Brent@GMATPrepNow wrote: ↑

Tue Oct 26, 2021 12:06 pm

In the figure above, right triangle XYZ has side lengths of a, b and c. What is the value of b?

(1) a and c are prime numbers less than 20 such that c - a = 8
(2) a = 5 and c = 13

Answer: E
Source: www.gmatprepnow.com

I created this question to illustrate the point that the diagrams in data sufficiency questions are not necessarily drawn to scale.
So, even though we're told triangle XYZ is a RIGHT triangle, there's no way to be certain which of the three angles is 90°

Since we have no idea which angle is 90°, we can jump straight to . . .

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: a = 5, c = 13 and ∠X = 90°. When we apply the Pythagorean theorem we can write: a² + b² = c². Substitute values to get: 5² + b² = 13². Solve to get b = 12.
Case b: a = 5, c = 13 and ∠Y = 90°. When we apply the Pythagorean theorem we can write: a² + c² = b². Substitute values to get: 5² + 13² = c². Solve to get b = √194.
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent