ISAT Mathematical Problem-Solving 3 — Questions and Answers
Question 1: Two workers together can complete a job in 6 hours. Worker A alone takes 10 hours. How many hours does Worker B need alone?
- 15 (Correct answer)
- 12
- 18
- 20
Correct answer: 15
1/10 + 1/B = 1/6 → 1/B = 1/6 − 1/10 = 1/15, so B = 15 hours.
Question 2: A circle has center (2, −3) and passes through (6, 0). What is the area of the circle?
- 25π (Correct answer)
- 16π
- 5π
- √25 π
Correct answer: 25π
Radius = √((6−2)² + (0+3)²) = √(16+9) = 5, so area = π(5²) = 25π.
Question 3: If 3^(2x) = 81, what is x?
- 2 (Correct answer)
- 4
- 3
- 1
Correct answer: 2
81 = 3⁴, so 3^(2x) = 3⁴ → 2x = 4 → x = 2.
Question 4: A store discounts an item by 20%, then discounts the sale price by an additional 15%. What is the total percentage discount from the original price?
- 32% (Correct answer)
- 35%
- 30%
- 33%
Correct answer: 32%
Remaining price = 0.80 × 0.85 = 0.68 of original, so the total discount is 32%.
Question 5: Solve for x: |2x − 5| = 9
- x = 7 or x = −2 (Correct answer)
- x = 7 or x = 2
- x = −7 or x = 2
- x = 4 or x = −4
Correct answer: x = 7 or x = −2
2x − 5 = 9 gives x = 7; 2x − 5 = −9 gives x = −2.
Question 6: If the average (mean) of 5 numbers is 12 and four of the numbers are 8, 10, 15, and 14, what is the fifth number?
- 13 (Correct answer)
- 11
- 12
- 15
Correct answer: 13
Total sum = 5 × 12 = 60; sum of four known = 47; fifth number = 60 − 47 = 13.
Question 7: A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?
- 25 (Correct answer)
- 26
- √(625)
- 31
Correct answer: 25
Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25.
ISAT Mathematical Problem-Solving 3
Two workers together can complete a job in 6 hours.
Worker A alone takes 10 hours.
How many hours does Worker B need alone?