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Is XY>0

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Is XY>0

by kamalakarthi » Mon Oct 06, 2014 8:51 am
If x not = 0,is xy > 0?

1. x > 0
2. 1/x < y


I can understand why statement 1 is not sufficient but not able to understand why statement 2 is not sufficient. It tells 1/x < y and I converted as 1 < xy or xy > 1 so I thought statement 2 is sufficient.

Can you please help me on this. Thank you.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Oct 06, 2014 9:00 am
kamalakarthi wrote:If x not = 0,is xy > 0?

1. x > 0
2. 1/x < y


I can understand why statement 1 is not sufficient but not able to understand why statement 2 is not sufficient. It tells 1/x < y and I converted as 1 < xy or xy > 1 so I thought statement 2 is sufficient.

Can you please help me on this. Thank you.
The part in blue (above) is incorrect.
You have taken 1/x < y and multiplied both sides by x to get 1 < xy, however we can't conclude this, because we don't know whether x is POSITIVE or NEGATIVE.
If x is POSITIVE, then it's true that 1 < xy
If x is NEGATIVE, then we must reverse the inequality sign to get: 1 > xy
So, either inequality (1 < xy or 1 > xy) can be true.

Cheers,
Brent
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by [email protected] » Mon Oct 06, 2014 11:12 am
Hi kamalakarthi,

As Brent pointed out, you have to be very careful when a variable is in the denominator of a fraction - that variable COULD be positive OR negative and you're responsible to deal with both possibilities.

This DS question is perfect for TESTing VALUES:

We're told that X cannot = 0. We're asked if XY > 0. This is a YES/NO question.

The question itself is based on a series of Number Properties:
If X and Y are BOTH Negative, then the answer is YES.
If X and Y are BOTH Positive, then the answer is YES.
If either X or Y = 0, then the answer is NO.
If X and Y have DIFFERENT signs, then the answer is NO.

Fact 1: X > 0

If....
X = 1, Y = 2, then the answer to the question is YES.
X = 1, Y = -2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

Fact 2: 1/X < Y

If....
X = 1, Y = 2, then the answer to the question is YES.
X = -1, Y = 2, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know....
X is positive
1/X < Y

Since X is positive, 1/(positive) = positive AND we can now deduce that positive < Y.
X and Y MUST both be positive, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

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Rich
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