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

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by layzzer » Sun May 09, 2010 7:11 pm
If -2x > 3y, is x negative?

1) y > 0

2) 2x+5y-20=0

from a practice exam.

Obviously (1) is sufficient and I put down A, that's wrong

the correct answer is D, both alone sufficient.

I can't really wrap my brain around how exactly (2) is sufficient

Help please!!
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Source: — Data Sufficiency |

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by Rahul@gurome » Sun May 09, 2010 7:31 pm
(1) y > 0 implies y will take positive values and for -2x > 3y, x will have to be a negative value as negative * negative = positive. So, x is negative.
Hence, (1) is SUFFICIENT to answer the question.

(2) -2x > 3y implies 2x + 3y < 0.
Add 2y on both sides of 2x + 3y < 0, we get 2x + (3y + 2y) < 2y
2x + 5y < 2y. But it is given in statement (2) that 2x + 5y = 20
So, 20 < 2y implies y > 10 which means y will take positive values greater than 10.
Since, -2x > 3y so for -2x to be positive, x should also be negative.

Hence, (2) is SUFFICIENT to answer the question.

The correct answer is (D).
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