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

151,229

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

312,271

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

1,383,357

by: bb

16 Apr 2026, 14:28

ER

The function f is defined as f(x,y) = xy for positive numbers x and y.

805+ (Hard) | Algebra, Functions and Custom Characters

805+ (Hard) | Algebra, Functions and Custom Characters hide tags

Bunuel

04 Oct 2023, 01:30

10

2

3,046

by: bumpbot

14 Aug 2025, 15:40

ER

If f(n) = 1154*1156 for some integer, n, which of the following expres

805+ (Hard) | Algebra +2 tags

805+ (Hard) | Algebra, Functions and Custom Characters, Number Properties hide tags

Bunuel

28 Nov 2019, 00:05

65

16

5,584

by: bumpbot

14 Aug 2025, 15:33

ER

For any numbers w and z, w#z = w^3z(8 - w^2). If both z and w#z are po

655-705 (Hard) | Algebra, Functions and Custom Characters

655-705 (Hard) | Algebra, Functions and Custom Characters hide tags

Bunuel

24 Mar 2026, 02:12

17

9

6,624

by: bumpbot

13 Aug 2025, 08:07

ER

Let f(x) = min{x^2 - 2, 1 - 2x}, for any positive number x. What is th

705-805 (Hard) | Algebra +2 tags

705-805 (Hard) | Algebra, Functions and Custom Characters, Min-Max Problems hide tags

Bunuel

17 Jan 2022, 03:15

12

2

3,169

by: bumpbot

12 Aug 2025, 16:21

ER

For which of the following functions is g(c-d) = g(c) - g(d)

605-655 (Medium) | Algebra, Functions and Custom Characters

605-655 (Medium) | Algebra, Functions and Custom Characters hide tags

exploringm

11 Feb 2013, 10:09

99

14

16,112

by: bumpbot

10 Aug 2025, 10:07

ER

The three solutions of the equation f(x)=0 are −2,0 and 3. T

655-705 (Hard) | Functions and Custom Characters

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

Emdad

23 Sep 2021, 23:26

29

3

6,376

by: bumpbot

07 Aug 2025, 11:58

ER

What is the minimum value of f(n) = 2n^2 - 7n + 8, if n

605-655 (Medium) | Algebra +2 tags

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Bunuel

28 Mar 2023, 05:45

20

5

4,891

by: bumpbot

07 Aug 2025, 11:06

ER

The function g(x) is defined for integers x such that if x

805+ (Hard) | Algebra, Functions and Custom Characters

805+ (Hard) | Algebra, Functions and Custom Characters hide tags

1, 2

bhandariavi

14 Feb 2011, 18:22

300

20

32,124

by: bumpbot

06 Aug 2025, 08:22

ER

x# is defined for every positive even integer x as the product of all

655-705 (Hard) | Functions and Custom Characters

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

Bunuel

27 May 2021, 05:45

8

4

5,345

by: ronaldo07mba

02 Aug 2025, 10:05

ER

Fresh Meat!!!

655-705 (Hard) | Fractions and Ratios +3 tags

655-705 (Hard) | Fractions and Ratios, Functions and Custom Characters, Multiples and Factors, Must or Could be True hide tags

1, 2, 3

Bunuel

17 Apr 2013, 06:11

764

58

131,963

by: WhitEngagePrep

27 Jul 2025, 17:26

ER

If f(x^2 – 1) = x^4 – 7x^2 + k1 and f(x^3 – 2) = x^6 – 9x^3 + k2, find

705-805 (Hard) | Algebra, Functions and Custom Characters

705-805 (Hard) | Algebra, Functions and Custom Characters hide tags

DisciplinedPrep

16 Sep 2019, 20:50

37

5

9,777

by: bumpbot

26 Jul 2025, 22:34

ER

For all positive integers m and n, the expression m △ n represents the

555-605 (Medium) | Functions and Custom Characters

555-605 (Medium) | Functions and Custom Characters hide tags

MathRevolution

23 Dec 2016, 21:33

15

8

10,636

by: bumpbot

25 Jul 2025, 19:48

ER

If [X] denotes the greatest integer less than or equal to x, what is

705-805 (Hard) | Arithmetic +2 tags

705-805 (Hard) | Arithmetic, Functions and Custom Characters, Roots hide tags

Bunuel

25 May 2020, 09:56

42

6

11,975

by: Krunaal

24 Jul 2025, 19:57

ER

In the coordinate plane there is the area of the region shaded surroun

705-805 (Hard) | Functions and Custom Characters

705-805 (Hard) | Functions and Custom Characters hide tags

indu1954

24 Mar 2019, 01:46

7

2

2,076

by: bumpbot

24 Jul 2025, 02:21

ER

A function f is defined recursively by f(1) = f(2) = 1 and f(n) = f(n-

805+ (Hard) | Functions and Custom Characters

805+ (Hard) | Functions and Custom Characters hide tags

Bunuel

11 Jun 2022, 03:45

9

3

5,583

by: bumpbot

24 Jul 2025, 01:55

ER

f(x) has the properties, f(x+y) = x + f(y) and f(0) = 5. What is the

505-555 (Easy) | Functions and Custom Characters

505-555 (Easy) | Functions and Custom Characters hide tags

Bunuel

23 May 2023, 04:30

6

4

2,106

by: bumpbot

23 Jul 2025, 14:13

ER

If f(x)=ax^2-x, and f(4)=28, what is f(-2)?

Sub 505 (Easy) | Algebra, Functions and Custom Characters

Sub 505 (Easy) | Algebra, Functions and Custom Characters hide tags

Ravixxx

22 Mar 2020, 07:10

9

5

3,157

by: bumpbot

23 Jul 2025, 11:27

ER

If f(n + 3) = f(n) and f(-1) = 6, f(0) = 5, f(1) = 4, then what is the

555-605 (Medium) | Functions and Custom Characters

555-605 (Medium) | Functions and Custom Characters hide tags

Rashed12

04 Mar 2019, 07:43

16

5

3,239

by: bumpbot

22 Jul 2025, 05:45

ER

If g(x^2 - 2) = x^4 - 4*x^2 for all real numbers x, g(x) could be ?

655-705 (Hard) | Functions and Custom Characters

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

Bunuel

27 Jan 2022, 03:00

23

3

2,819

by: bumpbot

22 Jul 2025, 05:38

ER

If [x] is the lowest even integer greater than x, then [4.3]+[−6.7]/[−

505-555 (Easy) | Functions and Custom Characters

505-555 (Easy) | Functions and Custom Characters hide tags

Bunuel

16 Oct 2019, 23:11

10

8

2,814

by: bumpbot

21 Jul 2025, 02:53

ER

In the xy-plane, a triangle ABC consists of 3 points A(0,0), B(6,0),

705-805 (Hard) | Functions and Custom Characters

705-805 (Hard) | Functions and Custom Characters hide tags

MathRevolution

02 May 2016, 23:21

56

10

7,772

by: bumpbot

21 Jul 2025, 02:01

ER

We define that K@J is the product of j number from k in increasing ord

505-555 (Easy) | Functions and Custom Characters

505-555 (Easy) | Functions and Custom Characters hide tags

MathRevolution

10 Feb 2016, 21:57

6

3

3,580

by: bumpbot

20 Jul 2025, 22:32

ER

The function f(n) is defined as the product of all integers from 1 to

705-805 (Hard) | Functions and Custom Characters +3 tags

705-805 (Hard) | Functions and Custom Characters, Must or Could be True, Number Properties, Sequences hide tags

EgmatQuantExpert

16 Nov 2018, 04:08

122

9

8,280

by: bumpbot

20 Jul 2025, 08:07

ER

For all real numbers a and b, where a ⋅ b =/ 0, let a◊b = ab

705-805 (Hard) | Algebra +2 tags

705-805 (Hard) | Algebra, Functions and Custom Characters, Must or Could be True hide tags

gettinit

04 Jul 2019, 01:08

54

7

11,922

by: bumpbot

19 Jul 2025, 07:39

ER

12 Easy Pieces (or not?)

555-605 (Medium) | Algebra +9 tags

555-605 (Medium) | Algebra, Combinations, Exponents, Functions and Custom Characters, Geometry, Inequalities, Must or Could be True, Number Properties, Probability, Word Problems hide tags

1, 2, 3, 4

Bunuel

21 Jan 2012, 06:10

2.1k

65

215,687

by: Bunuel

16 Jul 2025, 08:38

ER

If F(X) = 1/X - 1/(X+1), what is the sum of F(1) through F(200), inclu

555-605 (Medium) | Arithmetic, Functions and Custom Characters

555-605 (Medium) | Arithmetic, Functions and Custom Characters hide tags

Bunuel

04 Jan 2021, 23:15

50

4

6,605

by: bumpbot

14 Jul 2025, 07:44

ER

If {x} is the product of all integer multiples of 5 from 1 to x, inclu

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

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Bunuel

02 Oct 2017, 00:59

30

7

4,580

by: BrushMyQuant

12 Jul 2025, 04:44

ER

Define x?y = x^3 - y. What is h?(h?h) ?

555-605 (Medium) | Algebra, Functions and Custom Characters

555-605 (Medium) | Algebra, Functions and Custom Characters hide tags

Bunuel

25 Mar 2019, 00:21

11

4

4,761

by: bumpbot

11 Jul 2025, 13:14

ER

Which of the following function follows the rule: f(a + b) = f(a)*f(b)

655-705 (Hard) | Algebra, Functions and Custom Characters

655-705 (Hard) | Algebra, Functions and Custom Characters hide tags

Bunuel

08 Jul 2019, 08:00

145

17

17,694

by: bumpbot

07 Jul 2025, 03:07

ER

For any numbers x and y, x#y = xy - x - y if x#y=1 which

605-655 (Medium) | Algebra, Functions and Custom Characters

605-655 (Medium) | Algebra, Functions and Custom Characters hide tags

bmwhype2

24 Dec 2013, 01:44

106

13

27,940

by: bumpbot

06 Jul 2025, 09:43

ER

If function f(x) satisfies f(x) = f(x^2) for all x, which of the follo

705-805 (Hard) | Functions and Custom Characters, Must or Could be True

705-805 (Hard) | Functions and Custom Characters, Must or Could be True hide tags

sriharimurthy

18 Nov 2009, 10:07

59

6

26,549

by: Krunaal

06 Jul 2025, 08:03

ER

If [x] denotes the least integer greater than or equal to x and [x] =

555-605 (Medium) | Functions and Custom Characters, Inequalities

555-605 (Medium) | Functions and Custom Characters, Inequalities hide tags

1, 2

goodyear2013

29 Aug 2014, 07:09

218

21

44,139

by: bumpbot

06 Jul 2025, 05:55

ER

Which of the following functions has as its domain the set of all real

705-805 (Hard) | Algebra, Functions and Custom Characters

705-805 (Hard) | Algebra, Functions and Custom Characters hide tags

LamboWalker

25 Feb 2024, 23:59

41

11

8,606

by: ManishaPrepMinds

06 Jul 2025, 03:45

ER

GMAT Club Olympics 2025 (Day 4): Let [x] represent the greatest intege

655-705 (Hard) | Functions and Custom Characters, Number Properties

655-705 (Hard) | Functions and Custom Characters, Number Properties hide tags

1, 2...6, 7

Bunuel

03 Jul 2025, 08:00

130

127

4,963

by: A_Nishith

04 Jul 2025, 08:00

ER

For every positive even integer n, the function h(n)

Sub 505 (Easy) | Functions and Custom Characters, Number Properties

Sub 505 (Easy) | Functions and Custom Characters, Number Properties hide tags

skamal7

24 Mar 2013, 06:30

73

8

19,371

by: bumpbot

03 Jul 2025, 23:48

ER

If n is a positive integer greater than 2

705-805 (Hard) | Functions and Custom Characters

705-805 (Hard) | Functions and Custom Characters hide tags

rhnbansal

09 May 2018, 11:06

87

6

11,046

by: bumpbot

01 Jul 2025, 23:23

ER

If f(x) = (x + 6)^2 and g(x) = 9x, which of the following

605-655 (Medium) | Functions and Custom Characters

605-655 (Medium) | Functions and Custom Characters hide tags

Sajjad1994

29 Oct 2020, 11:15

26

5

4,465

by: bumpbot

30 Jun 2025, 04:47

ER

If [z] denotes the greatest integer less than or equal to z and [z] =

555-605 (Medium) | Functions and Custom Characters

555-605 (Medium) | Functions and Custom Characters hide tags

sguptashared

06 Nov 2017, 20:51

216

15

44,596

by: Bunuel

27 Jun 2025, 08:21

ER

For all positive integers j and k, the operation k j is defined to b

505-555 (Easy) | Functions and Custom Characters, Number Properties

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

LamboWalker

18 Aug 2024, 22:00

13

5

5,495

by: gmatuser523

27 Jun 2025, 06:50

ER

The function max(a, b) returns the largest, and min(a, b) returns the

655-705 (Hard) | Absolute Values, Functions and Custom Characters

655-705 (Hard) | Absolute Values, Functions and Custom Characters hide tags

Bunuel

21 Jan 2024, 11:00

23

3

6,496

by: shubhim20

25 Jun 2025, 02:19

ER

If X and Y are sets of integers, X@Y denotes the set of inte

555-605 (Medium) | Functions and Custom Characters, Overlapping Sets

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Bunuel

29 May 2012, 09:09

174

13

34,928

by: sidc07

24 Jun 2025, 11:58

ER -1

For all numbers a and b, the operation is defined by ab = a^2 - ab.

655-705 (Hard) | Algebra, Functions and Custom Characters

655-705 (Hard) | Algebra, Functions and Custom Characters hide tags

Bunuel

19 Mar 2015, 06:31

43

10

23,084

by: VasundharaS

23 Jun 2025, 07:26

ER

For positive integer values of n, the operation n# is defined as the

555-605 (Medium) | Arithmetic, Functions and Custom Characters

555-605 (Medium) | Arithmetic, Functions and Custom Characters hide tags

Bunuel

17 Jul 2015, 01:17

9

8

6,763

by: Bunuel

23 Jun 2025, 06:37

ER

If x is an integer greater than 2, the function f(x) represents the pr

555-605 (Medium) | Algebra, Functions and Custom Characters

555-605 (Medium) | Algebra, Functions and Custom Characters hide tags

s55day

22 Aug 2018, 23:42

19

4

6,271

by: bumpbot

18 Jun 2025, 04:24

ER

Which of the following functions f(x) satisfies the condition f(y −z)

605-655 (Medium) | Functions and Custom Characters

605-655 (Medium) | Functions and Custom Characters hide tags

Bunuel

27 May 2021, 08:30

13

3

4,775

by: bumpbot

16 Jun 2025, 02:28

ER

For a three-digit number xyz, where x, y, and z are the

655-705 (Hard) | Exponents +2 tags

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JCLEONES

12 Jul 2014, 03:44

153

17

25,948

by: bumpbot

13 Jun 2025, 09:09

ER

For all positive integers x and y, the expression xy is defined as

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

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Bunuel

12 Aug 2023, 12:00

131

11

19,352

by: KarishmaB

11 Jun 2025, 23:43

ER

If the symbols Δ and ◊ each represent digits in the following subtract

555-605 (Medium) | Arithmetic +2 tags

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pratikshr

01 Aug 2014, 02:21

143

9

20,358

by: bumpbot

11 Jun 2025, 20:38

ER

If the operation @ is defined for all integers a and b by a@b = a+b-ab

655-705 (Hard) | Functions and Custom Characters, Must or Could be True

655-705 (Hard) | Functions and Custom Characters, Must or Could be True hide tags

cmugeria

18 Sep 2010, 20:16

556

18

176,029

by: bumpbot

11 Jun 2025, 03:33

ER

If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim

605-655 (Medium) | Algebra +2 tags

605-655 (Medium) | Algebra, Functions and Custom Characters, Min-Max Problems hide tags

Bunuel

26 Oct 2021, 06:15

44

8

9,933

by: iamchinu97

09 Jun 2025, 09:57