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

151,808

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

312,304

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

1,383,524

by: bb

16 Apr 2026, 14:28

ER

What is the highest integer k for which 81^k perfectly divides 300! ?

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

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

ExpertsGlobal5

18 Jan 2026, 22:00

8

3

777

by: RickyMon

27 Jan 2026, 00:41

ER

What is the highest power of 4 that completely divides 110! + 105!?

805+ (Hard) | Multiples and Factors

805+ (Hard) | Multiples and Factors hide tags

gun1234

11 Nov 2024, 05:19

16

3

2,283

by: bumpbot

26 Jan 2026, 07:07

ER

How many factors of 60^2 are multiples of 3 ?

655-705 (Hard) | Multiples and Factors

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

ExpertsGlobal5

18 Jan 2026, 22:00

13

7

803

by: impeditrem

26 Jan 2026, 01:57

ER

If x is a product of 4 consecutive integers, and x is

655-705 (Hard) | Multiples and Factors

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

jackfr2

24 Oct 2019, 10:57

24

4

10,486

by: bumpbot

25 Jan 2026, 12:07

ER

K = 10^26 + 2^26, and K is a multiple of 2^n but NOT a multiple of 2

705-805 (Hard) | Exponents, Multiples and Factors

705-805 (Hard) | Exponents, Multiples and Factors hide tags

BrentGMATPrepNow

12 Aug 2020, 09:32

48

8

5,892

by: bumpbot

25 Jan 2026, 10:24

ER

How many positive divisors of 6,300 have a units digit of 5?

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

kevincan

05 Mar 2026, 23:25

5

4

458

by: Siddharth17

25 Jan 2026, 08:25

ER

How many factors of 72^2 are multiples of 6 ?

655-705 (Hard) | Multiples and Factors

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

ExpertsGlobal5

22 Jan 2026, 22:00

7

3

597

by: ExpertsGlobal5

24 Jan 2026, 10:30

ER

X is the smallest integer that has three different factors greater

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

ExpertsGlobal5

20 Jan 2026, 22:00

5

2

579

by: ExpertsGlobal5

24 Jan 2026, 06:15

ER

If P is a positive integer and Q = 120P 60, which of the following

Sub 505 (Easy) | Multiples and Factors, Must or Could be True

Sub 505 (Easy) | Multiples and Factors, Must or Could be True hide tags

ExpertsGlobal5

19 Jan 2026, 22:00

3

5

603

by: ExpertsGlobal5

24 Jan 2026, 04:15

ER

How many prime numbers between 25 and 125 are factors of 723609?

805+ (Hard) | Multiples and Factors

805+ (Hard) | Multiples and Factors hide tags

Bunuel

23 May 2024, 01:30

36

4

3,467

by: laborumplaceat

24 Jan 2026, 02:53

ER

If n is a 27-digit positive integer, all of whose digits are the same,

555-605 (Medium) | Multiples and Factors

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

Bunuel

13 Feb 2020, 07:36

18

6

4,495

by: bumpbot

23 Jan 2026, 05:34

ER

A number N^2 has 35 factors. How many factors can N have?

605-655 (Medium) | Multiples and Factors

605-655 (Medium) | Multiples and Factors hide tags

Mahmud6

20 Oct 2017, 05:07

58

5

20,450

by: bumpbot

23 Jan 2026, 03:11

ER

For the positive integers a, b, and k, a^k||b means that a^k

505-555 (Easy) | Exponents +3 tags

505-555 (Easy) | Exponents, Functions and Custom Characters, Multiples and Factors, Number Properties hide tags

1, 2

Walkabout

12 Dec 2012, 03:59

392

22

87,848

by: egmat

22 Jan 2026, 23:08

ER

If a and b are positive integers, which of the following CANNOT be the

655-705 (Hard) | Multiples and Factors

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

Aabhash777

17 Nov 2022, 01:48

10

6

4,358

by: egmat

22 Jan 2026, 22:56

ER

For the positive integers a, b, and k, a^k ? b

555-605 (Medium) | Multiples and Factors

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

GMATBusters

13 Apr 2020, 11:56

5

3

2,792

by: bumpbot

22 Jan 2026, 10:50

ER

p, q, and r are positive integers. If p, q, and r are assembled into

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

Bunuel

24 Jan 2022, 08:15

31

6

4,025

by: bumpbot

22 Jan 2026, 09:03

How many positive integers k are there in the range 10 k 30, such

555-605 (Medium) | Multiples and Factors

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

dolorprovident

16 Jan 2026, 06:15

1

328

by: Kinshook

22 Jan 2026, 03:58

ER

How many integers from 1 to 100 (both inclusive) have odd number of

655-705 (Hard) | Multiples and Factors, Number Properties

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

GMATinsight

15 Jul 2015, 18:32

33

13

16,534

by: bumpbot

22 Jan 2026, 00:24

ER

How many odd integers from 1 to 200 (both inclusive) have odd number o

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

GMATinsight

15 Jul 2015, 20:43

17

10

9,156

by: bumpbot

22 Jan 2026, 00:09

ER

The least common multiple of two numbers is 1820 and their highest com

505-555 (Easy) | Multiples and Factors

505-555 (Easy) | Multiples and Factors hide tags

Bunuel

06 Aug 2021, 04:15

6

3

2,044

by: bumpbot

21 Jan 2026, 11:43

ER

For which of the following values of n is (100+n)/n NOT an

Sub 505 (Easy) | Arithmetic +2 tags

Sub 505 (Easy) | Arithmetic, Multiples and Factors, Number Properties hide tags

Bunuel

23 Jul 2012, 04:19

86

19

61,802

by: Mosaib

20 Jan 2026, 21:37

ER

The 180 students in a group are to be seated in rows so that

Sub 505 (Easy) | Multiples and Factors

Sub 505 (Easy) | Multiples and Factors hide tags

sarb

29 Jun 2012, 03:30

125

18

59,599

by: joshishr

20 Jan 2026, 06:05

ER

What is the biggest number that always divides the product of three co

555-605 (Medium) | Multiples and Factors

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

GMATinsight

08 Jun 2017, 05:38

5

7,957

by: bumpbot

19 Jan 2026, 05:54

ER

If the least common multiple of a positive integer x, 4^3 and 6^5

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

Bunuel

02 Jul 2025, 23:47

130

8

17,840

by: Bunuel

18 Jan 2026, 14:05

ER

If x and y are odd positive integers, and x and y both have an odd

705-805 (Hard) | Algebra, Multiples and Factors

705-805 (Hard) | Algebra, Multiples and Factors hide tags

BrentGMATPrepNow

15 Sep 2019, 06:51

197

14

15,341

by: vasu1104

18 Jan 2026, 09:24

ER

For integers x, y, and z, if (3^x) (4^y) (5^z) = 3,276,800,0

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

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

TheNona

17 Mar 2013, 01:05

36

8

8,193

by: bumpbot

18 Jan 2026, 08:31

ER

If a, b, c, d are four integers greater than 1, which of the following

555-605 (Medium) | Multiples and Factors, Number Properties

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

ExpertsGlobal5

01 Dec 2025, 22:21

7

3

912

by: Bunuel

18 Jan 2026, 06:30

ER

The positive difference between the greatest common factor and the lea

505-555 (Easy) | Multiples and Factors

505-555 (Easy) | Multiples and Factors hide tags

Bunuel

12 Dec 2016, 12:36

3

2

2,485

by: bumpbot

18 Jan 2026, 05:35

ER

Which of the following must be true about two integers a and b

605-655 (Medium) | Multiples and Factors, Number Properties

605-655 (Medium) | Multiples and Factors, Number Properties hide tags

stonecold

28 Nov 2016, 11:38

5

2

2,787

by: bumpbot

18 Jan 2026, 05:06

ER

If 48^x is a factor of 200! and x is a positive integer, what is the

705-805 (Hard) | Exponents +2 tags

705-805 (Hard) | Exponents, Multiples and Factors, Number Properties hide tags

ExpertsGlobal5

17 Nov 2025, 00:05

19

4

1,309

by: Bunuel

18 Jan 2026, 03:15

ER

Jim starts climbing up a tree to get a mango 30 feet away.

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

CrackverbalGMAT

01 Dec 2020, 22:28

19

11

4,165

by: bumpbot

18 Jan 2026, 00:30

ER

Find the number of factors of a three digit even number xyz

655-705 (Hard) | Multiples and Factors

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

kiran882

27 May 2013, 04:47

27

8

12,095

by: bumpbot

18 Jan 2026, 00:29

ER

12 Days of Christmas GMAT Competition - Day 5: If k is an integer from

805+ (Hard) | Multiples and Factors, Probability

805+ (Hard) | Multiples and Factors, Probability hide tags

Bunuel

20 Dec 2024, 09:00

51

9

5,482

by: bumpbot

18 Jan 2026, 00:26

ER

p, m, and n are positive integers greater than 1 such that p = m x n a

655-705 (Hard) | Multiples and Factors

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

ExpertsGlobal5

15 Jan 2026, 22:00

8

4

514

by: ExpertsGlobal5

17 Jan 2026, 10:45

ER

What is the highest integer k for which 135^k perfectly divides 200! ?

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

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

ExpertsGlobal5

14 Jan 2026, 22:00

11

4

731

by: ExpertsGlobal5

17 Jan 2026, 09:45

ER

If a and b are both odd prime numbers and a < b, then how many differe

555-605 (Medium) | Multiples and Factors, Number Properties

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

Bunuel

30 Jan 2020, 03:48

13

6

6,675

by: bumpbot

17 Jan 2026, 08:00

ER

What is the highest integer k for which 1260^k perfectly divides 500!

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

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

ExpertsGlobal5

12 Jan 2026, 22:00

10

3

673

by: ExpertsGlobal5

17 Jan 2026, 04:30

ER

A and B are integers greater than 1 and A^3 x B is a multiple of 10.

705-805 (Hard) | Multiples and Factors, Must or Could be True

705-805 (Hard) | Multiples and Factors, Must or Could be True hide tags

ExpertsGlobal5

11 Jan 2026, 22:00

7

3

574

by: ExpertsGlobal5

17 Jan 2026, 03:30

ER

12 Days of Christmas GMAT Competition - Day 9: p, m, and n are positiv

705-805 (Hard) | Multiples and Factors, Number Properties

705-805 (Hard) | Multiples and Factors, Number Properties hide tags

Bunuel

22 Dec 2021, 07:00

23

3

5,037

by: bumpbot

16 Jan 2026, 10:32

ER

If N=2^7*3^5*5^6*7^8. How many factors of N are divisible by

705-805 (Hard) | Multiples and Factors

705-805 (Hard) | Multiples and Factors hide tags

GMATtracted

05 May 2013, 22:56

84

11

25,926

by: bumpbot

16 Jan 2026, 08:55

ER

A class has 150 students numbered from 1 to 150. All even numbered stu

705-805 (Hard) | Multiples and Factors, Overlapping Sets

705-805 (Hard) | Multiples and Factors, Overlapping Sets hide tags

Bunuel

23 Apr 2020, 01:53

49

16

12,138

by: bumpbot

16 Jan 2026, 08:55

ER

What is the greatest value of x such that 2^x is a factor of 768? (A)

Sub 505 (Easy) | Exponents, Multiples and Factors

Sub 505 (Easy) | Exponents, Multiples and Factors hide tags

Russ19

16 Jul 2020, 07:44

6

5

2,750

by: bumpbot

16 Jan 2026, 08:55

ER

What is the biggest positive integer which will always divide n(n+1)(n

705-805 (Hard) | Multiples and Factors, Number Properties

705-805 (Hard) | Multiples and Factors, Number Properties hide tags

GMATinsight

12 Sep 2018, 07:10

9

7

3,318

by: bumpbot

15 Jan 2026, 10:20

ER

If the greatest integer k for which 3^k is a factor of n! is 8, what

705-805 (Hard) | Exponents +2 tags

705-805 (Hard) | Exponents, Min-Max Problems, Multiples and Factors hide tags

Rocky1304

18 Dec 2016, 22:51

143

13

16,385

by: bumpbot

15 Jan 2026, 08:34

ER -1

What is the remainder when 25! is divided by 10^7

805+ (Hard) | Multiples and Factors, Remainders

805+ (Hard) | Multiples and Factors, Remainders hide tags

Chethan92

03 Oct 2018, 19:30

82

14

14,585

by: bumpbot

14 Jan 2026, 14:53

ER

If n is an integer greater than 6, which of the following mu

555-605 (Medium) | Multiples and Factors, Must or Could be True

555-605 (Medium) | Multiples and Factors, Must or Could be True hide tags

1, 2

gregspirited

30 Jan 2019, 05:12

675

38

77,959

by: AndyRugger

14 Jan 2026, 12:59

ER

How many integers from 1 to 603, inclusive, are multiples of 2 or 3?

505-555 (Easy) | Multiples and Factors

505-555 (Easy) | Multiples and Factors hide tags

Bunuel

29 May 2025, 00:30

6

5

995

by: AndyRugger

14 Jan 2026, 12:36

ER

If p and q are different prime numbers, m and n are integers, and pq

655-705 (Hard) | Multiples and Factors +2 tags

655-705 (Hard) | Multiples and Factors, Must or Could be True, Number Properties hide tags

yrozenblum

09 Oct 2023, 03:24

163

9

21,564

by: bumpbot

14 Jan 2026, 07:19

ER

What is the number of positive integers n in the range 12 n 40

655-705 (Hard) | Multiples and Factors, Number Properties

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

Bunuel

14 Jan 2026, 02:15

2

1

365

by: gchandana

14 Jan 2026, 03:22

ER

For all integers p, f is the number of distinct factors of p that are

655-705 (Hard) | Multiples and Factors

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

Bunuel

31 Jul 2019, 00:03

8

3

2,978

by: bumpbot

14 Jan 2026, 01:08