GMAT Quantitative: Algebraic Word Problems 2 — Questions and Answers
Question 1: A train travels 240 miles at a constant speed. If the speed had been 20 mph faster, the trip would have taken 1 hour less. What was the original speed?
- 40 mph (Correct answer)
- 60 mph
- 80 mph
- 48 mph
Correct answer: 40 mph
240/x − 240/(x+20) = 1 gives x² + 20x − 4800 = 0, so x = 40.
Question 2: The sum of two numbers is 30 and their difference is 8. What is the larger number?
- 19 (Correct answer)
- 11
- 22
- 15
Correct answer: 19
Adding the equations gives 2x = 38, so the larger number is 19.
Question 3: A number increased by 25% equals 80. What is the number?
- 64 (Correct answer)
- 60
- 100
- 55
Correct answer: 64
1.25x = 80, so x = 64.
Question 4: Tom is twice as old as Jerry. In 6 years, the sum of their ages will be 42. How old is Tom now?
- 20 (Correct answer)
- 10
- 14
- 24
Correct answer: 20
2x + 6 + x + 6 = 42 gives x = 10, so Tom is 20.
Question 5: A rectangle's length is 3 more than twice its width. If the perimeter is 36, what is the width?
- 5 (Correct answer)
- 6
- 8
- 4
Correct answer: 5
2(2w+3) + 2w = 36 gives 6w = 30, so w = 5.
Question 6: If 3 pencils and 2 pens cost $13, and 2 pencils and 3 pens cost $12, what is the cost of one pen?
- $2 (Correct answer)
- $3
- $1
- $4
Correct answer: $2
Solving the system gives pencil = $3 and pen = $2.
Question 7: A worker can paint a fence in 6 hours. With a helper, the job takes 4 hours. How long would the helper take alone?
- 12 hours (Correct answer)
- 10 hours
- 8 hours
- 2 hours
Correct answer: 12 hours
1/6 + 1/h = 1/4 gives 1/h = 1/12, so h = 12.
GMAT Quantitative: Algebraic Word Problems 2
A train travels 240 miles at a constant speed.
If the speed had been 20 mph faster, the trip would have taken 1 hour less.
What was the original speed?