Question

The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is

• A. 25
• B. 27
• C. 33
• D. 81
• E. 49

Answer 1

The correct option is B

27

Let the numbers be x and (x + 3), Then,

$x^2$ + ${(x+3)}^2$​ = 369

$⟹$$x^2$​ + 3x -180 = 0

$⟹$(x+15)(x-12) = 0

$\therefore$ x = 12 (since -15 is not possible)

So, the numbers are 12 and 15.

$\therefore$ Required sum = (12 + 15) = 27.