AMC 8 Word Problems & Logic

Question 1

A train travels 240 miles in 4 hours. What is its average speed in miles per hour?

Accepted Answer

60

Answer

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?

Accepted Answer

16

Answer

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?

Accepted Answer

$4.00

Answer

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?

Accepted Answer

12

Answer

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?

Accepted Answer

4

Answer

By inclusion-exclusion, 18 + 14 − 6 = 26 play at least one sport, so 30 − 26 = 4 play neither.

AMC 8 - American Mathematics Competition 8 Practice Test