • (C) S and Y
  • (D) T and Z
  • (E) X and Z

Question 89:

If T is assigned to the same class as V, which of the following must be assigned to the same class as each other?

  • (A) R and T
  • (B) S and X
  • (C) S and Y
  • (D) X and Y
  • (E) Y and Z

Question 90:

If V is assigned to a different class from Z, which of the following must be true?

  • (A) S is assigned to Class 1.
  • (B) S is assigned to Class 2.
  • (C) T is assigned to Class 2.
  • (D) V is assigned to Class 2.
  • (E) X is assigned to Class 1.

Question 91:

Politician: Each year, small businesses create more jobs than do large established businesses. Therefore, in order to reduce unemployment in the long term, we should provide incentives for starting small businesses rather than for expanding established large businesses.

Which of the following, if true, casts the most doubt on the politician's argument?

  • (A) In general, people employed by small businesses report higher job satisfaction than do people employed by large businesses.
  • (B) Among the currently unemployed are many people with sufficient job skills to perform the jobs that small businesses would create.
  • (C) Providing an effective incentive for starting a business generally costs significantly less than providing an effective incentive for expanding a large business.
  • (D) A high proportion of small businesses fail within three years of starting because of their owners' inexperience.
  • (E) The average large business contributes more money to politicians' campaign funds than the average small business does.

Question 92:

In the workplace, influenza is typically spread by infected individuals to others with whom they work in close quarters. A new medication that suppresses the symptoms of influenza therefore will actually increase the number of influenza cases, because this medication will allow people who would otherwise be home in bed to return to work while infected.

Which of the following, if true, most seriously challenges the prediction?

  • (A) Coughing, a symptom of influenza that the new medication suppresses, is a primary mechanism in the spread of this illness.
  • (B) Some medications that are used to suppress symptoms of influenza are also used by many people to treat symptoms that are caused not by influenza but by other illnesses.
  • (C) Many workers who now remain at home when infected with influenza do so because the symptoms of influenza prevent them from performing their jobs effectively.
  • (D) Most adults who are immunized against influenza in order to avoid being infected are over 65 years old and retired and thus do not work outside the home.
  • (E) Symptoms of an illness are often the body's means of curing itself of the illness, and therefore suppression of symptoms can prolong the illness that causes them.

Question 93:

Editorial: Critics of nuclear power complain about the allegedly serious harm that might result from continued operation of existing nuclear power plants. But such concerns do not justify closing these plants; after all, their operation has caused no more harm than that caused by pollution generated by coal-and oil-burning power plants, the most important other sources of energy.

Which of the following is an assumption on which the argument depends?

  • (A) Existing nuclear power plants should be closed only if it can be conclusively demonstrated that their continued operation is likely to cause harm more serious than the harm their operation has already caused.
  • (B) Closing existing nuclear power plants would require greatly increased reliance on coal-and oil-burning power plants.
  • (C) The harm that has resulted from operation of existing coal-and oil-burning power plants has been significant.
  • (D) The harm that a nuclear power plant is likely to cause as it continues to operate can be reliably predicted from the past history of nuclear power plants.
  • (E) The only harm that has resulted from operation of existing coal-and oil-burning power plants has resulted from the pollution generated by these plants.

Question 94:

If U is displayed in gallery 2, which of the following must be true?

  • (A) P is displayed in gallery 1.
  • (B) R is displayed in gallery 2.
  • (C) S is displayed in gallery 1.
  • (D) T is displayed in gallery 2.
  • (E) W is displayed in gallery 1.

Question 95:

If S is displayed in gallery 2, the other two statues displayed in gallery 2 can be

  • (A) P and Q
  • (B) P and T
  • (C) Q and T
  • (D) T and W
  • (E) U and W

Question 96:

If P is displayed in gallery 1 and W is displayed in gallery 2, then the display in gallery 1 can include any of the following pairs of statues EXCEPT

  • (A) Q and R
  • (B) Q and T
  • (C) Q and U
  • (D) R and U
  • (E) S and T

Question 97:

If P and Q are displayed in gallery 1, which of the following is a statue that must also be displayed in gallery 1?

  • (A) R
  • (B) S
  • (C) T
  • (D) U
  • (E) W

Question 98:

If S is displayed in gallery 1, which of the following must be true?

  • (A) P is displayed in gallery 1.
  • (B) Q is displayed in gallery 1.
  • (C) R and U are displayed in the same gallery as each other.
  • (D) P and Q are not displayed in the same gallery as each other.
  • (E) Q and R are not displayed in the same gallery as each other.

Question 99:

If T is displayed in gallery 2, which of the following is a pair of statues that CANNOT be displayed in the same gallery as each other?

  • (A) P and S
  • (B) Q and R
  • (C) Q and W
  • (D) R and U
  • (E) T and W

Question 100:

If Q is displayed in the same gallery as S. Which of the following must be true?

  • (A) P is displayed in gallery 1.
  • (B) R is displayed in gallery 2.
  • (C) Q and S are displayed in gallery 2.
  • (D) P is displayed in the same gallery as W.
  • (E) R is displayed in the same gallery as U.

Question 101:

Drug manufacturer: Although our company requires that patients who use our new drug also purchase from us nonreusable kits for weekly blood testing, the expense of those kits is an entirely necessary one: weekly blood testing must be done to monitor the drug's potential side effects, which can be very dangerous.

Which of the following, if true, most seriously weakens the manufacturer's argument?

  • (A) The expense of purchasing the blood-test kits has not prevented any patients from obtaining them or the drug.
  • (B) Medical laboratories can perform the blood testing at a lower cost to patients or their insurers than the price the manufacturer charges for the kits.
  • (C) A one-year supply of the drug and the weekly blood-test kits can cost patients or their insurers over
    (10,000.
  • (D) Most government and other health insurance programs will not reimburse patients for the full cost of both the drug and the blood-test kits.
  • (E) Patients who suffer one or more of the dangerous side effects of the drug can incur heavy expenses for the treatment of those side effects.

Question 102:

Virginia and her brother William disagree over when their father was born: Virginia claims it was in 1935 and William claims it was in 1933. The hospital where their father was born has no records for 1933 but has complete records for 1935--records that do not include a birth record for their father. Therefore, he must have been born in 1933.

The argument depends on which of the following assumptions?

  • (A) Either Virginia's claim or William's claim is correct.
  • (B) The records of the hospital where their father was born date back to 1933.
  • (C) Virginia and William know the day and the month of their father's birth.
  • (D) There are urgent practical reasons why Virginia and William must know the date of their father's birth.
  • (E) None of their other relatives knows the year in which Virginia and William's father was born.

Question 103:

RESULTS OF TWO SURVEYS OF OPINIONS REGARDING THE EFFECTS OF SCIENCE ON HUMAN SOCIETY

A table shows survey responses for August 1991 and August 1992.

- Mostly beneficial: 25% (1991) \(\rightarrow\) 81% (1992)

- Equally harmful and beneficial: 37% (1991) \(\rightarrow\) 9% (1992)

- Mostly harmful: 20% (1991) \(\rightarrow\) 7% (1992)

- No opinion: 18% (1991) \(\rightarrow\) 3% (1992)

Which of the following, if true, contributes most to explaining the shift in opinions about the effects of science on human society?

  • (A) The surveys questioned people who regularly watch prime-time television, and an innovative weekly prime-time television series called "Wonders of Science" had been steadily winning viewers since its widely seen premiere in January 1992.
  • (B) The surveys questioned college-educated adults, and a report called "The State of the Nation's Schools," published in June 1992, noted an increase in students' interest in science courses since 1982.
  • (C) The surveys were conducted in a suburban shopping area near a company that ceased operation in April 1992 as a result of lawsuits arising from unexpected toxic effects of the company's products.
  • (D) Both survey forms were mailed to equally large samples of the population; after returning the 1991 survey forms, respondents were sent discount coupons for food products, and after returning the 1992 survey forms, respondents were sent a pamphlet on recycling.
  • (E) The surveys questioned first-year college students across the country, and the people who did the questioning were all research scientists.

Question 1:

Which of the following is a list of the sites in an order in which the reporter can visit them, from the first site visited to the last site visited?

  • (A) Quin, Ram, Sud, Vara, Xilat, Tunin
  • (B) Quin, Sud, Vara, Tunin, Ram, Xilat
  • (C) Ram, Sud, Vara, Tunin, Quin, Xilat
  • (D) Xilat, Ram, Sud, Tunin, Quin, Vara
  • (E) Xilat, Tunin, Ram, Quin, Sud, Vara

Question 2:

If Sud is visited immediately after Quin is visited, which of the following can be the second site visited?

  • (A) Quin
  • (B) Sud
  • (C) Tunin
  • (D) Vara
  • (E) Xilat

Question 3:

If Tunin is visited as late in the trip as possible, which of the following must be the third site visited?

  • (A) Quin
  • (B) Ram
  • (C) Sud
  • (D) Vara
  • (E) Xilat

Question 4:

If Tunin is visited before Xilat is visited and if exactly one site is visited between the visit to Tunin and the visit to Xilat, which of the following must be true?

  • (A) Quin is visited second.
  • (B) Ram is visited third.
  • (C) Sud is visited fourth.
  • (D) Vara is visited fifth.
  • (E) Xilat is visited sixth.

Question 5:

If Xilat is visited immediately after Ram is visited. Which of the following must be true?

  • (A) Quin is visited at some time after Tunin is visited.
  • (B) Ram is visited at some time after Quin is visited.
  • (C) Tunin is visited at some time after Ram is visited.
  • (D) Tunin is visited at some time after Sud is visited.
  • (E) Xilat is visited at some time after Sud is visited.

Question 6:

If Ram is the fourth site visited, which of the following must be true?

  • (A) Quin is the first site visited.
  • (B) Tunin is the second site visited.
  • (C) Tunin is the third site visited.
  • (D) Vara is the sixth site visited.
  • (E) Xilat is the sixth site visited.

Question 7:

Which of the following can be true?

  • (A) Quin is the fifth site visited.
  • (B) Ram is the fifth site visited.
  • (C) Sud is the second site visited.
  • (D) Xilat is the second site visited.
  • (E) Xilat is the fifth site visited.

Question 8:

If the meetings are scheduled in the order W, X, Y, Z, which of the following can be the schedule of representatives for the meetings?

  • (A) W={G,H,J}, X={L,N}, Y={O,P}, Z={K}
  • (B) W={J,L}, X={G,H}, Y={O,P}, Z={K,N}
  • (C) W={J,L,N}, X={G,H,O}, Y={P}, Z={K}
  • (D) W={J,L,N}, X={G,H}, Y={O,P}, Z={K}
  • (E) W={J,L}, X={G,H}, Y={O,P}, Z={K,N}

Question 9:

If Orson is scheduled for meeting Y, which of the following can be true?

  • (A) Gold is scheduled for the same meeting as Jones.
  • (B) Herrera is scheduled for the same meeting as Lowell.
  • (C) Jones is scheduled for the second meeting.
  • (D) Karami is scheduled for the third meeting.
  • (E) Lowell is scheduled for the fourth meeting.

Question 10:

If Gold and Jones are both scheduled for the third meeting, which of the following must be true?

  • (A) Herrera is scheduled for the first meeting.
  • (B) Lowell is scheduled for the first meeting.
    (C) Porter is scheduled for the first meeting.
    (D) Karami is scheduled for the same meeting as Nakamura.
    (E) Lowell is scheduled for the same meeting as Nakamura.

Question 11:

If Nakamura is scheduled for the third meeting and Karami is scheduled for the fourth meeting, which of the following must be true?

  • (A) Herrera is scheduled for the second meeting.
  • (B) Jones is scheduled for the second meeting.
  • (C) Lowell is scheduled for meeting Y.
    (D) Nakamura is scheduled for meeting Z.
  • (E) Porter is scheduled for meeting Y.

Question 12:

If no other representative is scheduled for the meeting for which Jones is scheduled, any of the following can be true EXCEPT:

  • (A) Jones is scheduled for the third meeting.
  • (B) Lowell is scheduled for the second meeting.
    (C) Nakamura is scheduled for the fourth meeting.
    (D) Lowell is scheduled for meeting Z.
    (E) Nakamura is scheduled for meeting Y.

Question 13:

The town of San Leonardo has recently enacted a law banning smoking in all restaurants within town limits. Since many smokers who normally dine in San Leonardo's restaurants will not want to refrain from smoking during their meals, San Leonardo's restaurants will undoubtedly lose many patrons and considerable income.

Which of the following, if true, most helps to strengthen the argument above?

  • (A) Most residents of San Leonardo who eat in restaurants are not smokers.
  • (B) Most smokers who dine in the company of non-smokers are willing to refrain from smoking during their meals.
    (C) If the law banning smoking in restaurants had not been enacted, it is likely that a more stringent law banning smoking in all public places in San Leonardo would have been enacted instead.
    (D) Prior to the enactment of the law banning smoking in San Leonardo's restaurant, the town had a law that required most restaurants to have nonsmoking sections.
    (E) None of the other communities adjacent to San Leonardo, which have restaurants comparable to those of San Leonardo, has enacted and enforces any antismoking legislation.

Question 14:

Children whose biological parents both have Tic Syndrome Z (TSZ), which is characterized by the involuntary contraction of certain muscles, are about four times more likely to develop such contractions than are children whose biological parents do not have TSZ. It is likely, therefore, that predisposition to TSZ is an inherited trait.

Which of the following, if true, would most strengthen the conclusion above?

  • (A) Children whose parents have TSZ are more likely to develop TSZ if they are under unusual stress at school or at home than if they are not under such stress.
  • (B) Children whose biological parents do not have TSZ are more likely to develop TSZ if they are raised by adoptive parents with TSZ than if they are raised by their biological parents.
    (C) Children whose biological parents have TSZ are as likely to develop TSZ if they are raised by adoptive parents who do not have TSZ as if they are raised by their biological parents.
    (D) Children whose biological parents have TSZ and who develop TSZ usually avoid developing a severe form of the syndrome if they seek treatment for TSZ shortly after developing the first signs of it.
    (E) Children with TSZ whose biological parents do not have TSZ are less likely to have the syndrome diagnosed when symptoms first appear than are children with TSZ whose biological parents have TSZ.

Question 15:

Playing eighteenth-century music on the instruments of that period provides valuable information about how the music originally sounded. Eighteenth-century instruments cannot be played without being restored, however, and restoring such an instrument destroys all of the information that researchers could obtain from it about eighteenth-century instrument-making techniques.

If the statements above are true, which of the following must be true on the basis of them?

  • (A) Eighteenth-century instruments cannot be used to provide information about the original techniques used in playing such instruments if they have been restored.
  • (B) Eighteenth-century instruments that have been restored can provide information only about how eighteenth-century music originally sounded.
    (C) Eighteenth-century instruments are the only source of information about the instrument-making techniques of that period.
    (D) An eighteenth-century instrument that has not been restored can provide more information than can one that has been restored.
    (E) An eighteenth-century instrument cannot serve as a source of new information about eighteenth-century instrument-making techniques once it can be played.

Question 16:

To the nearest hundredth, \(\pi = 3.14\) and \(\sqrt{10} = 3.16\)


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(\pi^2\) & 10

\end{tabular


Question 17:

A marble is to be drawn at random from a bag that contains 2 yellow marbles, 4 blue marbles, 6 green marbles, and no other marbles.


\begin{tabular}{p{5cm} p{5cm}}
\textbf{Column A} & \textbf{Column B}

The probability that the marble drawn will be green & The probability that the marble drawn will be yellow or blue

\end{tabular}


Question 18:


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(250 - \frac{1}{3}\) & \(250 - \frac{1}{2}\)

\end{tabular


Question 19:

\(x+y+n=15\)
\(x+y+k=9\)

\begin{tabular{l l
Column A & Column B
\(n-k\) & 6

\end{tabular

Correct Answer: The two quantities are equal.
View Solution




Step 1: Understanding the Concept:

This problem involves a system of two linear equations with four variables. We need to manipulate these equations to find the value of the expression in Column A.


Step 2: Key Formula or Approach:

The key is to notice the common term \(x+y\) in both equations. We can isolate this term in each equation and then set the results equal to each other. This will give us an equation with only \(n\) and \(k\).


Step 3: Detailed Explanation:

We are given the two equations:

1) \(x+y+n=15\)

2) \(x+y+k=9\)

From equation (1), we can isolate the term \(x+y\):
\[ x+y = 15 - n \]
From equation (2), we can also isolate the term \(x+y\):
\[ x+y = 9 - k \]
Since both expressions are equal to \(x+y\), we can set them equal to each other:
\[ 15 - n = 9 - k \]
The question asks for the value of \(n-k\). Let's rearrange the equation to solve for this expression. Add \(n\) to both sides:
\[ 15 = 9 - k + n \]
Subtract 9 from both sides:
\[ 15 - 9 = n - k \] \[ 6 = n - k \]
The value of the expression in Column A is exactly 6.


Step 4: Final Answer:

The value of Column A is 6, which is equal to the value in Column B.
Quick Tip: Another quick method is to subtract the second equation from the first: \((x+y+n) - (x+y+k) = 15 - 9\). The \(x\) and \(y\) terms cancel out, leaving \(n-k = 6\).


Question 20:

In the rectangular coordinate system, line \(k\) passes through the points (0,0) and (4,8); line \(m\) passes through the points (0,1) and (4,9).


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}

The slope of line \(k\) & The slope of line \(m\)

\end{tabular


Question 21:

The vertices of an equilateral triangle are on a circle.


\begin{tabular}{p{5cm} p{5cm}}
\textbf{Column A} & \textbf{Column B}

The length of a side of the triangle & The diameter of the circle

\end{tabular}


Question 22:


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(\frac{1}{11}\) & 0.09

\end{tabular


Question 23:




△XQY and △ZYR△ZYR are equilateral triangles, and the ratio of ZR to PR is 1 to 4.


 

Column A Column B
The perimeter of △XQY              The perimeter of parallelogram PXYZ  

Question 24:


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(x+y\) & \(2(x+y)\)

\end{tabular

Correct Answer: The relationship cannot be determined from the information given.
View Solution




Step 1: Understanding the Concept:

This question asks us to compare the value of an expression, \(x+y\), with twice the value of that same expression. The relationship will depend on whether the expression \(x+y\) is positive, negative, or zero.


Step 2: Key Formula or Approach:

Let's represent the expression \(x+y\) with a single variable, say \(k\). We are then comparing \(k\) (Column A) with \(2k\) (Column B). We should test different types of values for \(k\).


Step 3: Detailed Explanation:

Let \(k = x+y\). We are comparing \(k\) and \(2k\).


Case 1: \(x+y\) is positive.

Let \(x=1, y=1\), so \(x+y = 2\).

Column A: \(x+y = 2\).

Column B: \(2(x+y) = 2(2) = 4\).

In this case, Column B is greater than Column A (\(4 > 2\)).


Case 2: \(x+y\) is negative.

Let \(x=-1, y=-1\), so \(x+y = -2\).

Column A: \(x+y = -2\).

Column B: \(2(x+y) = 2(-2) = -4\).

In this case, Column A is greater than Column B (\(-2 > -4\)).


Case 3: \(x+y\) is zero.

Let \(x=1, y=-1\), so \(x+y = 0\).

Column A: \(x+y = 0\).

Column B: \(2(x+y) = 2(0) = 0\).

In this case, the two columns are equal.


Step 4: Final Answer:

Since the relationship between the two columns changes depending on the values of \(x\) and \(y\), the relationship cannot be determined from the information given.
Quick Tip: When a quantitative comparison involves variables with no constraints, always test positive, negative, and zero values. If you get different comparison results, the answer is always that the relationship cannot be determined.


Question 25:

In a certain store, computer X costs 30 percent more than computer Y, and computer Y costs 30 percent more than computer Z.

Column A Column B
The cost of computer X minus the cost of computer Y .       The cost of computer Y minus the cost of computer Z.   

Question 26:

\(x^2 y < 0\)


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(xy\) & 0

\end{tabular


Question 27:




\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(y\) & \(4x\)

\end{tabular

Correct Answer: The quantity in Column A is greater.
View Solution




Step 1: Understanding the Concept:

This problem requires us to find the values of angles \(x\) and \(y\) from a geometric diagram by applying properties of angles, such as those in a triangle and vertically opposite angles.


Step 2: Key Formula or Approach:

1. The sum of angles in a triangle is 180\(^\circ\).

2. Vertically opposite angles formed by intersecting lines are equal.

3. Angles on a straight line add up to 180\(^\circ\).


Step 3: Detailed Explanation:

Let's analyze the diagram. It shows two intersecting lines. A triangle is formed, with one of its vertices at the intersection point.

- Inside the triangle, we see angles labeled \(x\) and \(2x\). There is also a right-angle symbol, indicating an angle of 90\(^\circ\). The angle labeled \(x\) in the diagram is one of the triangle's internal angles.

- The sum of the angles in this triangle is 180\(^\circ\). Therefore, we can set up an equation:
\[ x + 2x + 90^\circ = 180^\circ \] \[ 3x = 180^\circ - 90^\circ \] \[ 3x = 90^\circ \] \[ x = 30^\circ \]
- Now, we need to find the value of \(y\). The angle \(y\) and the angle \(x\) inside the triangle are vertically opposite to each other at the intersection point.

- Therefore, \(y\) must be equal to the sum of the other two internal angles of the triangle, but this seems incorrect. Let's re-examine the diagram.

- A more plausible interpretation is that the angle \(y\) and the angle represented by the sum `(angle in triangle) + (right angle)` are vertically opposite. However, the most direct interpretation is that \(x\) and \(y\) are adjacent angles on a straight line along with another angle.
- Let's assume the standard interpretation where the two intersecting lines form four angles. The angle \(x\) inside the triangle is vertically opposite to another angle \(x\) outside the triangle. Angle \(y\) is shown as another angle at that same intersection. If \(x\) and \(y\) are adjacent angles, they sum to 180\(^\circ\).
\[ x + y = 180^\circ \]
With \(x = 30^\circ\), we can find \(y\):
\[ 30^\circ + y = 180^\circ \] \[ y = 150^\circ \]
Now we can compare the quantities in Column A and Column B.


For Column A:
\(y = 150\).


For Column B:
\(4x = 4 \times 30 = 120\).


Comparison:

Column A is 150 and Column B is 120. Since \(150 > 120\), the quantity in Column A is greater.


Step 4: Final Answer:

By solving for \(x\) using the triangle and then for \(y\) using the straight-line property, we find that \(y=150\) and \(4x=120\). Therefore, Column A is greater.
Quick Tip: When a geometry diagram is complex, break it down into simpler shapes and identify the basic rules that apply to each (e.g., sum of angles in a triangle, angles on a straight line). Solve for one variable first, then use that result to find the others.


Question 28:

\(m\) is a positive integer less than 4.

Column A Column B
(m+2)^m               m^(m+2)               

Question 29:

\(\frac{1-x}{x-1} = \frac{1}{x}\)
\(x \neq 1\)


\begin{tabular}{l l}
\textbf{Column A} & \textbf{Column B}
\(x\) & \(-\frac{1}{2}\)

\end{tabular

Correct Answer: The quantity in Column B is greater.
View Solution




Step 1: Understanding the Concept:

This question requires solving an algebraic equation for the variable \(x\) and then comparing the result to a given fraction.


Step 2: Key Formula or Approach:

The key to solving the equation is to recognize the relationship between the numerator and denominator of the fraction on the left side. The term \((1-x)\) is the negative of \((x-1)\).


Step 3: Detailed Explanation:

The equation is \(\frac{1-x}{x-1} = \frac{1}{x}\).

Let's simplify the left side. We can factor -1 out of the numerator:
\[ 1-x = -(-1+x) = -(x-1) \]
Substitute this back into the equation:
\[ \frac{-(x-1)}{x-1} = \frac{1}{x} \]
Since we are given that \(x \neq 1\), the term \((x-1)\) is not zero, so we can cancel it from the numerator and denominator:
\[ -1 = \frac{1}{x} \]
To solve for \(x\), multiply both sides by \(x\):
\[ -x = 1 \]
Multiply by -1 to get the final value for \(x\):
\[ x = -1 \]
Now we compare the columns.

Column A: \(x = -1\).

Column B: \(-\frac{1}{2}\).

On a number line, -1 is to the left of \(-\frac{1}{2}\). Therefore, -1 is less than \(-\frac{1}{2}\).


Step 4: Final Answer:

The value of \(x\) is -1. Since \(-1 < -\frac{1}{2}\), the quantity in Column B is greater.
Quick Tip: A common algebraic trick is recognizing expressions of the form \(\frac{a-b}{b-a}\). As long as \(a \neq b\), this fraction always simplifies to -1. Spotting this pattern instantly solves the equation.


Question 30:

The median of 10, 15, x and y is 18.5, and x < y.
 

Column A Column B
x                            22                          


Question 31:

The cost, in dollars, for an appliance repair at a certain company is \(1.2p + 20h\), where \(p\) is the wholesale price of the parts, in dollars, and \(h\) is the number of hours it takes to repair the appliance. What is the cost of repairing an appliance if the wholesale price of the parts is $15 and it takes 2 hours to repair it?

  • (A) $12
  • (B) $18
  • (C) $20
  • (D) $40
  • (E) $58

Question 32:

For what value of \(x\) will \(8 + (x-3)^2\) have the least value?

  • (A) -3
  • (B) 0
  • (C) 3
  • (D) 5
  • (E) 8

Question 33:

How many integers from 3 to 30, inclusive, are odd?

  • (A) 13
  • (B) 14
  • (C) 15
  • (D) 16
  • (E) 17

Question 34:




In the figure above, ABCE is a square. What are the coordinates of point B?

  • (A) (-4,2)
  • (B) (-2,4)
  • (C) (-2,6)
  • (D) (4,-6)
  • (E) (6,-2)

Question 35:

\(3.7(10^7) = \)

  • (A) 370,000
  • (B) 3,700,000
  • (C) 37,000,000
  • (D) 370,000,000
  • (E) 3,700,000,000

Question 36:

For how many of the years shown after 1950 was there a decrease from the previous year in the number of registered cars?

  • (A) Nine
  • (B) Eight
  • (C) Seven
  • (D) Six
  • (E) Five

Question 37:

The ratio of the population per registered car in 1985 to that in 1975 was most nearly

  • (A) 0.55
  • (B) 0.65
  • (C) 0.75
  • (D) 0.85
  • (E) 0.95

Question 38:

From 1972 to 1985, the percent increase in the number of registered cars was most nearly

  • (A) 60%
  • (B) 50%
  • (C) 45%
  • (D) 35%
  • (E) 15%

Question 39:

From 1950 to 1985, the population of Country X increased by approximately how many million people?

  • (A) 45
  • (B) 80
  • (C) 165
  • (D) 200
  • (E) It cannot be determined from the information given.

Question 40:

If the number of registered cars were to increase yearly through the year 2000 at the same average annual rate shown for the period 1981-1985, for which of the following years would the number of registered cars be closest to 76 million?

  • (A) 1995
  • (B) 1996
  • (C) 1997
  • (D) 1998
  • (E) 1999

Question 41:

A rectangular field is 400 feet long and 300 feet wide. If a square field has the same perimeter as the rectangular field, what is the length, in feet, of each side of the square field?

  • (A) 175
  • (B) 350
  • (C) 200\(\sqrt{2}\)
  • (D) 350\(\sqrt{2}\)
  • (E) 100\(\sqrt{3}\)

Question 42:

The expressions in the table above give the distance of each of two trains from Centerville at t hours after 12:00 noon. At what time will the trains be equidistant from Centerville?

Freight Train: \(-10t + 115\)

Passenger Train: \(-20t + 150\)

  • (A) 1:30 p.m.
  • (B) 3:30 p.m.
  • (C) 5:10 p.m.
  • (D) 8:50 p.m.
  • (E) 11:30 p.m.

Question 43:

In 1982, if the 1.8 billion dollars collected as child support payments was only 10 percent of the total court-ordered payments due, approximately how many billion dollars of court-ordered payments for child support were not collected?

  • (A) 1.6
  • (B) 14.4
  • (C) 16.2
  • (D) 17.2
  • (E) 18.0

Question 44:




If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

  • (A) \(\frac{\pi}{12}\)
  • (B) \(\frac{\pi}{36}\)
  • (C) \(\frac{\pi}{60}\)
  • (D) \(\frac{1}{6}\)
  • (E) \(\frac{1}{3}\)

Question 45:

If \(\frac{1}{4x} + \frac{1}{y} = \frac{1}{3} (\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?

Note: The OCR from the scanned image is ambiguous. This solution assumes the most likely intended equation is with plus signs, as this leads to one of the answer choices.

  • (A) 3 to 4
  • (B) 2 to 3
  • (C) 1 to 2
    (D) 1 to 8
  • (E) 1 to 9

Question 46:

Some activists believe that because the health-care system has become increasingly ---- to those it serves, individuals must ---- bureaucratic impediments in order to develop and promote new therapies.

  • (A) attuned.. avoid
  • (B) inimical.. utilize
  • (C) unresponsive.. circumvent
  • (D) indifferent.. supplement
  • (E) sensitized.. forsake

Question 47:

The acts of vandalism that these pranksters had actually ---- were insignificant compared with those they had ---- but had not attempted.

  • (A) hidden.. renounced
  • (B) advocated.. meditated
  • (C) inflicted.. dismissed
  • (D) committed.. effected
  • (E) perpetrated.. contemplated

Question 48:

Though one cannot say that Michelangelo was an impractical designer, he was, of all nonprofessional architects known, the most ---- in that he was the least constrained by tradition or precedent.

  • (A) pragmatic
  • (B) adventurous
  • (C) empirical
  • (D) skilled
  • (E) learned

Question 49:

Before adapting to changes in values, many prefer to ----, to ---- the universally agreed-on principles that have been upheld for centuries.

  • (A) innovate.. protect
  • (B) resist.. defend
  • (C) ponder.. subvert
  • (D) vacillate.. publicize
  • (E) revert.. ignore

Question 50:

Although the records of colonial New England are ---- in comparison with those available in France or England, the records of other English colonies in America are even more ----.

  • (A) sporadic.. irrefutable
  • (B) sparse.. incontrovertible
  • (C) ambiguous.. authoritative
  • (D) sketchy.. fragmentary
  • (E) puzzling.. unquestionable

Question 51:

High software prices are frequently said to ---- widespread illegal copying, although the opposite ---- that high prices are the cause of the copying -- is equally plausible.

  • (A) contribute to
  • (B) result from
  • (C) correlate with
  • (D) explain
  • (E) precede

Question 52:

Because early United States writers thought that the mark of great literature was grandiosity and elegance not to be found in common speech, they ---- the vernacular.

  • (A) dissected
  • (B) avoided
  • (C) misunderstood
  • (D) investigated
  • (E) exploited

Question 53:

OBSTRUCT: PROGRESS::

  • (A) reveal: information
  • (B) polish: illumination
  • (C) implicate: guilt
  • (D) inspire: artistry
  • (E) stunt: growth

Question 54:

INTERVIEW: APPLICANT::

  • (A) recital: pianist
  • (B) exercise: athlete
  • (C) audition: actor
  • (D) manuscript: writer
  • (E) flight plan: pilot

Question 55:

COMBUSTIBLE: IGNITE::

  • (A) impermeable: saturate
  • (B) impenetrable: pierce
  • (C) malleable: shape
  • (D) rigid: stretch
  • (E) sterile: extract

Question 56:

SLACKEN: TENSION::

  • (A) rarefy: expansion
  • (B) blunt: sharpness
  • (C) obscure: cloudiness
  • (D) quicken: animation
  • (E) oscillate: rotation

Question 57:

BIGOT: TOLERANCE::

  • (A) scoundrel: misdeed
  • (B) liar: honesty
  • (C) brat: annoyance
  • (D) outcast: respect
  • (E) snitch: information

Question 58:

IMPROVEMENTS: MASTERY::

  • (A) efforts: exertion
  • (B) savings: wealth
  • (C) performance: talent
  • (D) practice: intention
  • (E) diversification: proficiency

Question 59:

DILETTANTE: SUPERFICIALITY::

  • (A) partisan: bias
  • (B) crusader: passivity
  • (C) libertarian: authority
  • (D) champion: restlessness
  • (E) sage: argumentativeness

Question 60:

WINNOW: CHAFF::

  • (A) ferment: alcohol
  • (B) skim: cream
  • (C) pare: fruit
  • (D) refine: oil
  • (E) filter: impurities

Question 61:

STANZA: LINE::

  • (A) essay: theme
  • (B) scene: monologue
  • (C) play: vignette
  • (D) volume: issue
  • (E) concert: program

Question 62:

By using the word "interpretative" in line 40, the author is indicating which of the following?

  • (A) Some maps are based more on data from aerial photography than on data from field operations.
  • (B) Some maps are based almost exclusively on laboratory measurements.
  • (C) Some maps are based on incomplete data from field observations.
  • (D) Some maps show only large geologic features.
  • (E) Some maps can be three-dimensional.

Question 63:

With which of the following statements about geologic mapping would the author be most likely to agree?

  • (A) Geologic mapping is basically an art and not a science.
  • (B) Geologic mapping has not changed significantly since the early 1960's.
  • (C) Geologic mapping will have limited practical applications until remote-sensing systems are perfected.
  • (D) A developmental milestone in geologic mapping was reached in 1972.
  • (E) Without the present variety of remote-sensing techniques, geologic mapping could not be done.

Question 64:

According to the passage, measurements of which of the following can be provided by the optomechanical scanner but not by visible-light photography?

  • (A) The amount of visible light reflected from oceans
  • (B) The density of foliage in remote areas on the Earth's surface
  • (C) Daily temperature changes of areas on the Earth's surface
  • (D) The degree of radioactivity emitted by exposed rocks on the Earth's surface
  • (E) Atmospheric conditions over large landmasses

Question 65:

It can be inferred from the passage that a major disadvantage of photographic imaging in geologic mapping is that such photography

  • (A) cannot be used at night
  • (B) cannot focus on the details of a geologic area
  • (C) must be chemically processed
  • (D) is always enhanced by digital reconstruction
  • (E) cannot reflect changes over extended periods of time

Question 66:

The primary purpose of the passage is to

  • (A) build a case for increasing the development of new infrastructure
  • (B) advocate an alternative to government financing of infrastructure
  • (C) explain the failure of a privately financed venture
  • (D) suggest the types of infrastructure most appropriate for private financing
  • (E) argue against government restrictions on developing new infrastructure

Question 67:

The passage implies that the "governmental planning" mentioned in line 3 may lead to which of the following problems?

  • (A) Improper use of profits derived from user fees
  • (B) Unduly slow development of necessary new infrastructure
  • (C) Unrealistic decisions about developing new infrastructure
    (D) Incorrect predictions about profits to be gained from user fees
    (E) Obstruction of private financing for the development of new infrastructure

Question 68:

According to the passage, which of the following is true of the toll road mentioned in line 12?

  • (A) After it was built, it attracted too little traffic to pay for its construction.
  • (B) It was partially financed by the state of Virginia.
  • (C) Its development was authorized during an economic boom.
  • (D) Its construction was controversial among local residents.
  • (E) Its developers were discouraged by governmental restrictions on acquiring the necessary land.

Question 69:

The passage suggests that which of the following would occur if a privately financed bridge that proved to be profitable failed after a number of years to meet the demands of traffic?

  • (A) Private developers who financed the bridge would rely on governmental authorities to develop new infrastructure.
  • (B) User fees would be increased so that usage would become more costly.
  • (C) Governmental authorities would be reluctant to rely on private contractors to develop a new bridge.
  • (D) The success of the project would be jeopardized by public dissatisfaction with the project's adequacy.
  • (E) Profits generated by user fees would be used to help finance the construction of new infrastructure to alleviate the traffic problem.

Question 70:

EVOKE:

  • (A) try to hinder
  • (B) fail to elicit
  • (C) refuse to implore
  • (D) pretend to agree
  • (E) attempt to calm

Question 71:

OSTENTATION:

  • (A) austerity
  • (B) wisdom
  • (C) illumination
  • (D) superficiality
  • (E) agitation

Question 72:

BRISTLE:

  • (A) cower
  • (B) feint
  • (C) equivocate
  • (D) coerce
  • (E) apprise

Question 73:

AGGRANDIZE:

  • (A) conciliate
  • (B) undermine
  • (C) relegate
  • (D) remain unapologetic
  • (E) remain inexplicit

Question 74:

ENDEMIC:

  • (A) undeniable
  • (B) intermittent
  • (C) anomalous
  • (D) foreign
  • (E) unexpected

Question 75:

BELLICOSE:

  • (A) enervated
  • (B) disloyal
  • (C) honest
  • (D) likely to be generous
  • (E) inclined to make peace

Question 76:

ABJURE:

  • (A) affirm
  • (B) cajole
  • (C) insist
  • (D) pronounce
  • (E) shout

Question 77:

SALUTARY:

  • (A) unexpected
  • (B) transitory
  • (C) unhealthy
  • (D) disoriented
  • (E) dilapidated

Question 78:

LUGUBRIOUSNESS:

  • (A) orderliness
  • (B) shallowness
  • (C) believability
  • (D) cheerfulness
  • (E) dedication

Question 79:

PRESCIENCE:

  • (A) acuity
  • (B) myopia
  • (C) vacillation
  • (D) tardiness
  • (E) inhibition

Question 80:

INVETERATE:

  • (A) arbitrary
  • (B) occasional
  • (C) obvious
  • (D) progressive
  • (E) compelling

 

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