2025 · Q9
Consider a 2-digit number N. Let P be the product of the digits of the number. If P is added to square of the digit in the tens place of N, we get 84. If P is added to the square of the digit in the unit place of N, we get 60. What is the value of P + N ?
Elementary MathematicsNumber System
- A100
- B110
- C115
- D120
Explanation
Write N = 10a + b and P = ab with digits a ≠ 0, b. The conditions give a² + ab = 84 and b² + ab = 60, i.e. a(a+b) = 84 and b(a+b) = 60. Adding: (a+b)² = 144, so a + b = 12. Then a = 84/12 = 7 and b = 60/12 = 5, giving N = 75 and P = 35. Thus P + N = 110, option (b).