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?
- A. 100
- B. 110 ✓
- C. 115
- D. 120
Correct Answer: B. 110
Explanation
Let N = 10x + y. We have x^2 + xy = 84 \implies x(x+y)=84 and y^2 + xy = 60 \implies y(x+y)=60. Dividing the two equations gives \frac{x}{y} = \frac{84}{60} = \frac{7}{5}. So x=7 and y=5. Thus, N=75 and P=35. Finally, P+N = 35+75 = 110.
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