teal wrote:

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.

In fact, the given inequality can be rewritten as \((x-y)^2>(x+y)^2\) - we can square both sides, as they are both positive. Rearranging the terms, the question becomes \(xy<0\) (is the product xy negative)?

Then, it is much easier to understand that neither (1), nor (2) alone is sufficient.

Taking both statements, one can explicitly find the values of x and y (although not necessary), and check whether their product is negative.

That's why the correct answer should be C.

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PhD in Applied Mathematics

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