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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Nov 11, 2014 11:20 am
jaspreetsra wrote:if x < 0, is y > 0?

1) x/y < 0
2) y - x > 0
Target question: Is y POSITIVE?

Given: x is NEGATIVE

Statement 1: x/y < 0
We already know that x is NEGATIVE.
So, statement 1 tells us that (some NEGATIVE number)/y = a negative number.
We know that negative/negative = positive, and negative/positive = negative.
So, it must be the case that y is positive.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y - x > 0
Add x to both sides to get: y > x
In other words, y is greater than x
We're told that x is NEGATIVE, so statement 2 just tells us that y is greater than some negative value.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = -3 and y = 1, in which case y is POSITIVE
Case b: x = -3 and y = -2, in which case y is NEGATIVE
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by [email protected] » Tue Nov 11, 2014 11:21 am
Hi jaspreetsra,

This DS question can be solved with Number Properties (and/or TESTing VALUES).

We're told that X < 0. We're asked if Y > 0? This is a YES/NO question.

Fact 1: X/Y < 0

For X/Y to be negative, one variable MUST be positive while the other variable MUST be negative (+/- OR -/+).

Since we already know that X is negative, then Y MUST be positive. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: Y - X > 0

This can be rewritten as Y > X

We know that the X is negative, but the Y could be positive, 0 or negative.

If Y = positive, then the answer to the question is YES
If Y = 0, then the answer to the question is NO
If Y = negative, then the answer to the question is NO
Fact 2 is INSUFFICIENT

Final Answer: A

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by Mathsbuddy » Wed Nov 12, 2014 6:32 am
Here's the question on a number line:
x....0....y?

x is negative, so if x/y < 0 then y must be positive
Therefore Statement 1 is SUFFICIENT

Statement 2 can be rearranged to get
y > x
As x is negative, y could be negative, positive or zero
NOT SUFFICIENT
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