ISAT Mathematical Problem-Solving 3

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?

Accepted Answer

15

Answer

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?

Accepted Answer

25π

Answer

Radius = √((6−2)² + (0+3)²) = √(16+9) = 5, so area = π(5²) = 25π.

Question 3

If 3^(2x) = 81, what is x?

Accepted Answer

2

Answer

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?

Accepted Answer

32%

Answer

Remaining price = 0.80 × 0.85 = 0.68 of original, so the total discount is 32%.

Question 5

Solve for x: |2x − 5| = 9

Accepted Answer

x = 7 or x = −2

Answer

2x − 5 = 9 gives x = 7; 2x − 5 = −9 gives x = −2.

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