The sum of the squares of the digits of a positive two-digit number is 61, and the tens digit is 1 more than the units digit. Find the number.
A) 65
B) 45
C) 56
D) 54

Question

Quizplus · Accepted Answer

The tens digit is x and the units digit is y. We have x^2 + y^2 = 61 and x = y + 1. Substituting the second equation into the first, we get (y + 1)^2 + y^2 = 61, which simplifies to 2y^2 + 2y - 60 = 0. Factoring, we get (y - 6)(2y + 10) = 0, so y = 6 or y = -5. Since y is a digit, it must be positive, so y = 6. Therefore, x = y + 1 = 7, and the number is 76.

The Sum of the Squares of the Digits of a Positive