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GRE General Test study materials
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GRE General Test practice questions

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Question 1Quantitative, verbal and issue-essay reasoning foundations

The scientist's findings were initially met with __________, but subsequent replications by independent laboratories gradually __________ her original conclusions. Select the two words that best complete the sentence.

  1. skepticism … corroborated Correct answer.
  2. enthusiasm … undermined
  3. indifference … anticipated
  4. corroboration … challenged

Explanation

'Skepticism' fits the initial doubt typical when new findings challenge existing views, and 'corroborated' means confirmed or supported-exactly what independent replications would do. The sentence describes a narrative arc from doubt to validation.

Question 2Quantitative, verbal and issue-essay reasoning foundations

The philosopher's prose was notoriously __________: even her admirers admitted that untangling a single paragraph often required the patience of a scholar willing to read the same sentences repeatedly. Choose the word that best fits the blank.

  1. pellucid
  2. abstruse Correct answer.
  3. laconic
  4. sycophantic

Explanation

'Abstruse' means difficult to understand; obscure. This fits perfectly-the sentence says even admirers found her prose hard to parse. The clue 'untangling a single paragraph' signals complexity and opacity.

Question 3Quantitative, verbal and issue-essay reasoning foundations

Though the young diplomat was widely considered __________, her mentor warned that her willingness to voice unpopular positions in public forums could prove professionally damaging in the long run. Choose the word that best fits the blank.

  1. truculent
  2. indefatigable
  3. perspicacious Correct answer.
  4. obsequious

Explanation

'Perspicacious' means having a ready insight into things; shrewd. The sentence praises her (considered X by 'widely') yet warns about bold speech-perspicacity fits because sharp thinkers who speak candidly are sometimes praised and sometimes penalized.

Question 4Quantitative, verbal and issue-essay reasoning foundations

The newly elected mayor's administration was marked by a(n) __________ approach to urban planning: she solicited input from residents, businesses, and civic organizations before making any major zoning decisions. Choose the word that best fits the blank.

  1. autocratic
  2. precipitate
  3. consultative Correct answer.
  4. parsimonious

Explanation

'Consultative' means involving consultation or advice from others, which directly mirrors the described behavior of soliciting input from multiple groups before making decisions.

Question 5Quantitative, verbal and issue-essay reasoning foundations

The senator's speech was, at best, __________: it contained just enough factual content to appear substantive but was primarily designed to __________ the audience rather than to inform it. Choose the words that best complete both blanks (Blank 1, Blank 2).

  1. specious … enlighten
  2. tendentious … galvanize Correct answer.
  3. cogent … mislead
  4. pellucid … energize

Explanation

'Tendentious' means expressing a particular point of view; biased. 'Galvanize' means to shock or excite someone into action. Together they convey a speech designed to move an audience emotionally/politically rather than to genuinely inform-fitting the 'at best' qualifier and the rhetorical purpose described.

Question 6Quantitative, verbal and issue-essay reasoning foundations

Despite the public's __________ fascination with celebrity culture, serious cultural critics have found it a surprisingly __________ subject, capable of illuminating broader questions about identity, consumerism, and the construction of fame. Choose the words that best complete both blanks (Blank 1, Blank 2).

  1. highbrow … banal
  2. ostensibly trivial … fecund Correct answer.
  3. deeply intellectual … superficial
  4. earnest … contentious

Explanation

'Ostensibly trivial' captures the public's apparent-but possibly misleading-fascination with celebrity culture, and 'fecund' (intellectually productive) captures how critics find it surprisingly rich. The sentence's 'Despite … surprisingly' structure signals a contrast between surface impression and deeper value.

Question 7Quantitative, verbal and issue-essay reasoning foundations

The researcher's reputation for __________ was well-earned: she refused to publish results until they had been subjected to at least three rounds of internal peer review, and she once delayed a landmark paper for eighteen months to address a single statistical ambiguity. Choose the word that best fits the blank.

  1. imprudence
  2. equivocation
  3. probity Correct answer.
  4. loquacity

Explanation

'Probity' means strong moral principles and uprightness; in academic contexts it encompasses rigorous intellectual honesty. Her behavior-exhaustive internal review, delaying publication to resolve ambiguity-demonstrates scholarly integrity, i.e., probity.

Question 8Quantitative, verbal and issue-essay reasoning foundations

The committee's deliberations were characterized by an almost willful __________: members seemed determined to avoid reaching consensus, prolonging the meeting well past midnight. Choose the word that best fits the blank.

  1. alacrity
  2. obduracy Correct answer.
  3. magnanimity
  4. circumspection

Explanation

'Obduracy' means stubborn refusal to change one's opinion or course; it fits 'willful' avoidance of consensus. The clue 'determined to avoid reaching consensus' indicates entrenched stubbornness, which is precisely what obduracy means.

Question 9Quantitative, verbal and issue-essay reasoning foundations

The two critics' views on the novel were far from __________: one praised its intricate symbolism while the other condemned the same passages as pretentious and overwrought. Select the two words that, when used in the blank, produce sentences most alike in meaning.

  1. congruent Correct answer.
  2. divergent
  3. harmonious
  4. discordant

Explanation

The blank requires a word meaning 'in agreement.' 'Congruent' (matching, in accord) fits: the critics were 'far from congruent.' 'Harmonious' also means in accord-both words produce the same logical sentence meaning. On the real GRE you select TWO correct answers; here 'congruent' is the primary answer.

Question 10Quantitative, verbal and issue-essay reasoning foundations

The company's decision to __________ its long-standing environmental commitments in favor of short-term profitability drew sharp criticism from shareholders who had valued its reputation for corporate responsibility. Choose the word that best fits the blank.

  1. reaffirm
  2. abrogate Correct answer.
  3. extol
  4. promulgate

Explanation

'Abrogate' means to repeal or do away with; abandoning environmental commitments in favor of profit is precisely an abrogation of those commitments. The critical shareholder reaction confirms the action was a reversal of something previously valued.

Question 11Quantitative, verbal and issue-essay reasoning foundations

The novelist's later work was praised for its __________ prose-sentences so economically crafted that removing even a single word would weaken the effect. Select the two words that, when used in the blank, produce sentences most alike in meaning.

  1. lapidary Correct answer.
  2. verbose
  3. terse
  4. prolix

Explanation

'Lapidary' (precisely elegant, like text cut as gems) and 'terse' (brief and impactful) both describe economical precision. On the real GRE you select TWO; here 'lapidary' is the primary answer as it most precisely captures the quality of gemstone-like craftsmanship implied. The incorrect options (verbose, prolix) are synonyms for wordiness-the opposite of what the sentence describes.

Question 12Quantitative, verbal and issue-essay reasoning foundations

The politician's attempts at __________ were evident in his willingness to endorse contradictory positions within the same campaign speech, apparently calculating that few voters would notice the inconsistency. Choose the word that best fits the blank.

  1. equivocation Correct answer.
  2. forthrightness
  3. verisimilitude
  4. parsimony

Explanation

'Equivocation' is the use of ambiguous language to conceal truth or avoid commitment. Endorsing contradictory positions while hiding the contradiction is a textbook example of equivocation.

Question 13Quantitative, verbal and issue-essay reasoning foundations

The documentary was acclaimed for its __________ portrayal of the refugee crisis: by focusing on specific families rather than statistics, it made viewers viscerally aware of the human stakes. Choose the word that best fits the blank.

  1. anodyne
  2. tendentious
  3. humanizing Correct answer.
  4. polemical

Explanation

'Humanizing' best captures the method described: focusing on individual families to make abstract statistics concrete and personal. The sentence positively frames this approach ('acclaimed'), ruling out negative words.

Question 14Quantitative, verbal and issue-essay reasoning foundations

His academic writing was widely criticized as __________: readers complained that he used ten convoluted sentences to express ideas that a skilled writer would have stated in one. Select the two words that, when used in the blank, produce sentences most alike in meaning.

  1. turgid Correct answer.
  2. succinct
  3. bombastic
  4. pellucid

Explanation

'Turgid' (inflated and pompous in language) and 'bombastic' (high-sounding with little meaning) both describe writing that is overblown and needlessly complex-exactly what the sentence criticizes. On the real GRE you select TWO; here 'turgid' is the primary answer.

Question 15Quantitative, verbal and issue-essay reasoning foundations

Despite years of __________ research, the team failed to produce definitive results-a fact that led several frustrated colleagues to describe the project as __________ and call for its termination. Choose the words that best complete both blanks (Blank 1, Blank 2).

  1. assiduous … quixotic Correct answer.
  2. perfunctory … visionary
  3. desultory … fruitful
  4. meticulous … productive

Explanation

'Assiduous' (diligent, hard-working) for Blank 1 heightens the irony: despite great effort, no results. 'Quixotic' (foolishly idealistic, impractical) for Blank 2 fits colleagues calling for termination of a project that, despite effort, produced nothing-they see it as chasing an impossible dream.

Question 16Quantitative, verbal and issue-essay reasoning foundations

The artist's later canvases were marked by a __________ that her earlier, more polished work lacked: rough brushstrokes, unpainted edges, and visible pentimento gave the surfaces a raw, unfinished energy. Choose the word that best fits the blank.

  1. fastidiousness
  2. sprezzatura Correct answer.
  3. deliberateness
  4. insouciance

Explanation

'Sprezzatura' (the studied carelessness or effortless grace that conceals effort) is the ideal word here-an Italian concept meaning the art of making difficulty look easy or intentional roughness. 'Insouciance' (casual lack of concern) is a close runner-up, but sprezzatura specifically applies to artistic technique that conceals labor through apparent carelessness.

Question 17Quantitative, verbal and issue-essay reasoning foundations

The memoir was neither __________ nor self-congratulatory; it treated the author's failures with the same unflinching clarity it brought to her successes. Select the two words that, when used in the blank, produce sentences most alike in meaning.

  1. maudlin Correct answer.
  2. candid
  3. lachrymose
  4. incisive

Explanation

'Maudlin' (excessively sentimental) and 'lachrymose' (tearful; given to weeping) both describe overly emotional, self-pitying styles of memoir writing. On the real GRE you select TWO; here 'maudlin' is the primary answer as both it and 'lachrymose' produce the same sentence meaning.

Question 18Quantitative, verbal and issue-essay reasoning foundations

The city council's response to the housing crisis was criticized as __________ by affordable housing advocates, who argued that the modest incentives offered to developers would have negligible impact on the shortage. Choose the word that best fits the blank.

  1. precipitous
  2. anathema
  3. nugatory Correct answer.
  4. perspicacious

Explanation

'Nugatory' means of no value or importance; trifling. The advocates' criticism-that the incentives would have 'negligible impact'-is exactly the charge that measures are nugatory. The word precisely fits the semantic space of 'too small to matter.'

Question 19Quantitative, verbal and issue-essay reasoning foundations

The scholar's __________ use of primary sources was both her greatest strength and her chief vulnerability: by relying almost exclusively on diaries and letters, she produced vivid portraits but sometimes missed the broader structural forces shaping her subjects' lives. Choose the word that best fits the blank.

  1. judicious
  2. assiduous
  3. idiosyncratic Correct answer.
  4. tendentious

Explanation

'Idiosyncratic' means peculiar to an individual; her exclusive reliance on diaries and letters is a distinctive, personal methodological preference that yields both strengths and weaknesses. The sentence describes an approach that is characteristic of her and not necessarily standard practice.

Question 20Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The number of integers from 1 to 100 (inclusive) that are divisible by both 3 and 4. Quantity B: The number of integers from 1 to 100 (inclusive) that are divisible by 12. Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

Divisible by both 3 and 4 means divisible by lcm(3,4) = 12. So Quantity A = Quantity B = the count of multiples of 12 from 1–100. Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96 = 8. Both quantities equal 8.

Question 21Quantitative, verbal and issue-essay reasoning foundations

Quantity A: (3 + √5)² Quantity B: 14 + 6√5 Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

Expand Quantity A: (3 + √5)² = 9 + 6√5 + 5 = 14 + 6√5. This equals Quantity B exactly. Both quantities equal 14 + 6√5.

Question 22Quantitative, verbal and issue-essay reasoning foundations

A store marks up an item by 40% above its wholesale cost, then offers a 20% discount on the marked-up price. What is the net percent change in price from wholesale cost to the final sale price?

  1. 12% increase Correct answer.
  2. 20% increase
  3. 8% increase
  4. No change - it returns to cost

Explanation

Let cost = 100. Marked up 40%: 100 × 1.40 = 140. Discount 20%: 140 × 0.80 = 112. Net change = 112 − 100 = 12% increase over wholesale cost.

Question 23Quantitative, verbal and issue-essay reasoning foundations

If 2x − 3y = 12 and x + y = 1, what is the value of x?

  1. 3 Correct answer.
  2. −3
  3. 15/5
  4. 15/7

Explanation

From x + y = 1: y = 1 − x. Substituting: 2x − 3(1 − x) = 12 → 2x − 3 + 3x = 12 → 5x = 15 → x = 3. Check: y = −2. Verify: 2(3) − 3(−2) = 6 + 6 = 12. ✓

Question 24Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The area of a circle with diameter 10 Quantity B: The area of a square with perimeter 40 Compare the two quantities. (Use π ≈ 3.14159)

  1. Quantity A is greater.
  2. Quantity B is greater. Correct answer.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Explanation

Circle: diameter = 10, radius = 5, area = π(5²) = 25π ≈ 78.54. Square: perimeter = 40, side = 10, area = 100. Since 100 > 78.54, Quantity B is greater.

Question 25Quantitative, verbal and issue-essay reasoning foundations

A jar contains 4 red marbles, 6 blue marbles, and 2 white marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?

  1. 1/4
  2. 5/22 Correct answer.
  3. 3/11
  4. 36/144

Explanation

P(both blue) = C(6,2)/C(12,2) = (6×5/2)/(12×11/2) = 15/66 = 5/22. Total marbles = 4+6+2 = 12.

Question 26Quantitative, verbal and issue-essay reasoning foundations

If f(x) = 3x² − 2x + 1, what is f(−2)?

  1. 9
  2. 17 Correct answer.
  3. 13
  4. 21

Explanation

f(−2) = 3(−2)² − 2(−2) + 1 = 3(4) + 4 + 1 = 12 + 4 + 1 = 17.

Question 27Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The slope of the line passing through (2, 5) and (6, 13) Quantity B: The slope of the line 4x − 2y = 8 Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

Quantity A: slope = (13−5)/(6−2) = 8/4 = 2. Quantity B: rewrite 4x − 2y = 8 as 2y = 4x − 8, so y = 2x − 4; slope = 2. Both slopes equal 2.

Question 28Quantitative, verbal and issue-essay reasoning foundations

The sum of three consecutive even integers is 78. What is the largest of the three integers?

  1. 24
  2. 26
  3. 28 Correct answer.
  4. 30

Explanation

Let the integers be n, n+2, n+4. Then 3n + 6 = 78 → 3n = 72 → n = 24. The three integers are 24, 26, 28. The largest is 28.

Question 29Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The perimeter of a rectangle with length 8 and width 5 Quantity B: The circumference of a circle with radius 4 Compare the two quantities.

  1. Quantity A is greater. Correct answer.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Explanation

Quantity A: Perimeter = 2(8 + 5) = 2(13) = 26. Quantity B: Circumference = 2π(4) = 8π ≈ 25.13. Since 26 > 25.13, Quantity A is greater.

Question 30Quantitative, verbal and issue-essay reasoning foundations

A cylinder has radius 3 and height 8. A second cylinder has radius 6 and height 2. Which has the greater volume? Quantity A: Volume of the first cylinder (radius 3, height 8) Quantity B: Volume of the second cylinder (radius 6, height 2)

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

Volume = πr²h. Quantity A: π(3²)(8) = π(9)(8) = 72π. Quantity B: π(6²)(2) = π(36)(2) = 72π. Both cylinders have volume 72π - they are equal.

Question 31Quantitative, verbal and issue-essay reasoning foundations

If the average (arithmetic mean) of five numbers is 14, and four of the numbers are 10, 12, 16, and 18, what is the fifth number?

  1. 14 Correct answer.
  2. 16
  3. 10
  4. 13

Explanation

Sum of all five = 5 × 14 = 70. Sum of the four known numbers = 10 + 12 + 16 + 18 = 56. Fifth number = 70 − 56 = 14.

Question 32Quantitative, verbal and issue-essay reasoning foundations

Quantity A: x² + 6x + 9, where x = −4 Quantity B: (x + 3)², where x = −4 Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

x² + 6x + 9 = (x + 3)² by the perfect-square trinomial factoring. For any value of x, the two expressions are algebraically identical, so they are always equal. At x = −4: (−4 + 3)² = (−1)² = 1. Both equal 1.

Question 33Quantitative, verbal and issue-essay reasoning foundations

A train travels 300 miles in 4 hours. How many miles will it travel in 7 hours at the same average speed?

  1. 475 miles
  2. 525 miles Correct answer.
  3. 550 miles
  4. 450 miles

Explanation

Speed = 300/4 = 75 miles per hour. Distance in 7 hours = 75 × 7 = 525 miles.

Question 34Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The number of prime numbers between 20 and 40 (exclusive) Quantity B: 4 Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

Primes between 20 and 40 (exclusive): 23, 29, 31, 37. That is exactly 4 primes. Quantity A = 4 = Quantity B.

Question 35Quantitative, verbal and issue-essay reasoning foundations

Data table: Year | Revenue ($M) 2019 | 40 2020 | 50 2021 | 45 2022 | 60 2023 | 75 What was the percent increase in revenue from 2020 to 2023?

  1. 25%
  2. 50% Correct answer.
  3. 87.5%
  4. 40%

Explanation

Percent increase = (75 − 50)/50 × 100 = 25/50 × 100 = 50%. Revenue grew from $50M in 2020 to $75M in 2023, a 50% increase.

Question 36Quantitative, verbal and issue-essay reasoning foundations

A rectangular garden has length that is twice its width. If the perimeter of the garden is 84 feet, what is the area of the garden in square feet?

  1. 196 square feet
  2. 392 square feet Correct answer.
  3. 588 square feet
  4. 168 square feet

Explanation

Let width = w, length = 2w. Perimeter = 2(w + 2w) = 6w = 84, so w = 14. Length = 28. Area = 14 × 28 = 392 square feet.

Question 37Quantitative, verbal and issue-essay reasoning foundations

Quantity A: 0.3 × 0.3 × 0.3 Quantity B: (0.3)³ Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

0.3 × 0.3 × 0.3 = (0.3)³ by definition of exponentiation. Both equal 0.027. They are identical expressions.

Question 38Quantitative, verbal and issue-essay reasoning foundations

If x > 0, which of the following is equivalent to √(x³)?

  1. x√x Correct answer.
  2. x²
  3. x^(2/3)
  4. √x · x

Explanation

√(x³) = (x³)^(1/2) = x^(3/2) = x¹ · x^(1/2) = x√x. Also note option D: √x · x = x^(1/2) · x = x^(3/2) = x√x - options A and D are actually equivalent. However, on this question option A is the canonical simplified form.

Question 39Quantitative, verbal and issue-essay reasoning foundations

In a class of 30 students, 18 play soccer, 12 play basketball, and 6 play both sports. How many students play neither sport?

  1. 6 Correct answer.
  2. 4
  3. 0
  4. 8

Explanation

By inclusion-exclusion: students playing at least one sport = 18 + 12 − 6 = 24. Students playing neither = 30 − 24 = 6.

Question 40Quantitative, verbal and issue-essay reasoning foundations

If 5% of a number is 13, what is 20% of the same number?

  1. 52 Correct answer.
  2. 65
  3. 26
  4. 104

Explanation

5% of n = 13, so n = 13/0.05 = 260. Then 20% of 260 = 0.20 × 260 = 52. Alternatively, 20% = 4 × 5%, so 4 × 13 = 52.

Question 41Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The median of the set {3, 7, 7, 9, 11, 15, 15} Quantity B: The mode of the set {3, 7, 7, 9, 11, 15, 15} Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given. Correct answer.

Explanation

Median = middle value of 7-element set = 4th value = 9. Mode = most frequent value(s). Both 7 and 15 appear twice; the set is bimodal. The mode is not a single value, so a comparison is indeterminate-Quantity B has no unique value to compare.

Question 42Quantitative, verbal and issue-essay reasoning foundations

A rectangular box has dimensions 4 × 5 × 6. What is the length of the space diagonal (the diagonal from one corner to the opposite corner)?

  1. √77 Correct answer.
  2. √61
  3. √52
  4. √45

Explanation

Space diagonal = √(l² + w² + h²) = √(16 + 25 + 36) = √77.

Question 43Quantitative, verbal and issue-essay reasoning foundations

If x² − 9 = 0, what are the possible values of x?

  1. x = 3 only
  2. x = −3 only
  3. x = 3 or x = −3 Correct answer.
  4. x = 9

Explanation

x² − 9 = 0 → x² = 9 → x = ±√9 = ±3. Both 3 and −3 are valid solutions because both satisfy the equation when squared.

Question 44Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The value of |−7| + |3| Quantity B: |−7 + 3| Compare the two quantities.

  1. Quantity A is greater. Correct answer.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Explanation

Quantity A: |−7| + |3| = 7 + 3 = 10. Quantity B: |−7 + 3| = |−4| = 4. Since 10 > 4, Quantity A is greater. This is the triangle inequality: |a| + |b| ≥ |a + b|.

Question 45Quantitative, verbal and issue-essay reasoning foundations

A data set has 10 values. The mean is 20 and the standard deviation is 4. If every value in the data set is multiplied by 2, what is the new standard deviation?

  1. 4
  2. 6
  3. 8 Correct answer.
  4. 16

Explanation

When every value in a data set is multiplied by a constant k, the standard deviation is also multiplied by |k|. Here k = 2, so the new standard deviation = 2 × 4 = 8.

Question 46Quantitative, verbal and issue-essay reasoning foundations

Triangle ABC has sides of length 5, 12, and 13. What type of triangle is it?

  1. Acute
  2. Obtuse
  3. Right Correct answer.
  4. Equilateral

Explanation

Check: 5² + 12² = 25 + 144 = 169 = 13². Since a² + b² = c², this is a right triangle. (5-12-13 is a classic Pythagorean triple.)

Question 47Quantitative, verbal and issue-essay reasoning foundations

Quantity A: (−2)⁵ Quantity B: −(2⁵) Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

(−2)⁵ = −(2⁵) = −32. A negative base raised to an odd power equals the negative of that power of the positive base. Both equal −32.

Question 48Quantitative, verbal and issue-essay reasoning foundations

A store sells notebooks in packs of 3 for $2.40, or individually for $0.90 each. How much does a customer save per notebook by buying in packs compared to buying individually?

  1. $0.10 Correct answer.
  2. $0.15
  3. $0.20
  4. $0.30

Explanation

Pack price per notebook = $2.40 / 3 = $0.80. Individual price = $0.90. Savings per notebook = $0.90 − $0.80 = $0.10.

Question 49Quantitative, verbal and issue-essay reasoning foundations

Quantity A: The number of ways to arrange 4 distinct books on a shelf Quantity B: 24 Compare the two quantities.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal. Correct answer.
  4. The relationship cannot be determined from the information given.

Explanation

The number of arrangements (permutations) of 4 distinct books = 4! = 4 × 3 × 2 × 1 = 24. Quantity A = 24 = Quantity B.

Question 50Quantitative, verbal and issue-essay reasoning foundations

If (x + 2)(x − 5) = 0, what are the solutions for x?

  1. x = 2 and x = −5
  2. x = −2 and x = 5 Correct answer.
  3. x = 2 and x = 5
  4. x = −2 and x = −5

Explanation

Zero product property: (x + 2) = 0 gives x = −2; (x − 5) = 0 gives x = 5. So x = −2 or x = 5.