2026 · Q23
A number N consists of two digits. The digit in the tens place is 3 times the digit in the units place. The digits are reversed and the resulting number is denoted by R. If N × R = 3627, then what is the product of the digits of the number N?
Elementary MathematicsNumber System
- A27
- B18
- C12
- D3
Explanation
Write N = 10a + b with a = 3b. Reversing gives R = 10b + a, and N·R = (10a + b)(10b + a) = 3627. Substituting a = 3b: 31b × 13b = 403b² = 3627, so b² = 9, b = 3 and a = 9. The product of the digits is 9 × 3 = 27, option A.