AMC 8 Word Problems & Logic 2

Question 1

A car travels at 50 mph for 2 hours and then at 70 mph for 3 hours. What is the total distance traveled?

Accepted Answer

310

Answer

Distance = 50 × 2 + 70 × 3 = 100 + 210 = 310 miles.

Question 2

A 15-foot ladder leans against a wall with its base 9 feet from the wall. How high up the wall does the ladder reach?

Accepted Answer

12

Answer

By the Pythagorean theorem: h = √(15² − 9²) = √(225 − 81) = √144 = 12 feet.

Question 3

If three-quarters of a number is 21, what is the number?

Accepted Answer

28

Answer

(3/4)n = 21, so n = 21 × (4/3) = 28.

Question 4

A tank is 1/3 full. After adding 20 gallons it is 1/2 full. What is the tank's total capacity?

Accepted Answer

120

Answer

The 20 gallons fills 1/2 − 1/3 = 1/6 of the tank, so the total capacity = 20 × 6 = 120 gallons.

Question 5

In a survey, 60% prefer coffee, 30% prefer tea, and 10% prefer juice. If 150 people prefer tea, how many prefer coffee?

Accepted Answer

300

Answer

30% = 150 people, so 10% = 50 and the total is 500; then 60% of 500 = 300.

AMC 8 - American Mathematics Competition 8 Practice Test