GRE Mixed Quantitative Reasoning (Problem Solving) 2 — Questions and Answers
Question 1: A store marks up an item by 40%, then offers a 25% discount on the marked-up price. What is the net percent change from the original price?
- 5% increase (Correct answer)
- 10% increase
- 15% increase
- No change
Correct answer: 5% increase
1.40 × 0.75 = 1.05, a 5% increase.
Question 2: If 3^x = 81, what is the value of 3^(x-2)?
- 3
- 9 (Correct answer)
- 27
- 81
Correct answer: 9
3^x = 81 means x = 4, so 3^(4-2) = 3^2 = 9.
Question 3: A car travels 120 miles at 40 mph, then 120 miles at 60 mph. What is the average speed for the whole trip?
- 46 mph
- 48 mph (Correct answer)
- 50 mph
- 52 mph
Correct answer: 48 mph
Total time = 3 + 2 = 5 hours for 240 miles, so 240/5 = 48 mph.
Question 4: The ratio of boys to girls in a class is 3:5. If there are 20 girls, how many students are in the class?
- 28
- 32 (Correct answer)
- 36
- 40
Correct answer: 32
5 parts = 20, so 1 part = 4; total 8 parts = 32.
Question 5: If x and y are positive integers and x + y = 10, what is the maximum possible value of xy?
- 20
- 24
- 25 (Correct answer)
- 30
Correct answer: 25
The product is maximized when x = y = 5, giving 25.
Question 6: A solution is 30% acid. How many liters of pure water must be added to 12 liters to make it 20% acid?
- 4
- 6 (Correct answer)
- 8
- 10
Correct answer: 6
Acid = 3.6 L stays constant; 3.6/0.20 = 18 L total, so 18 - 12 = 6 L added.
Question 7: What is the units digit of 7^23?
- 1
- 3 (Correct answer)
- 7
- 9
Correct answer: 3
Units digits of 7 cycle 7,9,3,1; 23 mod 4 = 3, giving the third value, 3.
GRE Mixed Quantitative Reasoning (Problem Solving) 2
A store marks up an item by 40%, then offers a 25% discount on the marked-up price.
What is the net percent change from the original price?