Data Sufficiency

We know from the question stem that we want to find out information about x - y and x + y. We can express Statement 1 as:

(x - y) (x + y) = 9

Using Statement 2, we can substitute 2 in for x - y:

2 (x + y) = 9
x + y = 9/2

So |x - y| = |2| = 2, and |x + y| = |9/2| = 9/2

So |x - y| is NOT greater than |x + y|. Both statements together are sufficient.

Vincen wrote:Is |x - y| > |x + y|?

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

The OA is C.

I don't know how to use both statements together. Experts, may you show me how to do it? Thanks.

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

Case 1: Say x = 3 and y = 0, then 3^2 - 0^2 = 9. We see that |x - y| > |x + y| => |3 - 0| > |3 + 0| => 3 = 3. The answer is No.
Case 2: Say x = -4 and y = 1, then (-4)^2 - 1^2 = 9. We see that |x - y| > |x + y| => |-4 - 1| > |-4 + 1| => 5 > 3. The answer is Yes.
No unique answer. Insufficient.

(2) x - y = 2

Case 1: Say x = 2 and y = 0, then 2 - 0 = 2. We see that |x - y| > |x + y| => |2 - 0| > |2 + 0| => 2 = 2. The answer is No.
Case 2: Say x = 1 and y = -1, then 1 + 1 = 2. We see that |x - y| > |x + y| => |1 + 1| > |1 - 1| => 2 > 0. The answer is Yes.
No unique answer. Insufficient.

(1) and (2) combined together

From (2), we get that x = y + 2. Plugging in the value of x in (1), we get x^2 - y^2 = 9 => (y + 2)^2 - y^2 = 9 => (y+2+y).(y+2-y) = 9 => (2y+2).2 = 9 => y = 5/4. Thus, x = 13/4.

At x = 13/4 and y = 5/4, we see that we see that |x - y| > |x + y| => |13/4 - 5/4| > |13/4 + 5/4| => 2 < 9/2 . The answer is No. Sufficient,

The correct answer: C

Hope this helps!

-Jay
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