(†¥)² - (¥†)² is a perfect square. What is the perfe

Hi funky_munky,

This question is tougher than a typical GMAT "symbolism" question (most symbolism question are based around basic arithmetic or algebra) and whoever wrote it didn't use proper phrasing (the question should ask "Which of the following COULD be that perfect square?"

The logic behind this prompt is built around some rarer arithmetic Number Property rules….

First off, the prompt can be re-written as X^2 - Y^2 = a perfect square (note that X and Y are both 2-digit numbers with none of the digits as 0 and the two numbers are "mirrors" of one another e.g. 14 and 41).

X^2 - Y^2 = (X + Y)(X - Y)

Now, as to the Number Properties:

1) If you add two "mirrored" 2-digit numbers, then you ALWAYS get a multiple of 11.

eg
14 + 41 = 55…..a multiple of 11
27 and 72 = 99….a multiple of 11
87 and 78 = 165….a multiple of 11

2) If you subtract two "mirrored" 2-digit numbers, then you ALWAYS get a multiple of 9.

41 - 14 = 27…a multiple of 9
72 - 27 = 45…a multiple of 9
87 - 78 = 9…a multiple of 9

This ultimately means that the final answer MUST be a multiple of 11 (because X + Y is a multiple of 11) AND a multiple of 9 (because X - Y is a multiple of 9).

The only answer that fits these rules is E

GMAT assassins aren't born, they're made,
Rich