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

329

12

153,569

by: ekfdskfe

13 Jul 2025, 19:03

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100 Hardest and easiest questions for PS as of April 2026

Bunuel

01 Jan 2026, 05:45

1.2k

8

313,313

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

1,387,162

by: bb

16 Apr 2026, 14:28

ER

How many integers less than 1000 have no factors (other than 1) in com

705-805 (Hard) | Multiples and Factors

1, 2

mehdiov

26 Jan 2024, 10:47

369

21

42,329

by: pappal

18 May 2026, 13:51

ER

x is an integer. If x>9, and x^3+3x^2+2x is not divisible

655-705 (Hard) | Multiples and Factors

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

BrentGMATPrepNow

14 Aug 2019, 08:51

22

6

6,955

by: bumpbot

18 May 2026, 04:52

ER

If the greatest common factor of positive integers n and m is 15, and

705-805 (Hard) | Exponents +2 tags

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Bunuel

02 Dec 2019, 00:35

78

10

7,671

by: bumpbot

18 May 2026, 04:45

ER

What is the greatest positive integer n such that 5^n divides 10! – (2

805+ (Hard) | Exponents, Multiples and Factors

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

parkhydel

27 Apr 2020, 15:46

605

16

51,227

by: Usernamevisible

17 May 2026, 21:05

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What is the least five-digit positive integer which when divided by 8,

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

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

Bunuel

05 Aug 2021, 07:45

41

6

5,924

by: bumpbot

17 May 2026, 20:35

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How many of the positive integers less than 10,000 are divisible by 3

705-805 (Hard) | Multiples and Factors

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

Bunuel

27 Nov 2019, 01:41

26

5

8,753

by: bumpbot

17 May 2026, 04:51

ER

Perry buys a book that has pages numbered from 1 to 980. He then selec

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

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

Bunuel

26 Nov 2019, 01:56

20

5

3,723

by: bumpbot

17 May 2026, 04:39

ER

If n is an integer greater than 10, then the expression (n^2 - 2n)(n +

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

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

Mkrishnabdrr

01 Jul 2017, 01:49

48

6

8,170

by: steffe440

17 May 2026, 00:10

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What is the sum of the multiples of 4 from 60 to 100, both inclusive?

555-605 (Medium) | Multiples and Factors

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

ExpertsGlobal5

14 May 2026, 19:00

2

4

160

by: ExpertsGlobal5

16 May 2026, 10:00

ER

Which of the following CANNOT be the least common multiple of two posi

555-605 (Medium) | Arithmetic +2 tags

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

PareshGmat

09 Sep 2014, 02:09

177

15

19,179

by: bumpbot

16 May 2026, 09:02

ER

If the positive integer x is a multiple of 8 and 12, then x must be a

605-655 (Medium) | Multiples and Factors, Must or Could be True

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Bunuel

05 Jan 2023, 09:00

3

2

1,829

by: bumpbot

15 May 2026, 23:39

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A set consists of all three-digit positive integers with the following

805+ (Hard) | Combinations, Multiples and Factors

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

Bunuel

10 Nov 2022, 08:05

15

4

5,634

by: EpicKnot

15 May 2026, 21:04

ER

What is the fifth greatest divisor of 25,600?

705-805 (Hard) | Multiples and Factors

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

kevincan

14 May 2026, 13:40

3

2

139

by: kevincan

15 May 2026, 12:05

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How many positive integers have more than 3 positive divisor

805+ (Hard) | Multiples and Factors

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kevincan

11 Apr 2026, 02:00

3

6

322

by: Ravisoni

15 May 2026, 01:14

ER

How many positive two-distinct-digit numbers are odd and not divisible

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

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

fskilnik

25 Feb 2019, 07:05

35

5

5,162

by: HarshavardhanR

14 May 2026, 22:00

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If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest value of

805+ (Hard) | Exponents +2 tags

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

1, 2

aalriy

10 Dec 2010, 07:20

956

21

84,554

by: bumpbot

14 May 2026, 11:20

ER

If integer k is equal to the sum of all even multiples of 15

705-805 (Hard) | Multiples and Factors

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

1, 2

yangsta8

11 Nov 2009, 05:27

199

21

41,515

by: bumpbot

14 May 2026, 08:31

ER

If x is the number of positive integers that will leave no remainder

605-655 (Medium) | Multiples and Factors, Remainders

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

Bunuel

21 Apr 2016, 00:30

35

6

9,095

by: Bunuel

13 May 2026, 08:11

ER

How many divisors of 12! are 1 greater than or 1 less than a

805+ (Hard) | Multiples and Factors

805+ (Hard) | Multiples and Factors hide tags

kevincan

12 May 2026, 22:23

2

175

by: sujoykrdatta

13 May 2026, 04:34

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If the greatest common divisor of (n-1)!, n!, and (n+1)! is 5040, what

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

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

MathRevolution

14 Aug 2018, 17:47

23

5

4,520

by: bumpbot

13 May 2026, 01:22

ER

Find the unit place of 2^1!+2!+3!+ .....+10! !

805+ (Hard) | Exponents, Multiples and Factors

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

Raksat

16 Mar 2020, 12:05

14

5

2,151

by: KarishmaB

12 May 2026, 22:48

ER

If 5^a is a factor of n!, and the greatest integer value of a is 6, wh

655-705 (Hard) | Exponents +2 tags

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patnaiksonal

14 Sep 2018, 09:50

58

10

10,420

by: bumpbot

12 May 2026, 06:16

ER

If the LCM of a amd 12 is 36 what could be the possible values of a?

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

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

dimri10

07 Jun 2011, 00:22

47

11

12,578

by: bumpbot

11 May 2026, 22:36

ER

How many integers N in the set of integers (1, 2, 3 ... 100) are there

705-805 (Hard) | Exponents +2 tags

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Kushchokhani

29 May 2022, 07:18

25

2

5,760

by: bumpbot

11 May 2026, 11:47

ER

What is the greatest value of x such that 8^x is a factor of 16! ?

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

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

Bunuel

14 Dec 2016, 05:57

61

8

6,779

by: bumpbot

11 May 2026, 10:32

ER

The product of two positive integers is 5760 and their highest common

805+ (Hard) | Multiples and Factors

805+ (Hard) | Multiples and Factors hide tags

Bunuel

16 Jan 2023, 10:00

9

2

2,508

by: bumpbot

11 May 2026, 10:29

ER

If x and y are integers and [m]xy^3-xy[/m] is a divisor of [

705-805 (Hard) | Algebra +2 tags

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

kevincan

11 May 2026, 08:18

4

1

190

by: AdarshSambare

11 May 2026, 09:48

ER

A number is called "mystic" if it can be expressed as the sum of at le

805+ (Hard) | Multiples and Factors, Sequences

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

fskilnik

11 May 2026, 02:52

15

7

3,983

by: Kinshook

11 May 2026, 02:46

ER

When positive integer n is divided by 5, the remainder is 1. When n is

505-555 (Easy) | Multiples and Factors, Remainders

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

Bunuel

08 Aug 2022, 03:34

855

19

148,470

by: minionbaba

10 May 2026, 06:40

ER

If two positive integers a and b are chosen at random between 1 and 50

805+ (Hard) | Exponents +2 tags

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

Bunuel

18 Jan 2022, 06:15

26

4

3,646

by: bumpbot

10 May 2026, 04:32

ER

'x' is a positive integer and x^3 is divisible by 27. Which of the

655-705 (Hard) | Exponents +2 tags

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ann1111

16 Jan 2020, 08:49

64

8

7,623

by: Stella5200

10 May 2026, 02:53

ER

What is the greatest value of x such that 8^x is a factor of 18! ?

605-655 (Medium) | Exponents, Multiples and Factors

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

Bunuel

14 Dec 2016, 05:58

31

6

5,786

by: bumpbot

09 May 2026, 14:46

ER

When 9^4 - 7^4 is divided by 2^n, the result is an odd

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

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

kevincan

09 May 2026, 09:20

1

2

169

by: rajdeep212003

09 May 2026, 09:41

ER

If J equals the number of positive even integers less than or equal to

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

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

BrentGMATPrepNow

26 Aug 2022, 08:24

31

7

4,555

by: bumpbot

09 May 2026, 05:07

ER

y = x(x + 1)(x + 2) where x is an even integer. Which of the following

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

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

Bunuel

08 Jul 2017, 05:34

20

13

5,280

by: Bunuel

09 May 2026, 04:53

ER

What is the least positive five-digit integer which when divided by 12

655-705 (Hard) | Multiples and Factors

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

Bunuel

05 Aug 2021, 03:30

4

2,768

by: bumpbot

08 May 2026, 15:01

ER

Instead of dividing a number by 13, a student in an exam divided it by

655-705 (Hard) | Multiples and Factors

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

Bunuel

25 Jan 2021, 06:45

11

4

5,245

by: bumpbot

07 May 2026, 14:29

ER

If the least common multiplier of positive integers A and B is 120 and

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

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

Bunuel

20 Sep 2019, 05:51

31

5

7,609

by: bumpbot

07 May 2026, 11:18

ER

How many factors of 1764 are perfect squares ? A. 4 B. 7 C.

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

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

CareerGeek

23 Jun 2019, 11:20

28

6

5,708

by: bumpbot

07 May 2026, 08:41

ER

How many three-digit integers are divisible by 6 or by 9 but

705-805 (Hard) | Multiples and Factors

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

kevincan

07 May 2026, 01:47

1

123

by: rajdeep212003

07 May 2026, 02:14

ER

The integers from 1 to 100 inclusive are each written on a

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

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

Zem

09 Apr 2005, 01:13

65

17

20,424

by: bumpbot

07 May 2026, 01:44

ER

If 30!/10! is written as the product of consecutive integers, the larg

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

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

MDK

12 Nov 2014, 04:27

101

18

49,215

by: bumpbot

07 May 2026, 01:10

ER

Mary chose an even 4-digit number n. She wrote down all the divisors

805+ (Hard) | Multiples and Factors, Number Properties

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

Bunuel

12 May 2022, 01:30

28

8

6,176

by: Kinshook

07 May 2026, 00:18

ER

If p and q are different prime numbers, and n = pq 2q, then which of

655-705 (Hard) | Multiples and Factors

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

BrentGMATPrepNow

24 Apr 2017, 07:19

38

5

10,702

by: MartyMurray

06 May 2026, 15:37

ER

When the positive integer A is divided by 5 and 7

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

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

BDSunDevil

06 Jun 2013, 06:22

93

8

13,074

by: bumpbot

06 May 2026, 00:54

ER

How many positive integers less than 30 are either a multiple of 2, an

805+ (Hard) | Multiples and Factors, Number Properties

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

1, 2

enigma123

08 Oct 2017, 04:15

184

22

43,161

by: Kinshook

05 May 2026, 03:52

ER

The sum of the first [m]n[/m] positive integers is given by

655-705 (Hard) | Functions and Custom Characters +2 tags

655-705 (Hard) | Functions and Custom Characters, Multiples and Factors, Sequences hide tags

kevincan

04 May 2026, 22:46

5

3

268

by: rajdeep212003

05 May 2026, 01:07

ER

If n is a positive integer and the product of all integers from 1 to n

505-555 (Easy) | Multiples and Factors, Number Properties

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

1, 2, 3

nailgmattoefl

07 Jul 2019, 23:23

776

43

221,144

by: PGTLrowanhand

04 May 2026, 13:30

ER

If the product of two positive integers is 540, which of the following

705-805 (Hard) | Multiples and Factors

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

Bunuel

09 Jun 2020, 05:11

41

7

5,503

by: bumpbot

04 May 2026, 09:27

ER

What is the sum of the integers from 100 to 200 inclusive

655-705 (Hard) | Multiples and Factors

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

Chethan92

28 Aug 2018, 03:53

47

5

8,284

by: bumpbot

04 May 2026, 05:50