100 Hardest and easiest questions for PS as of June 2025 : Problem Solving (PS)

Problem Solving (PS)

Rank

Title

Topics

1

For which of the following values of n is (100+n)/n NOT an

Difficulty: Sub 505 Level, Arithmetic, Multiples and Factors, Number Properties, Source: 1000 Series, Source: Official Guide, Source: OG 2015, Source: OG 12, Source: OG 11

2

For which of the following x is |x|+x>0 ?

Difficulty: Sub 505 Level, Absolute Values, Inequalities, Source: Math Revolution

3

If y = 5x^2 - 2x, and x = 3, then y = ?

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series

4

The price of a coat in a certain store is $500. If the price of the co

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016

5

If (7^(3/4))^n = 7, what is the value of n?

Difficulty: Sub 505 Level, Algebra, Exponents, Source: Official Guide, Source: OG 10, Source: Quant Review 1st

6

If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x +

Difficulty: Sub 505 Level, Algebra, Source: GMAT Prep (Classic), Source: Official Guide, Source: EA, Source: OG 12

7

On 3 sales John has received commissions of $240, $80, and $110, and

Difficulty: Sub 505 Level, Word Problems, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 10, Source: Quant Review 2nd, Source: Quant Review 1st

8

Which of the following is equivalent to the pair of

Difficulty: Sub 505 Level, Inequalities, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 2025-2026

9

During a trip that they took together, Carmen, Juan, Maria, a

Difficulty: Sub 505 Level, Statistics and Sets Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2025-2026

10

If n is an integer, which of the following must be even?

Difficulty: Sub 505 Level, Must or Could be True Questions, Number Properties, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

11

A bakery opened yesterday with its daily supply of 40 dozen

Difficulty: Sub 505 Level, Word Problems, Source: 1000 Series, Source: Official Guide, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

12

What is 45 percent of 7/12 of 240 ?

Difficulty: Sub 505 Level, Arithmetic, Percent and Interest Problems, Source: 1000 Series, Source: Official Guide, Source: OG 10

13

Working at a constant rate, a copy machine makes 20 copies of a one-pa

Difficulty: Sub 505 Level, Work and Rate Problems, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019

14

If x is an even integer, which of the following is an odd integer?

Difficulty: Sub 505 Level, Number Properties, Source: 1000 Series, Source: Official Guide (Pre-2000), Source: OG 1988

15

(1/2+1/3)/(1/4) =

Difficulty: Sub 505 Level, Arithmetic, Fractions and Ratios, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 1st

16

If x = -1, then -(x^4 + x^3 + x^2 + x) =

Difficulty: Sub 505 Level, Algebra, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2nd, Source: Quant Review 1st

17

If x = -(2 - 5), then x =

Difficulty: Sub 505 Level, Algebra, Source: Official Guide, Source: OG 10, Source: Quant Review 1st

18

If the population of a certain country increases at the rate of one

Difficulty: Sub 505 Level, Word Problems, Source: 1000 Series, Source: Official Guide, Source: OG 10

19

If |A| > 19, which of the following could NOT be equal to A ?

Difficulty: Sub 505 Level, Absolute Values, Inequalities, Source: Manhattan GMAT

20

If it is assumed that 60 percent of those who receive a questionnaire

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: Official Guide, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016

21

The ratio 2 to 1/3 is equal to the ratio

Difficulty: Sub 505 Level, Fractions and Ratios, Source: 1000 Series, Source: Official Guide, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

22

Bob drives at an average rate of 50 mph from Berkeley to Los Angeles,

Difficulty: Sub 505 Level, Distance and Speed Problems, Source: Magoosh

23

If x + 5y = 16 and x = -3y

Difficulty: Sub 505 Level, Algebra, Source: 1000 Series, Source: Official Guide, Source: OG 11, Source: OG 10

24

The number 2 - 0.5 is how many times the number 1 - 0.5?

Difficulty: Sub 505 Level, Algebra, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

25

What number when multiplied by 4/7 yields 6/7 as the result?

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

26

The table shows a summary of the ticket sales from four performances o

Difficulty: Sub 505 Level, Arithmetic, Graphs and Illustrations, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019

27

In the equation above, k is a constant. If y = 17 when x = 2, what is

Difficulty: Sub 505 Level, Algebra, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12

28

If 2/(1+2/y)=1, then y =

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 2015, Source: OG 12, Source: OG 11, Source: OG 10

29

What is the value of x^2yz xyz^2, if x = 2, y = 1, and z = 3?

Difficulty: Sub 505 Level, Algebra, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016

30

In the xy-coordinate plane, if the point (0,2) lies on the graph of th

Difficulty: Sub 505 Level, Coordinate Geometry, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019

31

The sum S of the first n consecutive positive even integers is given

Difficulty: Sub 505 Level, Arithmetic, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019

32

1/2/(1/4 + 1/6) =

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 10

33

If Albert can travel 200 miles in 4 hours, how many hours will it take

Difficulty: Sub 505 Level, Distance and Speed Problems, Source: Princeton Review

34

Which of the following is equal to x^18 for all positive values of x ?

Difficulty: Sub 505 Level, Exponents, Source: GMAT Prep (Classic), Source: Official Guide, Source: OG 10, Source: Quant Review 1st

35

Each week, a clothing salesperson receives a commission equal

Difficulty: Sub 505 Level, Word Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2025-2026

36

Kelly and Chris packed several boxes with books. If Chris packed 60 pe

Difficulty: Sub 505 Level, Fractions and Ratios, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 12, Source: OG 11, Source: OG 10

37

x=(1/4)sv^2 In the formula shown, if x/s = 25 and v > 0, what is the v

Difficulty: Sub 505 Level, Algebra, Source: GMAT Prep (Classic)

38

7/(1/5) + 5/(1/7) =

Difficulty: Sub 505 Level, Arithmetic, Fractions and Ratios, Source: 1000 Series, Source: Official Guide, Source: OG 12, Source: OG 11

39

If n is a prime number greater than 3, what is the remainder when n^2

Difficulty: Sub 505 Level, Remainders, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12

40

What is the median of the numbers shown?

Difficulty: Sub 505 Level, Statistics and Sets Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019

41

If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is

Difficulty: Sub 505 Level, Fractions and Ratios, Mixture Problems, Source: Official Guide

42

If m is an integer such that (-2)^2m = 2^{9 - m}, then m=

Difficulty: Sub 505 Level, Exponents, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2nd, Source: Quant Review 1st

43

In the figure above, the coordinates of point V are

Difficulty: Sub 505 Level, Coordinate Geometry, Source: 1000 Series, Source: Official Guide, Source: OG 2015, Source: OG 12, Source: OG 11, Source: OG 10

44

A souvenir vendor purchased 1,000 shirts for a special event at a pric

Difficulty: Sub 505 Level, Word Problems, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019

45

If x + y = 7 and x – y = 3, then x^2 - y^2 =

Difficulty: Sub 505 Level, Algebra, Source: Manhattan GMAT

46

If the tick marks on the number line shown are equally spaced, what is

Difficulty: Sub 505 Level, Graphs and Illustrations, Source: GMAT Prep (Classic)

47

A retail appliance store priced a video recorder at 20 percent above

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 11

48

150 is what percent of 30 ?

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: 1000 Series, Source: Official Guide, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

49

A certain restaurant that regularly advertises through the mail has

Difficulty: Sub 505 Level, Arithmetic, Word Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019

50

If x books cost $5 each and y books cost $8 each, then the average

Difficulty: Sub 505 Level, Fractions and Ratios, Source: 1000 Series, Source: Official Guide, Source: OG 10

51

Which of the following is equal to 85 percent of 160?

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: 1000 Series, Source: Official Guide (Pre-2000), Source: OG 1988

52

If x is negative and y is positive, which of the following must be

Difficulty: Sub 505 Level, Number Properties, Source: Princeton Review

53

If x is a positive integer and 4^x 3 = y, which of the following CAN

Difficulty: Sub 505 Level, Algebra, Exponents, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2025-2026

54

If the average (arithmetic mean) of x + 2, x + 4, and x + 6 is 0

Difficulty: Sub 505 Level, Arithmetic, Source: Grockit

55

Company C produces toy trucks at a cost of $5.00 each for the first 10

Difficulty: Sub 505 Level, Word Problems, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016

56

If x/y = 2, then (x-y)/y =

Difficulty: Sub 505 Level, Algebra, Source: Official Guide (Pre-2000), Source: OG 1988

57

If x > 0 and x^2 = 161, what is the best whole number approximation of

Difficulty: Sub 505 Level, Inequalities, Source: Official Guide (Pre-2000), Source: OG 1988

58

1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

Difficulty: Sub 505 Level, Arithmetic, Source: Official Guide, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016

59

While a family was away on vacation, they paid a neighborhood boy $11

Difficulty: Sub 505 Level, Word Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019

60

Last fall, 40 percent of the students at a certain high school partici

Difficulty: Sub 505 Level, Overlapping Sets, Source: GMAT Prep (Classic)

61

A certain machine produces 1,000 units of product P per hour. Working

Difficulty: Sub 505 Level, Work and Rate Problems, Source: GMAT Prep (Classic)

62

For which of the following values of s is (50+s)s an integer?

Difficulty: Sub 505 Level, Number Properties, Source: Veritas Prep

63

|−4|(|−20| − |5|) =

Difficulty: Sub 505 Level, Absolute Values, Arithmetic, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019

64

The 180 students in a group are to be seated in rows so that

Difficulty: Sub 505 Level, Multiples and Factors, Source: 1000 Series, Source: GMAT Prep (Classic)

65

There is a total of 120 marbles in a box, each of which is red, green,

Difficulty: Sub 505 Level, Probability, Source: 1000 Series, Source: GMAT Paper Tests

66

If the probability that event S will not occur is 1 - y, then the prob

Difficulty: Sub 505 Level, Probability, Source: GMAT Prep (Classic)

67

0.1 + 0.1^2 + 0.1^3 =

Difficulty: Sub 505 Level, Arithmetic, Exponents, Source: Official Guide, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

68

A certain builder is selling five homes for the following

Difficulty: Sub 505 Level, Statistics and Sets Problems, Source: GMAT Prep (Classic)

69

In a survey on sales of soft drinks, 65 percent of the surveyed

Difficulty: Sub 505 Level, Overlapping Sets, Source: GMAT Prep (Focus)

70

A certain method for calculating pediatric drug dosages states that if

Difficulty: Sub 505 Level, Arithmetic, Word Problems, Source: Official Guide, Source: OG 2024-2025, Source: OG 2025-2026

71

If Mario was 32 years old 8 years ago, how old was he x year

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

72

If s > 0 and (r/s)^1/2=s, what what is r in terms of s ?

Difficulty: Sub 505 Level, Algebra, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

73

(0.3)^5/(0.3)^3

Difficulty: Sub 505 Level, Arithmetic, Exponents, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 12, Source: OG 11, Source: OG 10

74

If the relations shown hold for the operation ⊕ and the numbers m, n,

Difficulty: Sub 505 Level, Functions and Custom Characters, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2025-2026

75

Which of the following fractions is equal to 0.16?

Difficulty: Sub 505 Level, Fractions and Ratios, Source: 1000 Series, Source: GMAT Paper Tests

76

As a salesperson, Phyllis can choose one of two methods of annual paym

Difficulty: Sub 505 Level, Word Problems, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2022, Source: OG 10, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st, Source: OG 2025-2026

77

1/(1+1/3)-1/(1+1/2)

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12

78

The average (arithmetic mean) of 6,8, and 10 equals the average

Difficulty: Sub 505 Level, Statistics and Sets Problems, Source: 1000 Series, Source: Official Guide, Source: OG 11, Source: OG 10

79

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

Difficulty: Sub 505 Level, Arithmetic, Functions and Custom Characters, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2025-2026

80

If 6 < 2x - 4 < 12, which of the following could be a value of x?

Difficulty: Sub 505 Level, Inequalities, Source: Manhattan GMAT

81

A fruit-salad mixture consists of apples, peaches, and grape

Difficulty: Sub 505 Level, Fractions and Ratios, Word Problems, Source: 1000 Series, Source: Official Guide, Source: OG 2015, Source: OG 12, Source: OG 11, Source: OG 10

82

A committee is composed of w women and m men. If 3 women and

Difficulty: Sub 505 Level, Probability, Source: 1000 Series, Source: Official Guide, Source: OG 2015, Source: OG 12, Source: OG 11, Source: OG 10

83

Which of the following must be equal to (x^6)(x^4) ?

Difficulty: Sub 505 Level, Exponents, Source: GMAT Prep (Classic)

84

A box contains 25 red blacks, 100 blue blocks, and 175 yellow blocks.

Difficulty: Sub 505 Level, Probability, Source: GMAT Prep (Classic)

85

A long-distance telephone company charges a monthly fee of $4.95 plus

Difficulty: Sub 505 Level, Word Problems, Source: GMAT Prep (Classic)

86

(-1)^2 - (-1)^3 =

Difficulty: Sub 505 Level, Exponents, Source: 1000 Series, Source: Official Guide (Pre-2000), Source: OG 1988

87

If x is positive and the distance between -7 and 0 is equal to the di

Difficulty: Sub 505 Level, Absolute Values, Source: Math Revolution

88

In the Johnsons' monthly budget, the dollar amounts allocate

Difficulty: Sub 505 Level, Fractions and Ratios, Source: Official Guide, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015, Source: OG 12, Source: OG 11

89

If 3 - x = 2x - 3, then 4x =

Difficulty: Sub 505 Level, Algebra, Source: Official Guide, Source: OG 10, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

90

In the figure above, the sum of the three numbers in the hor

Difficulty: Sub 505 Level, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

91

1/(3-1/(3-1/(3-1)))=

Difficulty: Sub 505 Level, Arithmetic, Fractions and Ratios, Source: Official Guide, Source: EA, Source: Quant Review 2019, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd

92

If p is an even integer and q is an odd integer, which of the followin

Difficulty: Sub 505 Level, Must or Could be True Questions, Number Properties, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 12, Source: OG 11, Source: OG 10

93

At the opening of a trading day at a certain stock exchange, the price

Difficulty: Sub 505 Level, Percent and Interest Problems, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021, Source: Quant Review 2020, Source: Quant Review 2019, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016

94

For the inequalities above, what is the maximum possible value of P +

Difficulty: Sub 505 Level, Arithmetic, Inequalities, Min-Max Problems, Source: GMAT Prep (Classic)

95

(1+5^1/2)(1-5^1/2)=

Difficulty: Sub 505 Level, Algebra, Arithmetic, Source: 1000 Series, Source: Official Guide, Source: OG 10, Source: Quant Review 2018, Source: Quant Review 2017, Source: Quant Review 2016, Source: Quant Review 2nd, Source: Quant Review 1st

96

(2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =

Difficulty: Sub 505 Level, Algebra, Roots, Source: 1000 Series, Source: GMAT Paper Tests, Source: Official Guide, Source: OG 11, Source: OG 10

97

A student’s average (arithmetic mean) test score on 4 tests is 80. Wh

Difficulty: Sub 505 Level, Arithmetic, Number Properties, Source: OG 12

98

What is the number of different committees of 4 people that can be sel

Difficulty: Sub 505 Level, Combinations, Source: GMAT Prep (Classic)

99

If x/y = 1, what is the value of |x| - |y|?

Difficulty: Sub 505 Level, Absolute Values, Source: GMAT Club Tests

100

If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

Difficulty: Sub 505 Level, Algebra, Source: 1000 Series, Source: GMAT Prep (Classic), Source: GMAT Prep (Focus), Source: OG 11, Source: OG 10

Problem Solving (PS)
Rank	Title	Topics
1	Two trucks travel from Alphaburg to Betaville along the same route.	Difficulty: 805+ Level, Distance and Speed Problems, Word Problems, Source: Kaplan
2	12 Days of Christmas GMAT Competition - Day 4: For each positive	Difficulty: 805+ Level, Number Properties, Source: Competition Questions, Source: GMAT Club Tests
3	A list of numbers has six positive integers. Three of those integers a	Difficulty: 805+ Level, Statistics and Sets Problems, Source: Veritas Prep
4	If two integers are chosen at random out of the set {2, 5, 7, 8}, what	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
5	Let a 2-placer be a terminating decimal, between 0 and 1, for which	Difficulty: 805+ Level, Combinations, Fractions and Ratios, Number Properties, Source: Manhattan GMAT
6	Arrow AB which is a line segment exactly 5 units along with	Difficulty: 805+ Level, Coordinate Geometry, Source: Manhattan GMAT
7	A box contains three pairs of blue gloves and two pairs of	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
8	In a hostel there are 250 students, 120 watch Fox News, 80 watch Sky S	Difficulty: 805+ Level, Overlapping Sets, Source: Jamboree
9	In a certain mathematical activity, we have five cards with five diffe	Difficulty: 805+ Level, Combinations, Source: Magoosh
10	A set of five positive integers has an arithmetic mean of 150. A parti	Difficulty: 805+ Level, Number Properties, Statistics and Sets Problems, Source: Veritas Prep
11	A bag contains 6 large marbles: 3 red, 2 green, and 1 yellow, and 3 sm	Difficulty: 805+ Level, Probability, Source: Magoosh
12	There are 500 cars on a sales lot, all of which have either two doors	Difficulty: 805+ Level, Overlapping Sets, Source: Magoosh
13	A bus from city M is traveling to city N at a constant speed while ano	Difficulty: 805+ Level, Distance and Speed Problems, Source: GMAT Club Tests
14	In the country of Celebria, the Q-score of a politician is computed fr	Difficulty: 805+ Level, Percent and Interest Problems, Word Problems, Source: Manhattan GMAT
15	For positive integers k and n, the k-power remainder of n is defined	Difficulty: 805+ Level, Min-Max Problems, Number Properties, Remainders, Source: Manhattan GMAT
16	If the product of all the unique positive divisors of n, a positive in	Difficulty: 805+ Level, Multiples and Factors, Number Properties, Source: Manhattan GMAT
17	A square is drawn in the coordinate plane with its vertices at the poi	Difficulty: 805+ Level, Coordinate Geometry, Source: Manhattan GMAT
18	Six friends live in the city of Monrovia. There are four nat	Difficulty: 805+ Level, Probability, Source: Veritas Prep
19	Two trains A and B start from two points P1 and P2 respectively at the	Difficulty: 805+ Level, Arithmetic, Source: Kaplan
20	GMAT Club World Cup 2022 (DAY 5): The infinite sequence of integers	Difficulty: 805+ Level, Sequences, Source: Competition Questions, Source: GMAT Club Tests
21	The random variable x has the following continuous probability distrib	Difficulty: 805+ Level, Coordinate Geometry, Probability, Source: Manhattan GMAT
22	An integer between 1 and 300, inclusive, is chosen at random	Difficulty: 805+ Level, Number Properties, Probability, Source: Manhattan GMAT
23	In the coordinate axis above, line segment AC is three times	Difficulty: 805+ Level, Coordinate Geometry, Source: Princeton Review
24	How many positive seven-digit integers include the sequence 123, in th	Difficulty: 805+ Level, Combinations, Source: Veritas Prep
25	On a partly cloudy day, Derek decides to walk back from work	Difficulty: 805+ Level, Distance and Speed Problems, Source: Veritas Prep
26	Question of the Week - 27 (q is a three-digit number, in which ......)	Difficulty: 805+ Level, Algebra, Multiples and Factors, Number Properties, Source: e-GMAT
27	Bill and Jane play a simple game involving two fair dice, each of	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
28	A botanist selects n^2 trees on an island and studies (2n +	Difficulty: 805+ Level, Remainders, Source: Princeton Review
29	Darcy, Gina, Ray and Susan will be the only participants at a meeting.	Difficulty: 805+ Level, Probability, Source: Kaplan
30	For how many different pairs of positive integers (a, b) can	Difficulty: 805+ Level, Arithmetic, Source: Manhattan GMAT
31	The median of n consecutive odd integers is 30. If the fifth term.....	Difficulty: 805+ Level, Number Properties, Statistics and Sets Problems, Source: e-GMAT
32	Theresa is a basketball player practicing her free throws. On her fir	Difficulty: 805+ Level, Fractions and Ratios, Probability, Source: Magoosh
33	Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one gr	Difficulty: 805+ Level, Combinations, Source: Magoosh
34	GMAT Club Olympics 2024 (Day 6): To be allowed to participate in the	Difficulty: 805+ Level, Min-Max Problems, Overlapping Sets, Source: Competition Questions, Source: GMAT Club Tests
35	How many distinct four-digit numbers can be formed by the	Difficulty: 805+ Level, Combinations, Source: Magoosh
36	Abe, Beth and Carl each start to write a science fiction book.	Difficulty: 805+ Level, Probability, Source: e-GMAT
37	In the year-end clearance sale, a music system is discounted by d%	Difficulty: 805+ Level, Percent and Interest Problems, Word Problems, Source: e-GMAT
38	4 individuals arrive separately at an orchestra concert with	Difficulty: 805+ Level, Probability, Source: Veritas Prep
39	Question of the Week - 43 (While working individually, each of A, B)	Difficulty: 805+ Level, Word Problems, Work and Rate Problems, Source: e-GMAT
40	Highmont private school polled the graduating class of 125 for the mus	Difficulty: 805+ Level, Overlapping Sets, Source: Magoosh
41	How many different pairs of integers (a, b) exist such that 2 <= a <=	Difficulty: 805+ Level, Algebra, Combinations, Inequalities, Source: Manhattan GMAT
42	If x and y are integers and 2x + 9y = 57, then the least possible valu	Difficulty: 805+ Level, Algebra, Source: Veritas Prep
43	A bicyclist travels 8 miles due west at a constant speed. Next, she	Difficulty: 805+ Level, Distance and Speed Problems, Source: Magoosh
44	If a, b, c, d, e, f, g, h, i and j are distinct positive integers, wha	Difficulty: 805+ Level, Exponents, Source: Magoosh
45	x = 10^10 - z, where z is a two-digit integer. If the sum of the digit	Difficulty: 805+ Level, Exponents, Number Properties, Source: Manhattan GMAT
46	A, B and C are three distinct single-digit positive numbers.	Difficulty: 805+ Level, Combinations, Number Properties, Source: e-GMAT
47	In a game of Numberball, teams can score in increments of 3, 4, or 7	Difficulty: 805+ Level, Algebra, Min-Max Problems, Source: Manhattan GMAT
48	Which of the following is/are true?	Difficulty: 805+ Level, Absolute Values, Inequalities, Source: Experts' Global
49	If the probability of rain on any given day is 50%, what is the probab	Difficulty: 805+ Level, Probability, Source: Veritas Prep
50	If the product of 6 distinct positive integers is 6^6. What is the min	Difficulty: 805+ Level, Exponents, Min-Max Problems, Statistics and Sets Problems, Source: GMAT Club Tests
51	How many numbers that are not divisible by 6 divide evenly	Difficulty: 805+ Level, Multiples and Factors, Source: Manhattan GMAT
52	If Whitney wrote the decimal representations for the first 300 positiv	Difficulty: 805+ Level, Combinations, Number Properties, Source: Official Guide
53	In the game of Yahtzee, a "full house" occurs when a player	Difficulty: 805+ Level, Probability, Source: Veritas Prep
54	If 7<x^2-4x+12, which of the following MUST be true?	Difficulty: 805+ Level, Exponents, Inequalities, Source: GMAT Prep Now
55	If a, b are integers, and (a-b)^2 + 8b^2=108, what is the number of th	Difficulty: 805+ Level, Algebra, Source: Math Revolution
56	Louie takes out a three-month loan of $1000. The lender charges him 10	Difficulty: 805+ Level, Percent and Interest Problems, Source: Magoosh
57	One side of a parking stall is defined by a straight stripe that consi	Difficulty: 805+ Level, Number Properties, Source: Official Guide, Source: Quant Review 2022, Source: Quant Review 2021
58	A bag contains 10 bulbs and 5 torches, out of which 3 bu	Difficulty: 805+ Level, Probability, Source: e-GMAT
59	Pam and Robin each roll a pair of fair, six-sided dice. What is the pr	Difficulty: 805+ Level, Probability, Source: Veritas Prep
60	For any positive integer n greater than 1, n! denotes the product of a	Difficulty: 805+ Level, Multiples and Factors, Source: e-GMAT
61	A sequence of numbers (geometric sequence) is given by the	Difficulty: 805+ Level, Absolute Values, Exponents, Sequences, Source: Grockit
62	A certain café sells bagels for $1.10 and muffins for $1.50	Difficulty: 805+ Level, Word Problems, Source: Princeton Review
63	On Friday, four people sat one behind the other in a movie theater.	Difficulty: 805+ Level, Combinations, Source: GMAT Club Tests
64	Ben and Shari have invited three other couples to their apar	Difficulty: 805+ Level, Combinations, Source: Princeton Review
65	If x is the reciprocal of a positive integer, then the maximum value o	Difficulty: 805+ Level, Min-Max Problems, Number Properties, Source: Manhattan GMAT
66	Patty and Selma play a gambling game in which Patty rolls a single fai	Difficulty: 805+ Level, Word Problems, Source: Veritas Prep
67	Ida had 5 cards with matching envelopes - same in design, different in	Difficulty: 805+ Level, Probability, Source: Experts' Global
68	If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative inte	Difficulty: 805+ Level, Absolute Values, Algebra, Exponents, Min-Max Problems, Source: Manhattan GMAT
69	How many different combinations of outcomes can you make by	Difficulty: 805+ Level, Combinations, Source: Jamboree
70	If x and y are integers such that 4x + 3y = 3xy, how many distinct	Difficulty: 805+ Level, Algebra, Source: GMAT Club Tests
71	W, X, Y and Z are four different positive integers. When X	Difficulty: 805+ Level, Remainders, Source: GMAT Prep Now
72	Bob invested one half of his savings in a bond that paid simple intere	Difficulty: 805+ Level, Percent and Interest Problems, Source: Veritas Prep
73	Rebecca runs at a constant rate on the treadmill and it takes her 2 ho	Difficulty: 805+ Level, Distance and Speed Problems, Source: GMAT Pill
74	List T consist of 30 positive decimals, none of which is an integer	Difficulty: 805+ Level, Min-Max Problems, Source: Official Guide, Source: OG 2022, Source: OG 2021, Source: OG 2020, Source: OG 2019, Source: OG 2018, Source: OG 2017, Source: OG 2016, Source: OG 2015
75	A computer program generates a single digit by a random process, accor	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
76	It takes 6 days for 3 women and 2 men working together to	Difficulty: 805+ Level, Work and Rate Problems, Source: 800 Score
77	Question of the Week- 25 (For a meeting, 9 speakers must be .........)	Difficulty: 805+ Level, Probability, Source: e-GMAT
78	Two different primes may be said to “rhyme” around an integer if they	Difficulty: 805+ Level, Number Properties, Source: Manhattan GMAT
79	What is the decreasing order from left to right of the following numbe	Difficulty: 805+ Level, Number Properties, Roots, Source: Princeton Review
80	Set A is composed of nine numbers, labeled A1 through A9. Set B is als	Difficulty: 805+ Level, Statistics and Sets Problems, Source: Manhattan GMAT
81	There are two solutions of water and spirit of different concentration	Difficulty: 805+ Level, Mixture Problems, Source: GMATWhiz
82	List L contains the 98 repeating decimals 0.010101..., 0.020202..., ..	Difficulty: 805+ Level, Number Properties, Source: Manhattan GMAT
83	A not-so-good clockmaker has four clocks on display in the w	Difficulty: 805+ Level, Distance and Speed Problems, Source: Power Prep
84	Three points are chosen independently an at random on the circumferenc	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
85	A soccer team played 25% more matches year-on-year in the second year	Difficulty: 805+ Level, Word Problems, Source: Official Guide, Source: OG 10
86	GMAT Club World Cup 2022 (DAY 7): Ronaldo puts an orange, an apple and	Difficulty: 805+ Level, Probability, Source: Competition Questions, Source: GMAT Club Tests
87	How many distinct positive integers d exist such that, when 48 is	Difficulty: 805+ Level, Remainders, Source: GMAT Club Tests
88	10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tou	Difficulty: 805+ Level, Word Problems, Source: GMAT Prep Now
89	A bag contains ten marbles of the same size: 3 are identical green mar	Difficulty: 805+ Level, Combinations, Source: Magoosh
90	A customer using a certain telephone calling plan pays a fee	Difficulty: 805+ Level, Word Problems, Source: Kaplan
91	On the number line shown, the distance between 0 and a . . .	Difficulty: 805+ Level, Absolute Values, Algebra, Source: e-GMAT
92	In a certain sequence, every term after the first is determi	Difficulty: 805+ Level, Sequences, Source: Manhattan GMAT
93	Ms. Barton has four children. You are told correctly that she has at	Difficulty: 805+ Level, Probability, Source: Manhattan GMAT
94	In the 6-digit integer 543, 2xy, x, and y are chosen from the digits	Difficulty: 805+ Level, Multiples and Factors, Probability, Source: Math Revolution
95	The ratio of a to b is twice the ratio of b to c. If a, b, and c are	Difficulty: 805+ Level, Fractions and Ratios, Number Properties, Source: Manhattan GMAT
96	If m^2 < 225 and n - m = -10, what is the sum f the smallest	Difficulty: 805+ Level, Algebra, Inequalities, Min-Max Problems, Source: GMAT Club Tests
97	A five-digit code for certain locks uses the digits 0,1,2,3,4,5,6,7,8,	Difficulty: 805+ Level, Combinations, Source: e-GMAT
98	A cyclist travels the length of a bike path that is 225 miles long, ro	Difficulty: 805+ Level, Distance and Speed Problems, Inequalities, Source: Manhattan GMAT, Source: Power Prep
99	List M consists of 50 decimals, each of which has a value between	Difficulty: 805+ Level, Algebra, Arithmetic, Word Problems, Source: Manhattan GMAT
100	If y = \|x + 5\| - \|x - 5\|, then y can take how many integer vales?	Difficulty: 805+ Level, Absolute Values, Source: GMAT Club Tests

100 Hardest and easiest questions for PS as of June 2025

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100 Hardest and easiest questions for PS as of June 2025

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