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

Final price = Original × 0.80 × 0.70 = Original × 0.56. 112 = 0.56 × P → P = 200.

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

3x − 7 = 2x + 8 → x = 15.

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

Combined speed = 60 + 80 = 140 mph. Time = 350/140 = 2.5 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

Width = w, length = 2w. Perimeter: 2(w + 2w) = 54 → 6w = 54 → w = 9. Length = 18. Area = 9 × 18 = 162 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

Start: 60g salt in 300g. Add x grams of salt: (60+x)/(300+x) = 0.25. 60+x = 75+0.25x → 0.75x = 15 → x = 20.

GRE Practice Test

GRE Practice Test

GRE Mixed Quantitative Reasoning (Problem Solving)