2023 · Q27
The product of two numbers is 2160 and their HCF is 12. If the sum of the squares of the two numbers is 4896, then what is the mean of the two numbers?
Elementary MathematicsHCF and LCM
- A24
- B36
- C48
- D96
Explanation
Write the numbers as 12x and 12y with coprime x, y. Then 144xy = 2160 gives xy = 15, and 144(x² + y²) = 4896 gives x² + y² = 34. So (x + y)² = 34 + 30 = 64, x + y = 8, the numbers sum to 96 and their mean is 48 (C).