GMAT Problem Solving (PS) Forum - Free Practice Questions

ER

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

Bunuel

03 Dec 2022, 14:23

321

12

151,885

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

312,349

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

1,383,684

by: bb

16 Apr 2026, 14:28

ER

For all integers a and b, where a ≠ b, a ★ b = |(a^2 - b^2)/(a - b)|

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

Bunuel

12 Mar 2019, 03:43

5

5,183

by: bumpbot

11 Sep 2024, 12:07

ER

Let h be a function such that h(x) = |5x| + c where c is constant. If

Sub 505 (Easy) | Absolute Values, Functions and Custom Characters

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

Bunuel

16 Nov 2020, 08:45

7

4

4,154

by: bumpbot

11 Sep 2024, 11:56

ER

Which of the following is(are) true for ab=ba?

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

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

MathRevolution

24 Feb 2016, 22:16

13

3

5,467

by: robert8035

04 Sep 2024, 07:09

ER

If A(k)=(k+1)^k, and k=0, what is the value of A(A(A(k)))? A. 0 B. 2

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

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

Bunuel

04 Sep 2024, 01:30

4

1

1,373

by: Krunaal

04 Sep 2024, 04:34

ER

For all integer values of n, n# is defined as 2^n. What is the value

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

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

Bunuel

23 Feb 2022, 09:15

9

3

2,583

by: bumpbot

01 Sep 2024, 03:17

ER

If f(a) = a^–3 – a^–2, then f(1/3) =

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

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

Bunuel

11 Dec 2020, 10:00

4

2,211

by: bumpbot

01 Sep 2024, 03:05

ER

Consider the function f(x) = x^2 – 5x. For which value(s) of x does

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

22 Jul 2019, 01:06

2

5

3,970

by: bumpbot

31 Aug 2024, 13:00

ER

If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one

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

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

Bunuel

14 Feb 2022, 07:15

9

4

6,983

by: bumpbot

31 Aug 2024, 12:59

ER

The operation & is defined in the following way for any two numbers:

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

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

Bunuel

12 Apr 2022, 03:15

4

3

2,673

by: bumpbot

30 Aug 2024, 13:06

ER

If x£y = 2(x^2)(y^3), which of the following represents possible value

505-555 (Easy) | Functions and Custom Characters

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

Bunuel

25 Jul 2018, 21:52

1

6

2,062

by: bumpbot

21 Aug 2024, 08:54

Given that g(h(x)) = 2x^2 + 3x, and h(g(x)) = x^2 + 4x - 4 for all the

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

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

nick1816

10 Aug 2019, 16:50

50

3

5,846

by: bumpbot

11 Aug 2024, 04:26

ER

If 1&2 = 3 and 2&3 = 7, which of the following could be equal to x&y

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

17 Apr 2018, 01:22

3

7

2,638

by: bumpbot

09 Aug 2024, 00:11

ER

If x@y = xy + y for all values of x and y, what is the value of 0@(3@(

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

08 Aug 2024, 01:30

2

3

911

by: Purnank

08 Aug 2024, 17:06

ER

x! is defined for all whole numbers x as the product of all the positi

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

29 Oct 2019, 01:53

5

3

2,805

by: bumpbot

07 Aug 2024, 11:03

ER

For which one of the following is g(x) greatest, if for all real numbe

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

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

Bunuel

05 Jan 2017, 04:08

1

4

3,170

by: bumpbot

07 Aug 2024, 03:06

ER

For any positive integer n, let f(n) = n(n + 1) if n is even, and f(n)

655-705 (Hard) | Functions and Custom Characters

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

Bunuel

03 Aug 2024, 21:45

3

1

1,060

by: Dooperman

03 Aug 2024, 22:37

ER

If 0 < x < 1000, and [x/2] + [x/3] + [x/5] = 31x/30 where [x] denotes

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

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

Bunuel

11 Mar 2020, 02:33

42

5

8,820

by: bumpbot

29 Jul 2024, 00:51

ER

If f(x)=x^2 and x is a positive integer, which of the following CANNOT

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

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

Bunuel

28 Feb 2016, 09:37

19

15

11,011

by: bumpbot

24 Jul 2024, 00:36

ER

If f is a function defined for every positive integer x in such a way

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

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

fskilnik

17 Mar 2019, 12:31

8

4

2,734

by: bumpbot

22 Jul 2024, 19:52

If f(x) = 90x^2 + 20x + 1, then find the sum of the digits of f(11111)

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

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

nick1816

23 Jun 2019, 22:08

36

7

5,318

by: Shrutyforu

22 Jul 2024, 11:37

ER

Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negat

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

23 Dec 2014, 09:49

13

8

6,022

by: bumpbot

19 Jul 2024, 05:26

ER

F(x) is a quadratic equation having value 4 at x=0 . The minimum valu

655-705 (Hard) | Functions and Custom Characters

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

sahilsahh

14 Jul 2024, 07:00

4

2

1,518

by: HarshavardhanR

14 Jul 2024, 14:41

ER

The figure shows the graph y = -2x2. Points A and B are on the graph.

505-555 (Easy) | Functions and Custom Characters, Graphs and Illustrations

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

MathRevolution

29 May 2020, 01:13

21

4

4,237

by: bumpbot

12 Jul 2024, 05:31

ER

For a positive integer n, E(n) represents the sum of even digits of n.

805+ (Hard) | Functions and Custom Characters

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

Bunuel

06 Jul 2023, 03:45

9

3

2,874

by: bumpbot

11 Jul 2024, 02:31

ER

If f(x) = 2x^2 − 4 and g(x) = 2x, for what values of x will f(x) = g(x

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

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

Bunuel

10 Mar 2020, 04:51

15

6

8,849

by: bumpbot

10 Jul 2024, 05:56

ER

The operation # is defined by x # y=x*y for all nonzero numbers x and

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

rohan2345

07 Sep 2019, 13:47

11

5

4,864

by: Bunuel

09 Jul 2024, 00:41

ER

If x# = x(x + 3), what is the value of x##

555-605 (Medium) | Functions and Custom Characters

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

sagarag

12 Jan 2015, 07:55

33

13

6,491

by: bumpbot

04 Jul 2024, 05:17

ER

The graph above shows a parabola that is symmetric about the x-axis.

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

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

Bunuel

17 Apr 2019, 00:38

12

3

4,029

by: bumpbot

04 Jul 2024, 01:35

ER

If g(x) = x^2 4bx + 9b^2, where b is any positive integer, then

805+ (Hard) | Functions and Custom Characters

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

Bunuel

23 Aug 2022, 01:30

11

3

1,983

by: bumpbot

24 Jun 2024, 12:17

ER

Let @x denote the sum of the digits of the positive integer x. For exa

705-805 (Hard) | Functions and Custom Characters

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

Bunuel

04 May 2022, 03:15

3

2,584

by: bumpbot

20 Jun 2024, 00:36

ER

A function D(a, 10b + c) is defined as the remainder when the sum a0 +

805+ (Hard) | Functions and Custom Characters +2 tags

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

Bunuel

09 Jun 2020, 07:13

15

9

2,724

by: bumpbot

12 Jun 2024, 17:54

ER

At time t = 0, a projectile was fired upward from an initial height of

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

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

Bunuel

11 Jun 2022, 19:00

27

3

4,840

by: stne

08 Jun 2024, 11:30

ER

A function f(x) is defined as f(x) = 3x^2 − 20x + c, where c is a cons

555-605 (Medium) | Functions and Custom Characters

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

Bunuel

03 Jun 2020, 10:06

3

4

2,436

by: BrushMyQuant

07 Jun 2024, 23:35

ER

A function f has the property that f(3x-1)=x^2+x+1 for all real number

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

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

Bunuel

26 Mar 2019, 23:14

6

8

7,271

by: bumpbot

30 May 2024, 05:52

ER

If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct

805+ (Hard) | Functions and Custom Characters

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

DisciplinedPrep

11 Jan 2021, 17:21

11

2

6,007

by: Oppenheimer1945

26 May 2024, 08:14

ER

A function * is defined for all even positive integers n as the number

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

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

Bunuel

05 Dec 2019, 01:33

17

5

7,201

by: bumpbot

22 May 2024, 10:45

ER

In the normal x-y coordinate plane there are 4 points A(-1,3), B(3,3),

705-805 (Hard) | Functions and Custom Characters

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

MathRevolution

13 Nov 2017, 01:12

23

4

2,986

by: bumpbot

21 May 2024, 23:38

ER

For every negative integer y, let [y] be defined as y^2 - y^3 + y^4.

705-805 (Hard) | Functions and Custom Characters

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

Bunuel

08 Jun 2022, 17:30

3

2,336

by: bumpbot

07 May 2024, 10:46

ER

If the domain of f(x) = x/5^(−x) is the set {–2, –1, 0, 2}, then f(x)

555-605 (Medium) | Algebra +2 tags

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

Bunuel

11 Dec 2020, 05:00

6

3

3,206

by: bumpbot

06 May 2024, 18:52

ER

If x£y represents the number of integers greater than x and less than

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

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

Bunuel

11 Jan 2019, 00:22

7

5

5,929

by: Bunuel

26 Apr 2024, 05:31

ER

In the x-y plane, a triangle ABC connected by 3 points A(0,4), B(-5,0)

655-705 (Hard) | Functions and Custom Characters

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

MathRevolution

16 May 2016, 20:06

21

6

4,895

by: bumpbot

22 Apr 2024, 07:39

ER

The function f is defined for each positive three-digit integer T by

555-605 (Medium) | Functions and Custom Characters

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

Bunuel

09 Apr 2021, 07:00

16

5

4,171

by: bumpbot

20 Apr 2024, 04:50

ER

If f(x) = x^2 and f(g(x)) = 1/(x^2 + 1), then g(x) could be which of

Sub 505 (Easy) | Functions and Custom Characters

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

Bunuel

22 Dec 2020, 09:30

6

4

2,049

by: bumpbot

19 Apr 2024, 10:38

ER

Let x and y be defined as the sum of all integers between x and y.

555-605 (Medium) | Functions and Custom Characters

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

Bunuel

30 Sep 2021, 06:15

5

3

2,478

by: BrushMyQuant

19 Apr 2024, 05:53

ER

If the operation $ is defined such that x$y = x^y*y^x, what is the val

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

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

Bunuel

06 Jan 2017, 03:08

3

6

3,049

by: bumpbot

08 Apr 2024, 21:17

ER

f(x) = x - 1/x and g(x) = x/x - 1. We have f(g(a)) = a. What is the

655-705 (Hard) | Functions and Custom Characters

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

MathRevolution

16 Jul 2020, 00:40

10

3

2,983

by: Oppenheimer1945

08 Apr 2024, 11:25

ER

Given f(x) = 2x/(2x − 1) and g(x) = (2x − 1)/2x, for what value of x

555-605 (Medium) | Functions and Custom Characters

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

Bunuel

22 Oct 2020, 12:51

12

6

5,712

by: bumpbot

31 Mar 2024, 14:07

ER

The minimum value of f(x) = |10 x| + |x 2| |4 x| is attained

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

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

Bunuel

10 Mar 2020, 02:47

24

14

10,820

by: bumpbot

31 Mar 2024, 00:11

ER

If n is an integer, f(n) = f(n-1) - n and f(4)=10. What is

505-555 (Easy) | Functions and Custom Characters

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

nimc2012

08 Feb 2012, 08:12

35

4

16,529

by: bumpbot

11 Mar 2024, 22:39

ER

For which of the following functions is f(-1/2) > f(2)?

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

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

Bunuel

22 Aug 2018, 02:04

12

10

8,122

by: bumpbot

10 Mar 2024, 13:00