Problem Solving (PS)

03 Dec 2024, 01:03

7!! ER

GMAT PS Question Directory by Topic & Difficulty

bb

22 Feb 2012, 11:27

3,181

0

1,354,217

by: bb

22 Feb 2012, 11:27

7!! ER

Bunuel's Algebra PS Diagnostic Test

505-555 Level | Absolute Values +11 tags

1, 2...9, 10

Bunuel

02 Oct 2022, 04:59

961

183

77,340

19 Nov 2025, 22:55

7!! ER

A function f(n) is defined as 2^(n-1) when n is odd or fractional...

555-605 Level | Exponents, Functions and Custom Characters

555-605 Level | Exponents, Functions and Custom Characters hide tags

ExpertsGlobal5

18 Nov 2025, 22:43

0

83

by: ExpertsGlobal5

18 Nov 2025, 22:43

7!! ER

The function f is defined for all numbers x by f(x) = |x + 3| + |x + 2

555-605 Level | Absolute Values, Functions and Custom Characters

555-605 Level | Absolute Values, Functions and Custom Characters hide tags

Bunuel

20 May 2019, 00:13

131

17

20,867

18 Nov 2025, 12:58

7!! ER

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

655-705 Level | Algebra +3 tags

655-705 Level | Algebra, Exponents, Functions and Custom Characters, Number Properties hide tags

1, 2

Orange08

11 Sep 2010, 06:40

1,629

22

113,835

17 Nov 2025, 02:19

7!! ER

The function f is defined for all positive integers n by the following

655-705 Level | Functions and Custom Characters, Number Properties

655-705 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

01 Nov 2019, 05:08

51

7

12,384

16 Nov 2025, 11:58

7!! ER

If f(x) = g(x - 1), where g(x) = |x| + 1, which of the following must

555-605 Level | Absolute Values, Functions and Custom Characters

555-605 Level | Absolute Values, Functions and Custom Characters hide tags

callumdye

09 Jan 2024, 09:37

66

12

11,368

by: GSV

16 Nov 2025, 08:23

7!! ER

Define the symbol * by the following equation: x* = 1 – x, for all non

555-605 Level | Algebra, Functions and Custom Characters

555-605 Level | Algebra, Functions and Custom Characters hide tags

Bunuel

21 May 2017, 12:21

11

6

5,356

15 Nov 2025, 08:38

7!! ER

Which of the following functions f defined for all numbers x has the

555-605 Level | Algebra, Functions and Custom Characters

555-605 Level | Algebra, Functions and Custom Characters hide tags

Bunuel

21 Jun 2018, 02:45

19

5

13,076

15 Nov 2025, 08:20

7!! ER

For all integers a, b, c, and d, *(a, b, c, d) is defined as a – b + c

Sub 505 Level | Functions and Custom Characters

Sub 505 Level | Functions and Custom Characters hide tags

pushpitkc

02 Nov 2018, 04:08

1

4

4,555

13 Nov 2025, 08:03

7!! ER

Let the function h be defined by h(x) = x^(1/2) + 2. If 3h(v) = 18

505-555 Level | Algebra, Functions and Custom Characters

505-555 Level | Algebra, Functions and Custom Characters hide tags

Bunuel

17 Apr 2019, 00:34

4

6

3,546

13 Nov 2025, 07:40

7!! ER

If 2f(x) + f(x^2 - 1) = 1, for all real numbers x, then what is the

805+ Level | Functions and Custom Characters

805+ Level | Functions and Custom Characters hide tags

Bunuel

24 Oct 2022, 01:30

17

6

3,063

12 Nov 2025, 11:32

7!! ER

If @(n) is defined as the product of the cube root of n and

605-655 Level | Algebra +3 tags

605-655 Level | Algebra, Exponents, Functions and Custom Characters, Roots hide tags

GMATD11

28 Feb 2011, 03:12

123

15

16,847

09 Nov 2025, 09:54

7!! ER

If the operation @ is defined for all a and b by the equatio

Sub 505 Level | Algebra, Functions and Custom Characters

Sub 505 Level | Algebra, Functions and Custom Characters hide tags

pete300

18 Sep 2003, 07:58

45

9

21,353

09 Nov 2025, 09:21

7!! ER

O(x) represents the least odd integer greater than x, whereas o(x)

655-705 Level | Functions and Custom Characters, Number Properties

655-705 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

01 Sep 2015, 22:28

34

18

9,398

03 Nov 2025, 13:32

7!!

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

555-605 Level | Functions and Custom Characters

555-605 Level | Functions and Custom Characters hide tags

Kinshook

22 Jul 2019, 07:45

6

3

2,836

03 Nov 2025, 10:44

7!! ER

The operators * and + operate only on the numbers 0 and 1 as defin

655-705 Level | Functions and Custom Characters

655-705 Level | Functions and Custom Characters hide tags

Bunuel

05 Oct 2021, 01:30

7

5

2,398

02 Nov 2025, 08:27

7!! ER

Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If

655-705 Level | Functions and Custom Characters, Remainders

655-705 Level | Functions and Custom Characters, Remainders hide tags

prakash85

06 Nov 2014, 03:55

49

16

10,870

31 Oct 2025, 00:03

7!! ER

Function F(x) is defined as follows: if x is positive or 0 then F(x) =

705-805 Level | Functions and Custom Characters

705-805 Level | Functions and Custom Characters hide tags

Bunuel

28 May 2020, 02:04

38

13

13,601

30 Oct 2025, 07:55

7!! ER

IF F(x + 1/x) = x^2 + 1/x^2....what is the value of

655-705 Level | Functions and Custom Characters

655-705 Level | Functions and Custom Characters hide tags

EgmatQuantExpert

27 Apr 2017, 23:09

71

11

12,786

28 Oct 2025, 11:15

7!! ER

For all real numbers a, b, c, d, e, and f, the operation Θ is defined

Sub 505 Level | Arithmetic, Functions and Custom Characters

Sub 505 Level | Arithmetic, Functions and Custom Characters hide tags

gmatt1476

20 Apr 2020, 11:30

20

11

20,189

by: DanTheGMATMan

25 Oct 2025, 19:28

7!! ER

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

655-705 Level | Functions and Custom Characters, Number Properties

655-705 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

21 Feb 2020, 05:57

39

4

8,002

25 Oct 2025, 09:29

7!! ER

Let the function g(a, b) = f(a) + f(b).

805+ Level | Functions and Custom Characters

805+ Level | Functions and Custom Characters hide tags

1, 2

gmatbull

29 Nov 2012, 19:17

325

22

36,077

21 Oct 2025, 05:04

7!! ER -1

The domain of the function f(x) = \frac{\sqrt{x - 1{x+1} is the

605-655 Level | Functions and Custom Characters, Number Properties

605-655 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

16 Aug 2023, 06:00

132

16

37,884

by: Su1206

21 Oct 2025, 04:53

7!! ER

For all positive integers x and y in the expression x&y, the symbol &

655-705 Level | Functions and Custom Characters, Probability

655-705 Level | Functions and Custom Characters, Probability hide tags

Bunuel

28 Apr 2015, 05:27

36

4

8,393

17 Oct 2025, 11:27

7!! ER

If f(x)=3xx and g(x)=x^2, what is f(g(4))?

Sub 505 Level | Algebra, Functions and Custom Characters

Sub 505 Level | Algebra, Functions and Custom Characters hide tags

Bunuel

09 Dec 2015, 08:26

7

6

8,686

16 Oct 2025, 22:54

7!! ER

If f(x) = 5x^3 - 2x + 8 and g(y) = 6y - 4, then g(f(x)) =

Sub 505 Level | Algebra, Functions and Custom Characters

Sub 505 Level | Algebra, Functions and Custom Characters hide tags

dzodzo85

23 Apr 2012, 05:33

19

4

14,696

16 Oct 2025, 10:07

7!! ER

For all numbers a, b, c, and d, is defined by the equation Which of

505-555 Level | Functions and Custom Characters

505-555 Level | Functions and Custom Characters hide tags

parkhydel

27 Apr 2020, 13:49

37

4

13,954

12 Oct 2025, 08:20

7!! ER

For all positive integers m and v, the expression m Θ v represents the

Sub 505 Level | Functions and Custom Characters, Remainders

Sub 505 Level | Functions and Custom Characters, Remainders hide tags

nycgirl212

08 Jun 2016, 10:13

94

8

33,776

12 Oct 2025, 08:18

7!! ER

When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[4]

655-705 Level | Functions and Custom Characters

655-705 Level | Functions and Custom Characters hide tags

galiya

06 May 2012, 08:28

53

9

14,211

10 Oct 2025, 12:46

7!! ER

If ⌈n⌉ denotes the least integer greater than or equal to n and ⌈n/2 -

605-655 Level | Functions and Custom Characters

605-655 Level | Functions and Custom Characters hide tags

ariellelouise

10 Apr 2020, 08:59

53

4

8,718

10 Oct 2025, 07:25

7!! ER

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when

555-605 Level | Arithmetic, Functions and Custom Characters

555-605 Level | Arithmetic, Functions and Custom Characters hide tags

1, 2

Guduna

08 Sep 2010, 06:38

695

21

146,665

10 Oct 2025, 01:13

7!! ER

When x, y are positive integers, x@y = xy/(x + y). If a, b, and c are

555-605 Level | Algebra, Functions and Custom Characters

555-605 Level | Algebra, Functions and Custom Characters hide tags

Bunuel

15 Jun 2023, 07:00

12

2

2,442

by: lamok

08 Oct 2025, 21:08

7!! ER

The range of a function is the set of all possible values of the func

705-805 Level | Functions and Custom Characters, Number Properties

705-805 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

13 Aug 2023, 12:00

216

17

41,146

08 Oct 2025, 06:10

7!! ER

The domain of the function f(x) = \sqrt{\sqrt{x+2} - \sqrt{4-x

655-705 Level | Functions and Custom Characters, Roots

655-705 Level | Functions and Custom Characters, Roots hide tags

Bunuel

13 Aug 2023, 06:00

391

17

48,673

08 Oct 2025, 06:08

7!! ER

For any integer n greater than 1, [n denotes the product of

605-655 Level | Functions and Custom Characters, Number Properties

605-655 Level | Functions and Custom Characters, Number Properties hide tags

Bunuel

09 Mar 2014, 15:11

434

18

50,605

08 Oct 2025, 06:00

7!!

A function f(x) is defined for all the real values of z such that 3f(x

655-705 Level | Algebra, Functions and Custom Characters

655-705 Level | Algebra, Functions and Custom Characters hide tags

Briickky

07 Oct 2025, 05:34

12

4

523

by: Briickky

08 Oct 2025, 01:54

7!! ER

A certain quantity is measured on two different scales, the R-scale

705-805 Level | Algebra, Functions and Custom Characters

705-805 Level | Algebra, Functions and Custom Characters hide tags

1, 2

appy001

26 Jun 2010, 12:40

617

23

47,579

06 Oct 2025, 06:36

7!! ER

The functions f and g are defined by f(x) = |2x +1| and g(x) = 3 for a

Sub 505 Level | Absolute Values, Functions and Custom Characters

Sub 505 Level | Absolute Values, Functions and Custom Characters hide tags

Bunuel

07 Dec 2018, 02:39

17

5

9,840

04 Oct 2025, 02:41

7!! ER

If f(3x + 2) = 9x² + 12x - 1, then f(k - 1) =

605-655 Level | Algebra, Functions and Custom Characters

605-655 Level | Algebra, Functions and Custom Characters hide tags

BrentGMATPrepNow

12 Aug 2018, 07:39

55

13

7,877

04 Oct 2025, 00:39

7!! ER

In the expression a $ b, the $ symbol represents one of the

805+ Level | Arithmetic +2 tags

805+ Level | Arithmetic, Functions and Custom Characters, Number Properties hide tags

emmak

19 Mar 2013, 10:40

127

10

12,184

03 Oct 2025, 01:56

7!! ER

How many common points have y = |x| and y = |x^2 - 4| ?

705-805 Level | Absolute Values, Functions and Custom Characters

705-805 Level | Absolute Values, Functions and Custom Characters hide tags

Bunuel

18 Jan 2022, 04:00

34

3

4,557

02 Oct 2025, 04:47

7!! ER

[x] is the greatest integer less than or equal to the real n

705-805 Level | Functions and Custom Characters, Number Properties

705-805 Level | Functions and Custom Characters, Number Properties hide tags

atalpanditgmat

08 Jun 2013, 02:54

230

12

26,599

02 Oct 2025, 04:15

7!! ER

For which of the following functions is f(a + b) = f(a) + f(b) for all

555-605 Level | Functions and Custom Characters

555-605 Level | Functions and Custom Characters hide tags

zz0vlb

23 Apr 2010, 16:24

1,013

19

210,645

01 Oct 2025, 12:02

7!! ER

If f is the function defined by f(x) = x^2*(1-x)^2 for all x, then f(1

555-605 Level | Algebra, Functions and Custom Characters

555-605 Level | Algebra, Functions and Custom Characters hide tags

petercao

14 Nov 2008, 16:41

24

9

14,001

01 Oct 2025, 01:28

7!! ER

If x*y = xy – 2(x + y) for all integers x and y, then 2* (–3) =

Sub 505 Level | Functions and Custom Characters, Number Properties

Sub 505 Level | Functions and Custom Characters, Number Properties hide tags

DeeptiM

18 Aug 2011, 11:47

20

7

19,298

28 Sep 2025, 07:54

7!! ER

A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of

705-805 Level | Functions and Custom Characters

705-805 Level | Functions and Custom Characters hide tags

MathRevolution

08 Oct 2019, 00:45

41

9

8,695

27 Sep 2025, 22:23

7!! ER

For an integer n greater than 1, n* denotes the product

655-705 Level | Functions and Custom Characters, Number Properties

655-705 Level | Functions and Custom Characters, Number Properties hide tags

Turkish

26 Mar 2015, 03:07

48

10

6,814

24 Sep 2025, 13:19

7!! ER

For all real numbers x, the operation Δ is defined as xΔ = . If (bΔ)Δ

555-605 Level | Algebra, Functions and Custom Characters

555-605 Level | Algebra, Functions and Custom Characters hide tags

AbdurRakib

10 Jun 2016, 04:28

31

5

6,334

24 Sep 2025, 12:00

7!! ER

For which of the following functions f is f(x) = f(1-x) for all x?

605-655 Level | Functions and Custom Characters

605-655 Level | Functions and Custom Characters hide tags

study

25 Oct 2009, 02:34

1,309

18

279,844

24 Sep 2025, 04:31

7!! ER

A function f(x) is defined as f(x+y)=f(x)+f(y) for all real value of x

655-705 Level | Functions and Custom Characters

655-705 Level | Functions and Custom Characters hide tags

nick1816

01 Dec 2019, 20:55

34

8

8,229