GRE Quantitative Quiz: Multiple Choice Single Answer
20 questions · exam conditions
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Multiple Choice Single AnswerQuestion 1 of 20

What is the value of 50−8\sqrt{50} - \sqrt{8}?

42\sqrt{42}
58\sqrt{58}
323\sqrt{2}
525\sqrt{2}
727\sqrt{2}
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GRE Quantitative Quiz

GRE Quantitative Quiz: Multiple Choice Single Answer

Practice Multiple Choice Single Answer in GRE Quantitative with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Multiple Choice Single Answer, giving you a quick way to practice the rules, question types, and explanations that matter most for GRE Quantitative.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

What is the value of 50−8\sqrt{50} - \sqrt{8}?

  1. 42\sqrt{42}
  2. 58\sqrt{58}
  3. 323\sqrt{2} (correct answer)
  4. 525\sqrt{2}
  5. 727\sqrt{2}
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is simplifying square roots by factoring out perfect squares. For √50 - √8, rewrite as √(252) - √(42) = 5√2 - 2√2 = 3√2. This simplification combines like terms under the radicals. The correct answer of 3√2 satisfies the expression because it is the exact simplified form. A representative incorrect option like 5√2 might result from adding instead of subtracting the terms. Another error, such as choosing √58, could stem from combining the numbers without factoring.

Question 2

If 2x−3=5x+122x - 3 = 5x + 12, what is the value of xx?

  1. −3-3
  2. 33
  3. 55
  4. −5-5 (correct answer)
  5. 99
Explanation: This is a Multiple Choice, Select One GRE Quant problem requiring solving a linear equation. The fundamental principle involves isolating the variable by combining like terms and using inverse operations. Starting with 2x - 3 = 5x + 12, we subtract 2x from both sides to get -3 = 3x + 12, then subtract 12 from both sides to get -15 = 3x. Dividing both sides by 3 yields x = -5. The Dorrect answer D (x = -5) satisfies the original equation: 2(-5) - 3 = -10 - 3 = -13, and 5(-5) + 12 = -25 + 12 = -13. A common mistake would be to incorrectly combine terms, such as getting x = 3 by making a sign error when moving terms across the equals sign.

Question 3

A store sells a jacket for 25%25\% off its original price. If the sale price of the jacket is $72, what was the original price of the jacket?

  1. $90
  2. $96 (correct answer)
  3. $54
  4. $88
  5. $100
Explanation: This is a Multiple Choice, Select One GRE Quant problem involving percent discount calculations. The core principle is that if an item is 25% off, the customer pays 75% of the original price. Since the sale price is $72 and this represents 75% of the original price, we can set up the equation: 0.75 × (original price) = $72. Solving for the original price: original price = $72 ÷ 0.75 = 96.TheBorrectanswerB(96. The Borrect answer B (96) satisfies the requirement because 0.75 × $96 = $72. A common error would be to add 25% of $72 to $72 (giving $90), which incorrectly treats the sale price as the base for the percentage calculation rather than recognizing that the discount is based on the original price.

Question 4

If xx and yy are positive integers such that x:y=3:5x:y = 3:5 and x+y=64x + y = 64, what is the value of xx?

  1. 2424 (correct answer)
  2. 4040
  3. 3232
  4. 2020
  5. 2828
Explanation: This is a Multiple Choice, Select One GRE Quant problem involving ratios and linear equations. The principle is that if x:y = 3:5, then x = 3k and y = 5k for some constant k. Given x + y = 64, we substitute to get 3k + 5k = 64, which gives 8k = 64, so k = 8. Therefore, x = 3×8 = 24 and y = 5×8 = 40. The Aorrect answer A (24) satisfies both conditions: x:y = 24:40 = 3:5 and x + y = 24 + 40 = 64. A common error would be to incorrectly set up the ratio relationship or make an arithmetic mistake when solving for k.

Question 5

If f(x)=x2−4x+1f(x) = x^2 - 4x + 1, what is the value of f(5)f(5)?

  1. 6 (correct answer)
  2. 0
  3. 10
  4. 1
  5. 16
Explanation: This is a Multiple Choice, Select One GRE Quantitative problem that tests function evaluation. The core principle involves substituting a given value into a function and performing the arithmetic operations. For f(x) = x² - 4x + 1, we substitute x = 5: f(5) = 5² - 4(5) + 1 = 25 - 20 + 1 = 6. The correct answer is 6 because it results from correctly applying the order of operations to evaluate the function at x = 5. Answer choice C (10) might result from an error such as calculating 5² - 4(5) + 5 or misapplying the function formula.

Question 6

If aa and bb are positive integers and lcm(a,b)=60\text{lcm}(a,b)=60 and gcd⁡(a,b)=6\gcd(a,b)=6, what is the value of abab?

  1. 60
  2. 120
  3. 180
  4. 360 (correct answer)
  5. 720
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is the relationship between least common multiple (LCM), greatest common divisor (GCD), and the product of two numbers, where LCM(a, b) * GCD(a, b) = a * b. Given LCM(a, b) = 60 and GCD(a, b) = 6, the product ab = 60 * 6 = 360. The correct answer of 360 satisfies the relationship because it directly follows from multiplying the given LCM and GCD. A representative incorrect option like 120 might result from dividing instead of multiplying the values. Another error, such as choosing 180, could stem from misapplying prime factorizations or assuming incorrect factors.

Question 7

An investment of \2{,}000$ increases in value by 12% in one year. What is the value of the investment after one year?

  1. \2{,}120$
  2. \2{,}240$ (correct answer)
  3. \2{,}012$
  4. \2{,}200$
  5. \2{,}400$
Explanation: This is a Multiple Choice, Select One GRE Quantitative problem that tests percentage increase calculations. The core principle involves calculating 12% of the initial value and adding it to the original amount. A 12% increase means the new value is 112% of the original: $2,000 × 1.12 = $2,240. Alternatively, 12% of $2,000 = 0.12 × $2,000 = $240, so the final value is $2,000 + $240 = $2,240. The correct answer is 2,240becauseitaccuratelyreflectsa122,240 because it accurately reflects a 12% increase from the initial investment. Answer choice A (2,120) incorrectly calculates only 6% increase instead of 12%, giving $2,000 × 1.06 = $2,120.

Question 8

A store sells notebooks for $3 each and pens for $2 each. If a customer buys a total of 14 items for $34, how many notebooks did the customer buy?

  1. 4
  2. 5
  3. 6 (correct answer)
  4. 8
  5. 10
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is setting up and solving a system of linear equations based on given totals. Let n represent the number of notebooks and p the number of pens; then n + p = 14 and 3n + 2p = 34. Substituting p = 14 - n into the second equation gives 3n + 2(14 - n) = 34, which simplifies to n + 28 = 34, so n = 6. The correct answer of 6 notebooks satisfies the equations because 6 notebooks cost $18 and 8 pens cost $16, totaling $34 for 14 items. A representative incorrect option like 4 might result from mistakenly assuming equal costs or miscalculating the substitution. Another error, such as choosing 8, could stem from swapping the prices in the equations.

Question 9

If 5x=27\frac{5}{x} = \frac{2}{7}, what is the value of xx?

  1. 107\frac{10}{7}
  2. 145\frac{14}{5}
  3. 352\frac{35}{2} (correct answer)
  4. 710\frac{7}{10}
  5. 514\frac{5}{14}
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is solving a proportion by cross-multiplying or inverting. Given 5/x = 2/7, cross-multiplying gives 2x = 35, so x = 35/2. Alternatively, x = 5 * (7/2) = 35/2. The correct answer of 35/2 satisfies the equation because 5/(35/2) = 5 * 2/35 = 10/35 = 2/7. A representative incorrect option like 14/5 might result from inverting incorrectly. Another error, such as choosing 7/10, could stem from swapping numerator and denominator.

Question 10

What is the value of 34+56\frac{3}{4} + \frac{5}{6}?

  1. 1924\frac{19}{24}
  2. 32\frac{3}{2}
  3. 712\frac{7}{12}
  4. 1912\frac{19}{12} (correct answer)
  5. 1124\frac{11}{24}
Explanation: This is a Multiple Choice, Select One GRE Quantitative problem that tests fraction addition with different denominators. The core principle requires finding a common denominator before adding fractions. To add 3/4 + 5/6, we first find the least common denominator, which is 12. Converting: 3/4 = 9/12 and 5/6 = 10/12. Therefore, 3/4 + 5/6 = 9/12 + 10/12 = 19/12. The correct answer is 19/12 because it represents the sum in its simplest form as an improper fraction. Answer choice A (19/24) incorrectly assumes 24 as the common denominator without properly converting the fractions, yielding 18/24 + 20/24 = 38/24, which doesn't equal 19/24.

Question 11

A right circular cylinder has radius 3 centimeters and height 10 centimeters. What is the volume of the cylinder, in cubic centimeters? (Use π\pi in your answer.)

  1. 30π30\pi
  2. 60π60\pi
  3. 90π90\pi (correct answer)
  4. 180π180\pi
  5. 300π300\pi
Explanation: This is a Multiple Choice, Select One GRE Quantitative problem that tests the volume formula for cylinders. The core principle is that the volume of a cylinder equals π times the radius squared times the height: V = πr²h. With radius r = 3 cm and height h = 10 cm, we calculate: V = π × 3² × 10 = π × 9 × 10 = 90π cubic centimeters. The correct answer is 90π because it correctly applies the cylinder volume formula with the given dimensions. Answer choice E (300π) might result from using diameter instead of radius, calculating π × 6² × 10 = 360π, or making another computational error.

Question 12

A value is increased by 25%, then decreased by 25%. The result is 90. What was the original value?

  1. 96 (correct answer)
  2. 100
  3. 120
  4. 90
Explanation: Let the original value be x. Increasing by 25% makes it 1.25x, then decreasing by 25% makes it 0.75(1.25x) = 0.9375x. Since that equals 90, x = 90 / 0.9375 = 96. A common trap is 90, thinking the increase and decrease cancel, but the decrease applies to the larger increased amount.

Question 13

If nn is a positive integer and n2n^2 is divisible by 6, what is the greatest integer that must divide nn?

  1. 12
  2. 2
  3. 3
  4. 6 (correct answer)
Explanation: Since n^2 is divisible by 6, it contains at least one factor 2 and one factor 3. In a square, prime factors appear in pairs, so n itself must contain at least one 2 and one 3. Therefore 6 must divide n. The tempting wrong answer is 12: n = 6 makes n^2 divisible by 6, but 12 does not divide 6, so 12 is not guaranteed.

Question 14

3 bagels and 4 muffins cost $15; 4 bagels and 3 muffins cost $13. What is the cost of one muffin?

  1. $1
  2. $3 (correct answer)
  3. $2
  4. $4
Explanation: Comparing the two purchases, the first has one extra muffin and one fewer bagel and costs $2 more, so a muffin costs $2 more than a bagel. If a bagel is b, the muffin is b + 2; then 3b + 4(b + 2) = 15 gives b = 1, so the muffin costs $3. Don't stop at $1; that is the bagel's cost, not the muffin's.

Question 15

A and B together can finish a job in 6 days; A alone can finish it in 10 days. How many days would B alone need?

  1. 8
  2. 16
  3. 15 (correct answer)
  4. 4
Explanation: Together A and B complete 1/6 of the job per day. A alone completes 1/10 per day, so B completes 1/6 - 1/10 = 1/15 of the job per day. Thus B alone needs 15 days. The tempting wrong answer is 4 days, but that just subtracts 10 - 6; rates add, not completion times.

Question 16

A rectangle has perimeter 28 and area 48. If its length is greater than its width, what is the length?

  1. 7
  2. 8 (correct answer)
  3. 6
  4. 14
Explanation: From perimeter, length + width = 14. From area, the two positive numbers with sum 14 and product 48 are 6 and 8. Since length is greater than width, the length is 8. The tempting 6 is only the width, not the answer.

Question 17

A line in the coordinate plane passes through the points (2,5)(2,5) and (6,13)(6,13). What is the slope of the line?

  1. 1
  2. 2 (correct answer)
  3. 12\frac{1}{2}
  4. 48\frac{4}{8}
  5. 84\frac{8}{4}
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is calculating the slope of a line using the formula (y2 - y1)/(x2 - x1). For points (2,5) and (6,13), slope = (13 - 5)/(6 - 2) = 8/4 = 2. This measures the rate of change. The correct answer of 2 satisfies the formula because the rise over run is 8 over 4. A representative incorrect option like 1/2 might result from inverting the fraction. Another error, such as choosing 19/20, could stem from using wrong coordinates.

Question 18

A car travels 120 miles at an average speed of 48 miles per hour and then travels another 60 miles at an average speed of 30 miles per hour. What is the car's average speed, in miles per hour, for the entire 180-mile trip?

  1. 36
  2. 38
  3. 40 (correct answer)
  4. 42
  5. 44
Explanation: This is a Multiple Choice, Select One GRE Quant problem. It involves calculating average speed as total distance divided by total time, not the arithmetic mean of speeds. The time for the first 120 miles at 48 mph is 120/48 = 2.5 hours, and for the next 60 miles at 30 mph is 60/30 = 2 hours, for a total time of 4.5 hours. The average speed is then total distance 180 miles divided by 4.5 hours, equaling 40 mph. The value 40 satisfies the requirements because it correctly accounts for the different times spent at each speed over the entire 180-mile trip. A representative incorrect option like 39, though not listed, or approximating to 38 (choice B) might result from an arithmetic slip, such as averaging the speeds directly (48 + 30)/2 = 39 without weighting by distance. This fails because it does not consider the longer time spent at the slower speed.

Question 19

A cube has volume 125 cubic units. What is the surface area of the cube, in square units?

  1. 25
  2. 75
  3. 100
  4. 150 (correct answer)
  5. 250
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is relating volume to side length and then to surface area for a cube. Volume 125 = s³, so s = 5; surface area = 6s² = 625 = 150. This uses the cube root and squaring. The correct answer of 150 satisfies the calculations because 5³ = 125 and 625 = 150. A representative incorrect option like 100 might result from using 4 sides instead of 6. Another error, such as choosing 75, could stem from halving the area mistakenly.

Question 20

In a certain class, the ratio of juniors to seniors is 5:35:3. If there are 48 students total in the class, how many seniors are in the class?

  1. 15
  2. 18 (correct answer)
  3. 20
  4. 24
  5. 30
Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is using ratios to divide a total into parts. The ratio of juniors to seniors is 5:3, so total parts are 5 + 3 = 8, and with 48 students, each part is 48 / 8 = 6. Seniors are then 3 parts, or 3 * 6 = 18. The correct answer of 18 satisfies the ratio because 30 juniors and 18 seniors give 5:3 and total 48. A representative incorrect option like 20 might result from misdividing the total or assuming equal parts. Another error, such as choosing 24, could stem from inverting the ratio accidentally.