Hi piyushkush,

This DS question can be solved with a mix of Number Properties and TESTing VALUES.

We're asked if 1/(X-Y) < Y - X. This is YES/NO question.

**Note: although the question does not state it, we're probably meant to infer that X does NOT equal Y. If X = Y, then we end up with an undefined value 1/0, which is a concept that is NOT tested on the GMAT. **

Fact 1: Y is POSITIVE

This doesn't tell us anything about X, so instinctively you're probably thinking that this is insufficient. Here's the proof though...

IF....
Y = 2
X = 1
1/-1 IS < (2-1) so the answer to the question is YES.

IF....
Y = 2
X = 3
1/1 is NOT < (2-3) so the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: X is NEGATIVE

Just as in Fact 1 (above), you're probably thinking that since this tells us nothing about Y, then it's probably insufficient. Here's the proof...

IF...
Y = 1
X = -1
1/-2 IS < (1 - -1) so the answer to the question is YES

IF...
Y = -2
X = -1
1/1 is NOT < (-2 - -1) so the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know....
Y is POSITIVE
X is NEGATIVE

So (X - Y) is NEGATIVE and (Y - X) is POSITIVE

By extension, 1/(X - Y) is negative and (Y - X) is always positive, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

piyushkush wrote:IS 1/(x-y) < y - x ?

S1) y is positive.
S2) x is negative.

Target question: Is 1/(x-y) < y - x ?

Statement 1: y is positive.
This statement does not FEEL sufficient to answer the target question (because we're only given information about 1 of the 2 variables), so I'm going to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 2, in which case 1/(x-y) is LESS THAN y - x
Case b: x = 2 and y = 1, in which case 1/(x-y) is GREATER THAN y - x
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x is negative
This statement does not FEEL sufficient either, so I'm going to TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = -1 and y = 0, in which case 1/(x-y) is LESS THAN y - x
Case b: x = -1 and y = -2, in which case 1/(x-y) is GREATER THAN y - x
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
If y is positive AND x is negative, then 1/(x-y) is NEGATIVE, and y-x is POSITIVE
So, we can be certain that 1/(x-y) is LESS THAN y - x
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent