GRE Mixed Quantitative Reasoning (Problem Solving)

Question 1

A store offers a 30% discount on an item already marked down 20% from its original price. If the final price is $112, what was the original price?
(A) $180
(B) $200
(C) $220
(D) $240

Accepted Answer

$200

Answer

$180

Answer

$220

Answer

$240

Question 2

If 3x − 7 = 2(x + 4), what is the value of x?
(A) 13
(B) 14
(C) 15
(D) 16

Accepted Answer

15

Answer

13

Answer

14

Answer

16

Question 3

Two trains leave the same station at the same time, traveling in opposite directions. Train A travels at 60 mph and Train B at 80 mph. After how many hours are they 350 miles apart?
(A) 2.0 hours
(B) 2.5 hours
(C) 3.0 hours
(D) 3.5 hours

Accepted Answer

2.5 hours

Answer

2.0 hours

Answer

3.0 hours

Answer

3.5 hours

Question 4

A rectangular garden has a perimeter of 54 meters. If its length is twice its width, what is the area of the garden?
(A) 81 m²
(B) 108 m²
(C) 162 m²
(D) 180 m²

Accepted Answer

108 m²

Answer

81 m²

Answer

162 m²

Answer

180 m²

Question 5

A solution is 20% salt by weight. How many grams of pure salt must be added to 300 grams of this solution to make it 25% salt?
(A) 15g
(B) 18g
(C) 20g
(D) 24g

Accepted Answer

20g

Answer

15g

Answer

18g

Answer

24g

Question 6

A car travels 120 miles at 40 mph, then another 120 miles at 60 mph. What is the average speed for the entire trip?
(A) 48 mph
(B) 50 mph
(C) 52 mph
(D) 55 mph

Accepted Answer

48 mph

Answer

50 mph

Answer

52 mph

Answer

55 mph

Question 7

A company's profits increased by 25% in 2022 and then decreased by 20% in 2023. What was the net percentage change over the two years?
(A) 0%
(B) +5%
(C) −5%
(D) +10%

Accepted Answer

0%

Answer

+5%

Answer

−5%

Answer

+10%

Question 8

In a class of 36 students, 20 passed the math test, 18 passed the English test, and 8 passed both. How many students failed both tests?
(A) 4
(B) 6
(C) 8
(D) 10

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Question 9

What is the slope of a line perpendicular to the line 3x − 4y = 12?
(A) 3/4
(B) 4/3
(C) −4/3
(D) −3/4

Accepted Answer

−4/3

Answer

3/4

Answer

4/3

Answer

−3/4

Question 10

A jar contains 5 red, 4 blue, and 3 green marbles. Two marbles are drawn without replacement. What is the probability that both are red?
(A) 5/33
(B) 5/22
(C) 2/11
(D) 5/12

Accepted Answer

5/33

Answer

5/22

Answer

2/11

Answer

5/12