GMAT Problem Solving (PS) Forum - Free Practice Questions

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Complete 1000 GMAT Problem Solving Series (PS-1000 Series) Questions

Bunuel

03 Dec 2022, 14:23

321

12

151,990

by: ekfdskfe

13 Jul 2025, 19:03

ER

100 Hardest and easiest questions for PS as of March 2026

Bunuel

01 Jan 2026, 05:45

1.1k

8

312,416

by: Shashankksharma

17 Apr 2026, 02:55

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GMAT PS Question Directory by Topic & Difficulty

bb

16 Apr 2026, 14:28

3.3k

0

1,383,917

by: bb

16 Apr 2026, 14:28

ER

If z = 3^4, then (3^z)^z =

Sub 505 (Easy) | Exponents

Sub 505 (Easy) | Exponents hide tags

Bunuel

15 Jul 2018, 08:27

9

4

3,927

by: bumpbot

18 Oct 2025, 04:25

ER

What is the value of the smallest positive integer n for which 6^n is

555-605 (Medium) | Exponents, Multiples and Factors

555-605 (Medium) | Exponents, Multiples and Factors hide tags

Bunuel

29 Nov 2018, 00:34

6

3

5,907

by: culpaquam

16 Oct 2025, 10:40

ER

How many values of x satisfy

555-605 (Medium) | Algebra, Exponents

555-605 (Medium) | Algebra, Exponents hide tags

GMATNinja

12 Feb 2024, 09:47

19

4

3,707

by: Demonicgod

15 Oct 2025, 19:18

ER

(17*19*23*29)^{31} = n. Lowering which of the following numbers by one

705-805 (Hard) | Exponents

705-805 (Hard) | Exponents hide tags

Bunuel

20 Jul 2017, 21:56

73

11

6,824

by: bumpbot

15 Oct 2025, 17:32

ER

What is the largest prime factor of the expression 3^8 − 2^12?

705-805 (Hard) | Exponents +2 tags

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Bunuel

10 Aug 2018, 03:24

46

9

8,047

by: bumpbot

15 Oct 2025, 12:28

ER

If N is the product of all multiples of 10 between 199 and 301, what i

805+ (Hard) | Exponents +2 tags

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Bunuel

06 Apr 2021, 12:00

37

9

12,404

by: bumpbot

14 Oct 2025, 02:52

ER

If n is a positive integer, then (-2^n)^{-2} + (2^{-n})^2 is equal to

655-705 (Hard) | Exponents

655-705 (Hard) | Exponents hide tags

lpetroski

07 Dec 2022, 11:05

566

13

99,947

by: egmat

14 Oct 2025, 02:45

ER

Which of the following is equal to 21^2 + 22^2 + 23^2 + 24^2 + 25^2 +

555-605 (Medium) | Arithmetic, Exponents

555-605 (Medium) | Arithmetic, Exponents hide tags

Bunuel

25 Apr 2016, 04:05

23

2

5,153

by: bumpbot

13 Oct 2025, 09:47

ER

If x and y are positive integers and x^y = y^x + 1, which of the follo

605-655 (Medium) | Exponents, Number Properties

605-655 (Medium) | Exponents, Number Properties hide tags

Bunuel

20 May 2019, 04:50

41

13

10,761

by: DanTheGMATMan

13 Oct 2025, 07:25

ER

If a and b are positive integers and x = 4^a and y = 9^b, which of the

Sub 505 (Easy) | Exponents, Number Properties

Sub 505 (Easy) | Exponents, Number Properties hide tags

Bunuel

23 Oct 2014, 00:50

77

9

19,775

by: bumpbot

13 Oct 2025, 02:43

ER

If 12!/3^x is an integer, what is the greatest possible value of x?

Sub 505 (Easy) | Exponents +2 tags

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Bunuel

28 Feb 2016, 09:13

41

14

15,696

by: gautam25gs

12 Oct 2025, 07:10

ER

If 9^y + 3^b = 10*3^b, then 2y ='

555-605 (Medium) | Algebra, Exponents

555-605 (Medium) | Algebra, Exponents hide tags

Bunuel

05 Jun 2015, 06:13

47

13

11,483

by: HRX273

11 Oct 2025, 16:17

ER

What is the highest integer power of of 2 that can divide (10! + 11!

655-705 (Hard) | Exponents, Multiples and Factors

655-705 (Hard) | Exponents, Multiples and Factors hide tags

Bunuel

10 Oct 2025, 00:06

14

4

1,170

by: Reon

11 Oct 2025, 07:36

ER

If x = 10^50 - 57, what is the sum of all the digits of x?

555-605 (Medium) | Exponents, Number Properties

555-605 (Medium) | Exponents, Number Properties hide tags

interceptor77

01 Nov 2016, 03:33

50

9

6,928

by: Ishaan30

11 Oct 2025, 03:57

ER

If 2^13*9^7 = 3(6^k), what is the value of k?

Sub 505 (Easy) | Exponents

Sub 505 (Easy) | Exponents hide tags

Bunuel

05 Oct 2021, 02:00

2

3

1,956

by: bumpbot

08 Oct 2025, 13:03

ER

If 2^k = 3, then 2^(3k+2) =

555-605 (Medium) | Exponents

555-605 (Medium) | Exponents hide tags

Bunuel

01 Apr 2015, 04:25

34

8

19,876

by: bumpbot

08 Oct 2025, 12:18

ER

Suppose that x = -2 is the only number that satisfices 2^x^2 + Bx

505-555 (Easy) | Algebra, Exponents

505-555 (Easy) | Algebra, Exponents hide tags

Bunuel

07 Aug 2023, 06:00

89

5

22,483

by: etperferendis

08 Oct 2025, 11:37

ER

What is the remainder when 8^1+ 8^2+ 8^3 + ... + 8^15 is divided by 6?

655-705 (Hard) | Exponents, Remainders

655-705 (Hard) | Exponents, Remainders hide tags

Bunuel

16 Nov 2021, 03:45

39

5

4,275

by: bumpbot

08 Oct 2025, 00:05

ER

What is the value of (2*2^(1/2))(6^(1/2)) + 2*3^(1/2) ?

Sub 505 (Easy) | Exponents, Roots

Sub 505 (Easy) | Exponents, Roots hide tags

Bunuel

05 Jun 2023, 01:30

8

3

2,609

by: bumpbot

07 Oct 2025, 08:59

ER

What the remainder when 2^96 is divided by 96?

705-805 (Hard) | Exponents, Remainders

705-805 (Hard) | Exponents, Remainders hide tags

Bunuel

21 Feb 2020, 06:16

62

6

17,609

by: bumpbot

07 Oct 2025, 03:59

ER

If (2^2x)(3^x−1)(1/4^x−2)(27^1/x)=(6^x+2)(1/2)(9^x−4), find x?

655-705 (Hard) | Algebra, Exponents

655-705 (Hard) | Algebra, Exponents hide tags

buan15

28 Jul 2020, 23:39

27

5

7,180

by: bumpbot

07 Oct 2025, 03:55

ER

What is the remainder when 25^25 is divided by 9?

605-655 (Medium) | Exponents, Remainders

605-655 (Medium) | Exponents, Remainders hide tags

Bunuel

21 Feb 2020, 06:13

129

18

25,897

by: bumpbot

07 Oct 2025, 03:53

ER

What is the remainder when (1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is

705-805 (Hard) | Exponents +2 tags

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Bunuel

01 May 2021, 09:00

52

4

5,508

by: bumpbot

06 Oct 2025, 23:36

ER

If k is a positive integer and 269!/2^k is a positive integer, what is

655-705 (Hard) | Exponents, Number Properties

655-705 (Hard) | Exponents, Number Properties hide tags

Bunuel

21 Mar 2023, 01:30

31

3

3,199

by: bumpbot

06 Oct 2025, 14:16

ER

If A = (1 + 1/3)(1 + 1/3^2)(1 + 1/3^4)(1 + 1/3^8), what is 1 - 2/3*A?

705-805 (Hard) | Algebra, Exponents

705-805 (Hard) | Algebra, Exponents hide tags

Bunuel

28 Mar 2023, 07:45

31

3

2,961

by: bumpbot

06 Oct 2025, 12:35

ER

If the product of 6 distinct positive integers is 6^6. What is the min

805+ (Hard) | Exponents +2 tags

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Bunuel

20 Apr 2020, 05:32

64

10

11,850

by: bumpbot

05 Oct 2025, 19:46

ER

If 2^(a + 3) = 4^(a + 2) - 48, then the value of a is

655-705 (Hard) | Exponents

655-705 (Hard) | Exponents hide tags

Bunuel

21 Dec 2021, 02:30

18

5

5,572

by: bumpbot

05 Oct 2025, 08:26

ER

If a and b are integers and (2^a)(3^b) is a factor of 100^40, what is

555-605 (Medium) | Exponents, Multiples and Factors

555-605 (Medium) | Exponents, Multiples and Factors hide tags

Bunuel

28 Apr 2016, 16:59

19

6

6,568

by: bumpbot

05 Oct 2025, 07:40

ER

What could be the value of n

605-655 (Medium) | Exponents, Inequalities

605-655 (Medium) | Exponents, Inequalities hide tags

MHIKER

18 Nov 2020, 05:46

63

11

8,704

by: bumpbot

05 Oct 2025, 05:07

ER

If x < y, and y(y − 2x) = 2 − x^2, what is the value of x − y?

655-705 (Hard) | Algebra, Exponents

655-705 (Hard) | Algebra, Exponents hide tags

Bunuel

01 May 2021, 07:45

21

8

7,285

by: bumpbot

05 Oct 2025, 02:25

ER

If 8^5*4^6/16^n = 32^(1-n), then n =

555-605 (Medium) | Exponents

555-605 (Medium) | Exponents hide tags

Bunuel

01 Apr 2015, 04:21

7

6

10,766

by: bumpbot

05 Oct 2025, 02:17

ER

For integers x, y, and z, if ((2^x)^y)^z = 131072 which of

655-705 (Hard) | Exponents, Number Properties

655-705 (Hard) | Exponents, Number Properties hide tags

joylive

12 Oct 2025, 10:36

84

15

15,416

by: bumpbot

04 Oct 2025, 12:22

ER

If x and n are integers and x^(n + 2) = 16x^2, what is the least possi

655-705 (Hard) | Exponents

655-705 (Hard) | Exponents hide tags

Bunuel

19 Feb 2019, 23:29

7

4

2,597

by: bumpbot

04 Oct 2025, 11:07

ER

If 25^5*4^6 = 10^x + a, and x is an integer, what could be the minimum

655-705 (Hard) | Exponents, Number Properties

655-705 (Hard) | Exponents, Number Properties hide tags

Bunuel

14 Jun 2021, 02:15

23

6

6,387

by: bumpbot

04 Oct 2025, 06:44

ER

If a and b are integers and 5^a - 5^a-2 = 75*2^b, what is the value of

605-655 (Medium) | Exponents

605-655 (Medium) | Exponents hide tags

Bunuel

10 Feb 2023, 14:55

32

4

4,575

by: bumpbot

04 Oct 2025, 03:48

ER

If x^x = 2^2048, what is the value of x?

605-655 (Medium) | Exponents

605-655 (Medium) | Exponents hide tags

Bunuel

01 Jan 2022, 04:42

13

4

30,244

by: bumpbot

04 Oct 2025, 02:49

ER

(R^c)(R^d)(R^e) = R^(-12). If R>0, and c, d, and e are each different

605-655 (Medium) | Exponents, Min-Max Problems

605-655 (Medium) | Exponents, Min-Max Problems hide tags

Bunuel

28 Feb 2022, 03:15

12

5

4,440

by: bumpbot

03 Oct 2025, 09:45

ER

3(4^5+4^6+4^7+4^8+4^9+4^10)/(2^5+2^6+2^7+2^8+2^9+2^10)

705-805 (Hard) | Arithmetic, Exponents

705-805 (Hard) | Arithmetic, Exponents hide tags

alinomoto

22 Jul 2024, 09:32

68

9

10,220

by: bumpbot

03 Oct 2025, 01:30

ER

What is the greatest value of x such that 6^x is a factor of 10! ?

555-605 (Medium) | Exponents, Multiples and Factors

555-605 (Medium) | Exponents, Multiples and Factors hide tags

Bunuel

10 Dec 2016, 06:14

10

4

4,825

by: Demonicgod

02 Oct 2025, 19:48

ER

If 8^(1/2) = 4^x, what is the value of x?

505-555 (Easy) | Exponents

505-555 (Easy) | Exponents hide tags

Bunuel

22 Jun 2017, 07:49

10

15

3,803

by: Demonicgod

02 Oct 2025, 19:41

ER

If 75^y*27^(2y + 1) = 5^4*3^x, what is the value of x?

555-605 (Medium) | Algebra, Exponents

555-605 (Medium) | Algebra, Exponents hide tags

Bunuel

25 Apr 2017, 02:39

30

5

5,540

by: bumpbot

02 Oct 2025, 11:13

ER

If a, b, and c are positive consecutive odd integers, what is the

655-705 (Hard) | Exponents, Number Properties

655-705 (Hard) | Exponents, Number Properties hide tags

Bunuel

06 Oct 2022, 01:30

34

6

4,883

by: bumpbot

02 Oct 2025, 05:20

ER

If a and b are integers and (a*b)^5 = 96y, y could be:

505-555 (Easy) | Algebra, Exponents

505-555 (Easy) | Algebra, Exponents hide tags

Bunuel

23 Jan 2015, 07:14

63

17

16,735

by: bumpbot

01 Oct 2025, 14:47

ER

If N = 2^0.15 and N^b = 16, b must equal

505-555 (Easy) | Exponents

505-555 (Easy) | Exponents hide tags

Bunuel

01 Oct 2025, 10:07

11

9

6,529

by: bumpbot

01 Oct 2025, 10:06

ER

2^x + 2^(x + 3) = (6^2)(2^18). What is the value of x?

505-555 (Easy) | Exponents

505-555 (Easy) | Exponents hide tags

Bunuel

28 Dec 2016, 11:08

20

7

5,562

by: bumpbot

01 Oct 2025, 09:43

ER

If 3^x – 3^(x – 1) =2(3^13), what is x?

505-555 (Easy) | Algebra, Exponents

505-555 (Easy) | Algebra, Exponents hide tags

Bunuel

25 Apr 2017, 02:45

41

5

6,562

by: bumpbot

01 Oct 2025, 05:51

ER

For how many integers k is k^3 = 3^k ?

555-605 (Medium) | Exponents

555-605 (Medium) | Exponents hide tags

Bunuel

02 Nov 2021, 08:00

2

5

1,944

by: bumpbot

30 Sep 2025, 09:32

ER

If 2^n = 128, then 2^(n - 1)*5^(n - 2) =

505-555 (Easy) | Exponents

505-555 (Easy) | Exponents hide tags

Bunuel

11 Mar 2019, 00:13

5

4

3,923

by: bumpbot

30 Sep 2025, 05:04

ER

5(2^4)(3^32) =

605-655 (Medium) | Exponents

605-655 (Medium) | Exponents hide tags

mikemcgarry

16 Jan 2015, 11:33

45

8

7,987

by: bumpbot

30 Sep 2025, 01:55

ER

Which of the following numbers is prime?

555-605 (Medium) | Exponents, Number Properties

555-605 (Medium) | Exponents, Number Properties hide tags

1, 2

honchos

01 Mar 2014, 23:56

515

26

33,668

by: CapedCrusader09

29 Sep 2025, 23:41