50 GRE Quant Practice Questions with Answers (Free PDF)

How to Use This Set

Work through all 50 questions before checking the answer key.
A basic calculator is allowed for the actual GRE, so feel free to use one here too — but try mental math first to build speed.
Answers and full explanations are in the Answer Key section at the end.

Part 1 — Quantitative Comparison (Questions 1–15)

For each question, compare Quantity A and Quantity B and choose:

(A) Quantity A is greater
(B) Quantity B is greater
(C) The two quantities are equal
(D) The relationship cannot be determined from the information given

1. $x > 0$

Quantity A	Quantity B
$x^2$	$x^3$

Quantity A	Quantity B
$\dfrac{3}{7}$	$0.43$

3. $n$ is a positive integer.

Quantity A	Quantity B
$(-1)^n \cdot n$	$0$

4. A circle has radius $5$ .

Quantity A	Quantity B
Area of the circle	$75$

5. $x + y = 10$ , and $x > y > 0$ .

Quantity A	Quantity B
$x$	$6$

Quantity A	Quantity B
$\sqrt{50}$	$7$

7. The perimeter of a rectangle is $20$ , and the length is twice the width.

Quantity A	Quantity B
The area of the rectangle	$20$

8. Set $S$ consists of $5$ consecutive integers whose sum is $40$ .

Quantity A	Quantity B
The median of $S$	$8$

9. $p$ is a prime number greater than $2$ .

Quantity A	Quantity B
$p$	$3$

10.

Quantity A	Quantity B
$2^{10}$	$10^2 \times 10$

11. In a triangle, two of the sides have lengths $7$ and $10$ .

Quantity A	Quantity B
The length of the third side	$3$

12. $x$ is an integer and $-3 < x < 3$ .

Quantity A	Quantity B
The number of possible values of $x$	$5$

13. A data set consists of $5, 10, 15, 20, 25$ .

Quantity A	Quantity B
The average (arithmetic mean) of the set	The median of the set

14. $y = |x - 3|$ for all real numbers $x$ .

Quantity A	Quantity B
The value of $y$ when $x = 1$	The value of $y$ when $x = 5$

15. Two fair six-sided dice are rolled.

Quantity A	Quantity B
The probability that the sum of the two dice is $7$	$\dfrac{1}{6}$

Part 2 — Multiple Choice: Select One Answer (Questions 16–40)

16. If $3x - 7 = 2x + 5$ , what is the value of $x$ ?

A) 5 B) 7 C) 10 D) 12 E) 17

17. If 5 pencils cost $2.50, what is the cost of 12 pencils at the same rate?

A) $5.00 B)$ 5.50 C) $6.00 D)$ 6.50 E) $7.00

18. What is 15 percent of 240?

A) 24 B) 30 C) 36 D) 40 E) 48

19. If $x^2 = 49$ , what is the product of all possible values of $x$ ?

A) $-49$ B) $-7$ C) $0$ D) $7$ E) $49$

20. Simplify: $\dfrac{3^4 \cdot 3^2}{3^3}$

A) 3 B) 9 C) 27 D) 81 E) 243

21. The average of 4 numbers is 20. If one of the numbers is removed, the average of the remaining 3 numbers is 18. What is the value of the number that was removed?

A) 18 B) 20 C) 22 D) 26 E) 28

22. Solve for $x$ : $\dfrac{2x}{3} = 8$

A) 4 B) 6 C) 8 D) 10 E) 12

23. A car travels 240 miles in 4 hours at a constant rate. At the same rate, how long will it take to travel 360 miles?

A) 5 hr B) 5.5 hr C) 6 hr D) 6.5 hr E) 7 hr

24. If $m$ and $n$ are positive integers and $mn = 36$ , what is the greatest possible value of $m + n$ ?

A) 13 B) 15 C) 20 D) 36 E) 37

25. What is the least positive integer divisible by both 8 and 12?

A) 16 B) 20 C) 24 D) 32 E) 48

26. If $f(x) = 2x^2 - 3x + 1$ , what is $f(2)$ ?

A) 1 B) 2 C) 3 D) 5 E) 7

27. Simplify $\sqrt{72}$ .

A) $6\sqrt{2}$ B) $8\sqrt{3}$ C) $12\sqrt{2}$ D) $6\sqrt{3}$ E) $3\sqrt{8}$

28. A store marks up its cost by 40 percent to set the retail price. If the retail price of an item is $84, what was the store's cost?

A) $50 B)$ 54 C) $58 D)$ 60 E) $64

29. In a class of 30 students, the ratio of boys to girls is 2 : 3. How many girls are in the class?

A) 10 B) 12 C) 15 D) 18 E) 20

30. $x$ is inversely proportional to $y$ . If $x = 8$ when $y = 3$ , what is $x$ when $y = 12$ ?

A) 1 B) 2 C) 3 D) 4 E) 6

31. What is the sum of the interior angles of a hexagon?

A) 360° B) 540° C) 720° D) 900° E) 1080°

32. If $a = 3$ and $b = -2$ , what is the value of $a^2 - b^3$ ?

A) 1 B) 5 C) 13 D) 17 E) 25

33. A jar contains 5 red, 4 blue, and 3 green marbles. If one marble is drawn at random, what is the probability that it is blue?

A) $\frac{1}{4}$ B) $\frac{1}{3}$ C) $\frac{3}{8}$ D) $\frac{5}{12}$ E) $\frac{1}{2}$

34. What is the sum of all solutions to $|2x - 5| = 9$ ?

A) $-2$ B) $2$ C) $5$ D) $7$ E) $9$

35. The perimeter of a square is 48. What is the length of its diagonal?

A) 12 B) $12\sqrt{2}$ C) 24 D) $6\sqrt{2}$ E) 48

36. Working alone, Machine A can complete a job in 6 hours; Machine B can complete the same job alone in 3 hours. Working together at their individual rates, how long will it take them to complete the job?

A) 1 hr B) 1.5 hr C) 2 hr D) 2.5 hr E) 4.5 hr

37. What is the value of $\dfrac{7!}{5!}$ ?

A) 2 B) 7 C) 21 D) 42 E) 5040

38. The ratio of $x$ to $y$ is 5 : 4, and $x + y = 63$ . What is the value of $y$ ?

A) 24 B) 27 C) 28 D) 32 E) 35

39. A rectangular garden is 3 times as long as it is wide and has a perimeter of 96 feet. What is the width of the garden?

A) 8 ft B) 10 ft C) 12 ft D) 16 ft E) 24 ft

40. What is the slope of the line passing through $(2, -1)$ and $(6, 7)$ ?

A) $\frac{1}{2}$ B) 1 C) 2 D) 3 E) 4

Part 3 — Multiple Choice: Select All That Apply (Questions 41–45)

Each question may have one, several, or all answer choices correct. Select every choice that applies.

41. Which of the following integers are factors of 60?

A) 4 B) 6 C) 9 D) 15 E) 18

42. $x$ is an integer and $3 < x^2 < 50$ . Which of the following could be the value of $x$ ?

A) $-7$ B) $-3$ C) $2$ D) $5$ E) $8$

43. Which of the following fractions are greater than $\dfrac{5}{8}$ ?

A) $\frac{3}{5}$ B) $\frac{7}{10}$ C) $\frac{11}{16}$ D) $\frac{9}{16}$ E) $\frac{4}{5}$

44. A data set has a mean of 50 and a standard deviation of 8. Which of the following values are more than 2 standard deviations from the mean?

A) 30 B) 33 C) 36 D) 66 E) 68

45. If $n$ is a positive integer, which of the following expressions must be even?

A) $2n$ B) $n^2 + n$ C) $4n + 3$ D) $n(n+1)$ E) $3n$

Part 4 — Numeric Entry (Questions 46–50)

Enter your answer as an integer, decimal, or fraction, as instructed.

46. If $4x - 9 = 15$ , what is the value of $x$ ?

Answer: __________

47. A recipe requires $\dfrac{2}{3}$ cup of flour to make 8 muffins. How many cups of flour are needed to make 20 muffins, assuming the ratio of flour to muffins stays constant? (Enter your answer as a fraction.)

Answer: __________

48. The average (arithmetic mean) of six numbers is 15. If the average of four of these numbers is 12, what is the average of the remaining two numbers?

Answer: __________

49. What is the greatest common factor of 84 and 126?

Answer: __________

50. A bag contains only red and blue chips, in a ratio of red to blue of $3:5$ . If there are 24 red chips in the bag, how many chips are in the bag in total?

Answer: __________

Answer Key & Explanations

Part 1 — Quantitative Comparison

#	Answer	Explanation
1	D	If $0 < x < 1$ (e.g., $x=0.5$ ), $x^2 > x^3$ . If $x > 1$ (e.g., $x=2$ ), $x^3 > x^2$ . Relationship varies.
2	B	$\frac{3}{7} \approx 0.4286$ , which is less than $0.43$ .
3	D	If $n$ is even, $(-1)^n \cdot n = n > 0$ . If $n$ is odd, $(-1)^n \cdot n = -n < 0$ .
4	A	Area $= 25\pi \approx 78.5$ , which is greater than $75$ .
5	D	$x$ can range anywhere from just above $5$ to just below $10$ (since $x>y>0$ and $x+y=10$ ), so $x$ could be less than, equal to, or greater than $6$ .
6	A	$\sqrt{50} \approx 7.07 > 7$ .
7	A	With $l = 2w$ : $2(w + 2w) = 20 \Rightarrow w = \frac{10}{3}$ , $l = \frac{20}{3}$ . Area $= \frac{200}{9} \approx 22.2 > 20$ .
8	C	For 5 consecutive integers, the sum equals $5 \times \text{median}$ , so median $= 40/5 = 8$ .
9	D	The smallest prime greater than 2 is 3, so $p \geq 3$ . $p$ could equal 3 (equal) or be larger (greater) — not determined.
10	A	$2^{10} = 1024$ ; $10^2 \times 10 = 1000$ . $1024 > 1000$ .
11	A	By the triangle inequality, the third side must satisfy $10 - 7 < \text{side} < 10 + 7$ , i.e., strictly greater than 3.
12	C	Integers strictly between $-3$ and $3$ : $-2, -1, 0, 1, 2$ — exactly 5 values.
13	C	Mean $= (5+10+15+20+25)/5 = 15$ . Median $= 15$ . Equal.
14	C	$
15	C	Sums of 7 on two dice: 6 combinations out of 36, so $6/36 = 1/6$ . Equal.

Part 2 — Multiple Choice (Select One)

#	Answer	Explanation
16	D (12)	$3x - 7 = 2x + 5 \Rightarrow x = 12$ .
17	C ($6.00)	Unit price $=$ 0.50 $;$ 12 \times 0.50 = $6.00$ .
18	C (36)	$0.15 \times 240 = 36$ .
19	A (−49)	Solutions are $7$ and $-7$ ; product $= -49$ .
20	C (27)	$3^{4+2-3} = 3^3 = 27$ .
21	D (26)	Sum of 4 numbers $= 80$ ; sum of remaining 3 $= 54$ ; removed number $= 80-54=26$ .
22	E (12)	$\frac{2x}{3}=8 \Rightarrow x = 12$ .
23	C (6 hr)	Rate $= 60$ mph; $360/60 = 6$ hours.
24	E (37)	To maximize the sum with fixed product, use the most "unequal" factor pair: $1 \times 36$ , sum $= 37$ .
25	C (24)	LCM of 8 and 12 is 24.
26	C (3)	$2(4) - 3(2) + 1 = 8 - 6 + 1 = 3$ .
27	A ( $6\sqrt2$ )	$\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt2$ .
28	D ($60)	$1.4c = 84 \Rightarrow c = 60$ .
29	D (18)	Girls $= \frac{3}{5}\times30 = 18$ .
30	B (2)	$xy = 24$ (constant); $x = 24/12 = 2$ .
31	C (720°)	$(6-2)\times180° = 720°$ .
32	D (17)	$9 - (-8) = 17$ .
33	B (1/3)	$4/12 = 1/3$ .
34	C (5)	$2x-5=9 \Rightarrow x=7$ ; $2x-5=-9 \Rightarrow x=-2$ . Sum $= 5$ .
35	B ( $12\sqrt2$ )	Side $=12$ ; diagonal $=12\sqrt2$ .
36	C (2 hr)	Combined rate $= 1/6+1/3 = 1/2$ job/hr; time $= 2$ hr.
37	D (42)	$7!/5! = 7\times6 = 42$ .
38	C (28)	Total parts $=9$ ; $y = \frac{4}{9}\times63=28$ .
39	C (12 ft)	$2(w+3w)=96 \Rightarrow 8w=96 \Rightarrow w=12$ .
40	C (2)	Slope $=(7-(-1))/(6-2)=8/4=2$ .

Part 3 — Multiple Choice (Select All That Apply)

#	Correct Choices	Explanation
41	A, B, D	Factors of 60 include 4, 6, and 15; 9 and 18 are not factors of 60.
42	A, B, C, D	$(-7)^2=49$ , $(-3)^2=9$ , $2^2=4$ , $5^2=25$ all fall strictly between 3 and 50; $8^2=64$ does not.
43	B, C, E	$5/8 = 0.625$ . $7/10=0.7$ , $11/16=0.6875$ , $4/5=0.8$ are all greater; $3/5=0.6$ and $9/16=0.5625$ are not.
44	A, B, E	2 SD range is $[34, 66]$ . Values more than 2 SD away: $30$ and $33$ (below 34), and $68$ (above 66). $36$ is inside the range; $66$ is exactly 2 SD, not "more than."
45	A, B, D	$2n$ is always even. $n(n+1) = n^2+n$ is a product of consecutive integers, always even. $4n+3$ is always odd. $3n$ is even only when $n$ is even (not guaranteed).

Part 4 — Numeric Entry

#	Answer	Explanation
46	6	$4x - 9 = 15 \Rightarrow 4x = 24 \Rightarrow x = 6$ .
47	5/3	Scale factor $= 20/8 = 2.5$ ; flour $= \frac{2}{3}\times2.5 = \frac{5}{3}$ cups.
48	21	Total sum $=6\times15=90$ ; sum of 4 numbers $=4\times12=48$ ; sum of remaining 2 $=42$ ; average $=21$ .
49	42	$84 = 2^2\cdot3\cdot7$ , $126=2\cdot3^2\cdot7$ ; GCF $=2\cdot3\cdot7=42$ .
50	64	Scale factor $=24/3=8$ ; blue chips $=5\times8=40$ ; total $=24+40=64$ .

Score Yourself

Score	Level
45–50 correct	Excellent — you're testing near the top of the GRE Quant range
35–44 correct	Strong — review the specific topics you missed
25–34 correct	Solid foundation — focus on timed practice and weak areas
Below 25	Build up core arithmetic, algebra, and geometry fundamentals first

This practice set is original content created for study purposes and is not affiliated with or sourced from ETS® or the official GRE® General Test.