AMC 8 Word Problems & Logic 2 — Questions and Answers
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?
- 250
- 280
- 300
- 310 (Correct answer)
Correct answer: 310
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?
- 10
- 11
- 12 (Correct answer)
- 13
Correct answer: 12
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?
- 24
- 28 (Correct answer)
- 32
- 36
Correct answer: 28
(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?
- 60
- 90
- 100
- 120 (Correct answer)
Correct answer: 120
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?
- 200
- 250
- 300 (Correct answer)
- 350
Correct answer: 300
30% = 150 people, so 10% = 50 and the total is 500; then 60% of 500 = 300.
Question 6: The product of two consecutive odd integers is 143. What is the larger integer?
- 11
- 13 (Correct answer)
- 15
- 17
Correct answer: 13
11 × 13 = 143, so the consecutive odd integers are 11 and 13; the larger is 13.
AMC 8 Word Problems & Logic 2
A car travels at 50 mph for 2 hours and then at 70 mph for 3 hours.
What is the total distance traveled?