M15 Q11

Is \(|x - y| \gt |x + y|\) ?

\(x^2 - y^2 = 9\)
\(x - y = 2\)

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. S1 gives us information about \((x - y)(x + y)\) but does not tell how \((x - y)\) and \((x + y)\) compare to each other.

Statement (2) by itself is insufficient. S2 gives no information about \((x + y)\) .

Statements (1) and (2) combined are sufficient. From S1 and S2 it follows that \(2(x + y) = 9\) from where \((x + y) = 4.5\) . Now we can state that \(|x - y| = 2 \lt |x + y| = 4.5\) .
The correct answer is C.

I can't get the right numbers to test statement 2 to prove it Insuff. Please help. All the numbers I tried have me NO. Please help.