AMC 8 Word Problems & Logic 1 — Questions and Answers
Question 1: A train travels 240 miles in 4 hours. What is its average speed in miles per hour?
- 50
- 60 (Correct answer)
- 70
- 80
Correct answer: 60
Speed = Distance ÷ Time = 240 ÷ 4 = 60 mph.
Question 2: Alice is 5 years older than Bob. The sum of their ages is 37. How old is Bob?
- 14
- 15
- 16 (Correct answer)
- 17
Correct answer: 16
If Bob = b, then b + (b+5) = 37 gives 2b = 32, so b = 16.
Question 3: A store sells apples for $0.40 each and bananas for $0.25 each. Lisa buys 5 apples and 8 bananas. How much does she spend?
- $3.80
- $4.00 (Correct answer)
- $4.25
- $4.50
Correct answer: $4.00
5 × $0.40 + 8 × $0.25 = $2.00 + $2.00 = $4.00.
Question 4: If 8 workers can build a wall in 6 days, how many days will 4 workers take to build the same wall?
- 8
- 10
- 12 (Correct answer)
- 14
Correct answer: 12
Total work = 8 × 6 = 48 worker-days; with 4 workers, time = 48 ÷ 4 = 12 days.
Question 5: In a class of 30 students, 18 play soccer and 14 play basketball, and 6 play both. How many students play neither sport?
- 2
- 4 (Correct answer)
- 6
- 8
Correct answer: 4
By inclusion-exclusion, 18 + 14 − 6 = 26 play at least one sport, so 30 − 26 = 4 play neither.
Question 6: A rectangle's length is increased by 20% and its width is decreased by 10%. By what percent does the area change?
- 8% increase (Correct answer)
- 10% increase
- 8% decrease
- 10% decrease
Correct answer: 8% increase
New area = 1.2 × l × 0.9 × w = 1.08lw, which is an 8% increase.
AMC 8 Word Problems & Logic 1
A train travels 240 miles in 4 hours.
What is its average speed in miles per hour?