Mathematical Problem-Solving Flashcards

Two workers together can complete a job in 6 hours. Worker A alone takes 10 hours. How many hours does Worker B need alone?

Answer: 15

1/10 + 1/B = 1/6 → 1/B = 1/6 − 1/10 = 1/15, so B = 15 hours.

A circle has center (2, −3) and passes through (6, 0). What is the area of the circle?

Answer: 25π

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

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

Answer: 2

81 = 3⁴, so 3^(2x) = 3⁴ → 2x = 4 → x = 2.

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?

Answer: 32%

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

Solve for x: |2x − 5| = 9

Answer: x = 7 or x = −2

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

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?

Answer: 13

Total sum = 5 × 12 = 60; sum of four known = 47; fifth number = 60 − 47 = 13.

A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?

Answer: 25

Hypotenuse = √(7² + 24²) = √(49 + 576) = √625 = 25.