What two-digit number is less than the sum of the square of its digits by 12 and exceeds their doubled product by 5? Choices: A) 95 B) 99 C) 26 D) 73 E) None of the Above
Let the digits be x and y. The number would be 10x + y.   We are given that 2xy + 5 = 10x +y = x^2 y^2 -12   Thus 2xy +5 = x^2 + y^2 - 12   x^2 + y^2 -2xy = 16   (x-y)^2 = 16   (x-y) = 4 or -4   Substituting the values of (x-y) in the equation 2xy +5 = 10x + y   x comes out to be 1 or 9... thus the two numbers can be 15 or 99   Thus the answer is 99
<result>B</result>
What two-digit number is less than the sum of the square of its digits by 12 and exceeds their doubled product by 5?