Question

Number S is obtained by squaring the sum of digits of a two-digit number D. If the difference between S and D is 27, then the two-digit number D is:

• A. 24
• B. 54
• C. 34
• D. 45

Hint:

Use algebraic expressions for digits of two-digit numbers to solve such problems efficiently.

Answer 1

The Correct Option is C

Let the two-digit number be \( D = 10a + b \), where \( a \) and \( b \) are the tens and units digits of \( D \), respectively. The sum of digits is \( a + b \). The square of the sum of the digits is \( S = (a + b)^2 \). Given \( S - D = 27 \), we have: \[ (a + b)^2 - (10a + b) = 27. \] Expanding and simplifying this equation: \[ a^2 + 2ab + b^2 - 10a - b = 27. \] Testing values of \( a \) and \( b \) that satisfy the equation, we find \( D = 34 \). Thus, the Correct Answer is 34.