GRE Quantitative Quiz: Multiple Choice Single Answer

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.

Question 1

1. $\sqrt{42}$
2. $\sqrt{58}$
3. $3\sqrt{2}$ (correct answer)
4. $5\sqrt{2}$
5. $7\sqrt{2}$

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

1. $-3$
2. $3$
3. $5$
4. $-5$ (correct answer)
5. $9$

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

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. 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

1. $24$ (correct answer)
2. $40$
3. $32$
4. $20$
5. $28$

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

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

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

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 $2,240 because it accurately reflects a 12$2,120) incorrectly calculates only 6% increase instead of 12%, giving $2,000 × 1.06 = $2,120.

Question 8

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

1. $\frac{10}{7}$
2. $\frac{14}{5}$
3. $\frac{35}{2}$ (correct answer)
4. $\frac{7}{10}$
5. $\frac{5}{14}$

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

1. $\frac{19}{24}$
2. $\frac{3}{2}$
3. $\frac{7}{12}$
4. $\frac{19}{12}$ (correct answer)
5. $\frac{11}{24}$

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

1. $30\pi$
2. $60\pi$
3. $90\pi$ (correct answer)
4. $180\pi$
5. $300\pi$

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

1. 1
2. 2 (correct answer)
3. $\frac{1}{2}$
4. $\frac{4}{8}$
5. $\frac{8}{4}$

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 13

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 14

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 15

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.

Question 16

1. $\sqrt{32}$
2. $2\sqrt{2}$ (correct answer)
3. $\sqrt{8}$
4. $\sqrt{2}$
5. $4\sqrt{2}$

Explanation: This is a Multiple Choice, Select One GRE Quant problem requiring simplification of square roots. The key principle is to factor out perfect squares from under the radical sign. We have √50 = √(25×2) = 5√2 and √18 = √(9×2) = 3√2. Therefore, √50 - √18 = 5√2 - 3√2 = 2√2. The Borrect answer B (2√2) properly applies the simplification rules. A common error would be to incorrectly simplify the radicals, such as writing √50 as 25√2 or attempting to subtract the numbers under the radicals before simplifying.

Question 17

1. $\frac{24}{7}$ (correct answer)
2. $\frac{7}{24}$
3. $\frac{14}{3}$
4. $\frac{48}{7}$
5. 7

Explanation: This is a Multiple Choice, Select One GRE Quantitative Reasoning problem. The core quantitative principle involved is combining work rates to find the time for joint effort in filling a tank. Pipe A fills at 1/6 tank per hour and Pipe B at 1/8 tank per hour, so together they fill (1/6 + 1/8) = (4/24 + 3/24) = 7/24 tank per hour. The time to fill one tank is then 1 / (7/24) = 24/7 hours. The correct answer of 24/7 satisfies the requirements because it is the reciprocal of the combined rate. A representative incorrect option like 7/24 might result from forgetting to take the reciprocal after adding rates. Another error, such as choosing 48/7, could stem from doubling the rates incorrectly.

Question 18

1. $-2$
2. $-6$
3. $0$
4. $2$ (correct answer)
5. $6$

Explanation: This is a Multiple Choice, Select One GRE Quant problem testing function evaluation. The core principle is to substitute the given value into the function and evaluate according to the order of operations. Given f(x) = x² - 5x + 6, we calculate f(4) = 4² - 5(4) + 6 = 16 - 20 + 6 = 2. The Dorrect answer D (2) results from proper substitution and arithmetic. A common error would be to make a sign error or incorrectly apply the order of operations, such as calculating 4² as 8 instead of 16, which might lead to answer A (-2).

Question 19

1. $\frac{2}{3}$
2. $\frac{2}{5}$ (correct answer)
3. $\frac{1}{4}$
4. $\frac{3}{5}$
5. $\frac{4}{6}$

Explanation: This is a Multiple Choice, Select One GRE Quant problem involving basic probability. The core principle is that probability equals the number of favorable outcomes divided by the total number of possible outcomes. The bag contains 6 red marbles and 4 blue marbles, giving a total of 10 marbles. The probability of selecting a blue marble is 4/10, which simplifies to 2/5. The Borrect answer B (2/5) satisfies this calculation perfectly. A common error would be to calculate the probability of red marbles (6/10 = 3/5) instead of blue marbles, or to incorrectly simplify the fraction.

Question 20

1. $240$
2. $80$
3. $60$ (correct answer)
4. $20$
5. $40$

Explanation: This is a Multiple Choice, Select One GRE Quant problem involving percentage calculations. The fundamental principle is that to find a percentage of a quantity, multiply the quantity by the percentage expressed as a decimal. The mixture is 20% sugar by volume, and the total volume is 300 milliliters. Therefore, the volume of sugar is 0.20 × 300 = 60 milliliters. The Correct answer C (60) satisfies this calculation. A common mistake would be to calculate 80% of 300 (giving 240) by confusing the sugar percentage with the water percentage, or to divide 300 by 20 instead of multiplying by 0.20.