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100 Hardest Problem Solving Questions (Jun 1st, 2025 - Jul 1st, 2025)
100 Easiest Problem Solving Questions (Jun 1st, 2025 - Jul 1st, 2025)
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 |