Data Sufficiency

If |y| > |x|, is x – y < 0?

(1) |x| + |y| > |x - y|
(2) x + y < 0

Answer: B
Source: www.gmatprepnow.com

Brent@GMATPrepNow wrote: ↑

Sun Sep 04, 2022 3:12 pm

If |y| > |x|, is x – y < 0?

(1) |x| + |y| > |x - y|
(2) x + y < 0

Answer: B
Source: www.gmatprepnow.com

Given: |y| > |x|
Strategy: If the given information in a data sufficiency question yields a small number (less than 5) possible cases, you can save some time by listing all of the possible cases and the corresponding answer to the target question before analyzing each statement.

So, if |y| > |x|, then there are exactly 4 possible cases that satisfy this information:
Case i: --------0----x----y (Is x - y < 0? YES)
Case ii: --y---------0----x (Is x - y < 0? NO)
Case iii: ----x----0----------y (Is x - y < 0? YES)
Case iv: -y---x----0---- (Is x - y < 0? NO))

Target question: Is x – y < 0?

Statement 1: |x| + |y| > |x - y|
Aside: |x| represents the distance on the number line from x to 0
Similarly, |y| represents the distance on the number line from y to 0
And |x - y| represents the distance on the number line from x to y

So, when we scan the 4 possible cases, we can see that cases i and iv both satisfy statement 1.
If case i is true, then the answer to the target question is YES.
If case iv is true, then the answer to the target question is NO.
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y < 0
When we scan the 4 possible cases, we can see that cases ii and iv both satisfy statement 1.
If case ii is true, then the answer to the target question is NO.
If case iv is true, then the answer to the target question is NO.
Since both possible cases yield the same answer to the target question (NO), we can answer the target question with certainty.
As such, statement 2 is SUFFICIENT

Answer: B