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if -2x > 3y ,is x negative ?

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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Sep 24, 2014 12:51 pm
guerrero wrote:if -2x > 3y ,is x negative ?

1)Y>0

2)2x+5y-20=0
Since -2x > 3y, x is negative only if y≥0.

Question stem, rephrased:
Is y≥0?

Statement 1: y>0
SUFFICIENT.

Statement 2: 2x+5y-20=0
2x+5y-20 = 0.
5y-20 = -2x.
Substituting 5y-20 for -2x in -2x>3y, we get:
5y-20>3y
2y>20
y>10.
SUFFICIENT.

The correct answer is D.
Last edited by GMATGuruNY on Tue Jan 27, 2015 9:04 am, edited 1 time in total.
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by [email protected] » Wed Sep 24, 2014 9:37 pm
Hi guerrero,

This DS question has a couple of Number Property "restrictions" built into it; recognizing those restrictions will make solving the problem easier.

We're told that -2X > 3Y, so we're faced with some immediate restrictions:

1) X and Y CANNOT BOTH be 0
2) X and Y CANNOT BOTH be positive

We're asked if X is NEGATIVE. This is YES/NO question.

Fact 1: Y > 0

This combined nicely with the restrictions we noted earlier. Since Y is positive, X CANNOT be positive. By TESTing Values (plug in any positive values you like for Y), you'll see that X CANNOT be 0 either. So if X cannot be positive nor 0, all that's left is for X to be negative. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

Fact 2: 2X + 5Y - 20 = 0

Notice that we have "2X" and the prompt has "-2X"; that is NOT a coincidence. It's there to provide you an opportunity to use a little algebra:

5Y - 20 = -2X

Now we can substitute in....

5Y - 20 > 3Y

2Y > 20
Y > 10

Since Y is positive, we can use the same Number Property deduction that we used in Fact 1: X MUST be negative and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

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