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

151,251

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

312,279

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

1,383,412

by: bb

16 Apr 2026, 14:28

ER

For all real numbers x, let x denote the number obtained by rounding

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

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

AnkurGMAT20

13 Aug 2024, 07:43

49

5

7,526

by: Bunuel

24 Mar 2025, 08:54

ER

If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)

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

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Bunuel

06 Apr 2015, 07:14

34

10

11,382

by: bumpbot

24 Mar 2025, 08:47

ER

If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what

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

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

olivite

09 Sep 2019, 03:57

73

11

20,362

by: bumpbot

24 Mar 2025, 05:47

ER

If f(x) = x^2 and g(x) = 2^x, for all x. Then what is the value of f(f

655-705 (Hard) | Algebra +2 tags

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Bunuel

03 Apr 2020, 04:39

9

3

3,954

by: bumpbot

23 Mar 2025, 02:01

ER

If is defined for all nonnegative integers b by b = (b + 1)^b, what

Sub 505 (Easy) | Functions and Custom Characters

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guddo

27 Jan 2024, 05:40

10

6

5,900

by: bdc

23 Mar 2025, 00:01

ER

A function f(x) is defined as (x + 1)*f(x + 1) + x*f(x) + (x – 1)*f(x

805+ (Hard) | Functions and Custom Characters

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

Bunuel

21 Sep 2020, 01:30

23

2

8,015

by: bumpbot

22 Mar 2025, 07:02

ER

f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following

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

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

Bunuel

21 Dec 2017, 20:25

30

6

8,816

by: bumpbot

22 Mar 2025, 02:47

ER

If F(x+y) = F(x) * F(y) Given : F(3) = 729

705-805 (Hard) | Functions and Custom Characters

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GMATBusters

05 Apr 2018, 08:42

40

6

5,261

by: kayarat600

21 Mar 2025, 12:54

ER

The function, a* is defined as a*=10a if a is a positive prime numb

605-655 (Medium) | Functions and Custom Characters

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siddhantvarma

14 Mar 2025, 05:20

6

3

1,105

by: Bunuel

21 Mar 2025, 09:53

ER

For any number y, y* is defined as the greatest positive

555-605 (Medium) | Functions and Custom Characters

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goodyear2013

18 Apr 2014, 09:50

14

4

7,846

by: Bunuel

21 Mar 2025, 00:01

ER

If f(x+1)=f(x)+1 for all values of x, and f(7)=3, what is the value of

505-555 (Easy) | Functions and Custom Characters

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Bunuel

13 Feb 2017, 03:21

15

6

12,065

by: bumpbot

19 Mar 2025, 04:18

ER

The function f is defined by f(x) = - 1/x for all nonzero numbers x.

505-555 (Easy) | Functions and Custom Characters

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

ajit257

16 Dec 2010, 18:37

108

13

44,541

by: bumpbot

18 Mar 2025, 07:31

ER

For which of the following functions f(x), is it always true that f(a/

555-605 (Medium) | Functions and Custom Characters

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

Bunuel

24 May 2021, 07:45

5

4

4,842

by: bumpbot

18 Mar 2025, 06:43

ER

If for all numbers P, where P 1, the function @ is defined by P@ =

505-555 (Easy) | Functions and Custom Characters

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

Bunuel

08 Sep 2020, 01:30

6

5

6,396

by: bumpbot

18 Mar 2025, 05:42

ER

Which of the following points is symmetric with y=x at (-1,-2)?

655-705 (Hard) | Functions and Custom Characters

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

MathRevolution

24 Aug 2016, 19:19

13

4

3,688

by: bumpbot

16 Mar 2025, 10:02

If g(3x + 4) = -5x, what is the value of g(7) ?

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

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

supremekai

23 Feb 2025, 19:43

10

4

1,428

by: Krunaal

12 Mar 2025, 11:48

If f(x) = 3x - 1 and g(x) = x/3 + 1, what is the value of 2f(g(3)) ?

Sub 505 (Easy) | Functions and Custom Characters

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

supremekai

05 Mar 2025, 23:24

1

594

by: Ayala2022

07 Mar 2025, 09:25

ER

The curve shown above is defined by the ordered-pairs (x,y) such that

805+ (Hard) | Coordinate Geometry +2 tags

805+ (Hard) | Coordinate Geometry, Functions and Custom Characters, Graphs and Illustrations hide tags

fskilnik

21 Feb 2019, 13:54

18

8

3,816

by: bumpbot

05 Mar 2025, 22:58

Given f(x) = 3x - 2 and g(x) = x^2 - 4. If g(k) = 221, what is f(k)

Sub 505 (Easy) | Functions and Custom Characters

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kingbucky

02 Mar 2025, 09:52

2

1

622

by: Missinga

02 Mar 2025, 20:16

ER

If c is a nonzero constant such that x*f(x) = c, variables x and y=f(x

705-805 (Hard) | Coordinate Geometry +2 tags

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fskilnik

13 Mar 2019, 08:49

24

5

4,932

by: bumpbot

02 Mar 2025, 12:08

ER

Let Z be a function satisfying Z(ab) = Z(a)/bfor all positive real num

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

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

Bunuel

13 Feb 2020, 07:59

29

4

4,678

by: bumpbot

01 Mar 2025, 13:47

ER

If x ? y is defined for all x and y as the sum of all integers from x

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

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

Bunuel

05 Sep 2017, 01:10

8

5

5,070

by: bumpbot

01 Mar 2025, 09:08

ER

Let f(x + 2) + f(5x + 6) = 2x – 1 for all real x. Find the value of f

555-605 (Medium) | Functions and Custom Characters

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Bunuel

23 Jun 2021, 02:45

9

4

2,844

by: bumpbot

28 Feb 2025, 15:53

ER

For a positive integer n, the function @n represents the product of al

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

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Bunuel

09 Jun 2020, 05:22

21

7

4,893

by: OJA

28 Feb 2025, 06:56

If |acbd| = ad - bc for all numbers a, b, c, and d, then |4 -3 6 5| =

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

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

supremekai

25 Feb 2025, 23:36

2

1

750

by: Missinga

26 Feb 2025, 08:05

ER

[x] denotes the greatest integer less than or equal to x and {x} denot

805+ (Hard) | Functions and Custom Characters

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Bunuel

19 Jul 2020, 06:48

13

2

9,864

by: bumpbot

26 Feb 2025, 01:42

ER

The function f is defined for all non-negative integers x by the follo

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

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

Bunuel

03 Dec 2020, 01:15

16

13

7,419

by: bumpbot

26 Feb 2025, 00:40

For all numbers a and b, the operation a b is defined as

Sub 505 (Easy) | Functions and Custom Characters

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shishimaru

22 Feb 2025, 22:46

1

528

by: Ayeka

23 Feb 2025, 08:22

ER

If h(x) = x^3 - 8 and h(m) = 19, then m =

Sub 505 (Easy) | Functions and Custom Characters

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kingbucky

22 Feb 2025, 22:43

1

409

by: Bunuel

23 Feb 2025, 01:18

ER

Let f be a function such that f(mn) = f(m)f(n) for every positive inte

655-705 (Hard) | Functions and Custom Characters

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

Bunuel

09 Apr 2020, 06:41

35

4

15,353

by: BrushMyQuant

22 Feb 2025, 03:50

If h(x) = 3x^2 + 15, what is h(10)?

Sub 505 (Easy) | Functions and Custom Characters

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supremekai

20 Feb 2025, 19:59

1

411

by: AARSHA

21 Feb 2025, 16:18

If p(x) = x^2 and q(x) = x + 4, then q(p(x)) =

Sub 505 (Easy) | Functions and Custom Characters

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kingbucky

20 Feb 2025, 20:06

1

469

by: Krunaal

20 Feb 2025, 22:42

ER

[x] denotes the largest integer less than or equal to x. If [x] = -1,

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

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

Bunuel

01 Apr 2026, 10:00

17

4

5,539

by: bumpbot

20 Feb 2025, 20:58

ER

A function f(x) is defined as x *<x>. If <x> is the greatest factor o

Sub 505 (Easy) | Functions and Custom Characters

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MathRevolution

06 Jan 2020, 01:40

8

4

1,532

by: bumpbot

20 Feb 2025, 07:57

ER

Operation F means “take the square root,” operation G means “multiply

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

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

Bunuel

04 Dec 2019, 01:44

38

7

8,295

by: Bunuel

18 Feb 2025, 05:45

ER

The “primeness” of a positive integer x is defined as

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

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

GyMrAT

05 Jul 2018, 23:38

7

6

3,810

by: giuseppemvn

18 Feb 2025, 04:28

ER

If g is a function defined for all x by g(x) = x^4/16, then what is

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

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

Bunuel

03 May 2017, 04:26

32

8

10,998

by: bumpbot

14 Feb 2025, 03:50

ER

If operation p # q is defined for all integers p and q, such that t p

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

Bunuel

17 Jun 2019, 01:03

7

4

6,269

by: BrushMyQuant

08 Feb 2025, 05:19

ER

The population of grasshoppers doubles in a particular field

555-605 (Medium) | Functions and Custom Characters

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jlgdr

18 Sep 2013, 16:48

55

10

14,603

by: hr1212

05 Feb 2025, 04:02

ER

If f(x) = x + x^2/(3x) + 4, which of the following numbers CANT be in

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

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

ShilpiAgnihotrii

04 Feb 2025, 10:44

13

9

1,462

by: KarishmaB

04 Feb 2025, 21:58

ER

For all positive, non-prime values of x greater than 1, f(x) is equal

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

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

Bunuel

03 Feb 2025, 01:30

5

3

1,191

by: ManifestDreamMBA

04 Feb 2025, 14:59

ER

For a positive integer n, f(n) and g(n) are defined as follows

805+ (Hard) | Functions and Custom Characters

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MathRevolution

30 Mar 2020, 01:21

10

4

2,345

by: bumpbot

31 Jan 2025, 11:48

ER

For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What

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

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SergeNew

08 Mar 2012, 15:48

39

7

9,107

by: ManifestDreamMBA

31 Jan 2025, 07:05

ER

Ax(y) is an operation that adds 1 to y

805+ (Hard) | Functions and Custom Characters

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Smita04

03 Jul 2012, 18:17

65

10

11,699

by: bumpbot

30 Jan 2025, 21:08

ER

If f(x) denotes the number of positive integers less than or equal to

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

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

Bunuel

30 Mar 2023, 07:45

15

4

3,624

by: bumpbot

26 Jan 2025, 12:25

ER

If h(n) is defined as (1 + f(n))(1 - g(n)), what is h(1) + h(2) + . +

655-705 (Hard) | Functions and Custom Characters

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

Bunuel

22 May 2023, 10:30

13

6

2,757

by: bumpbot

26 Jan 2025, 11:35

ER

Let f(x) denotes the sum of the digits of the positive integer x. For

805+ (Hard) | Functions and Custom Characters

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Bunuel

03 Aug 2018, 03:58

9

6

4,825

by: bumpbot

25 Jan 2025, 01:49

ER

The value of a* is the product of all positive, odd integers less the

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

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

Bunuel

31 Mar 2022, 03:15

10

5

2,462

by: BrushMyQuant

22 Jan 2025, 04:54

ER

For any integer x, [x] is defined by the equation [x] = x +

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

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

fozzzy

06 Jul 2013, 08:19

14

4

5,505

by: bumpbot

22 Jan 2025, 01:58

ER

If f(z) = 2z+1, then which of the following can be the value of x for

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

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niteshwaghray

29 May 2017, 12:04

30

3

3,505

by: bumpbot

22 Jan 2025, 00:08