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I'm starting to hate inequalities.. here another one!

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by Tryingmybest » Thu Mar 26, 2009 10:37 am
Given -2x>3y

A) y is positive means 3y is positive if -2x> 3y then - 2x must be positive implies x is negative

Sufficient

B) 2x+5y- 20 = 0 => 2x+5y = 20 ___A

Given -2x>3y => -2x-3y > 0 => -(2x+3y)>0 => 2x+3y<0

Rewrite Equation A=> 2x+3y+2y= 20 The bold portion is negative so y must be positive
y is positive means 3y is positive if -2x> 3y then - 2x must be positive implies x is negative

Sufficient

D
Last edited by Tryingmybest on Thu Mar 26, 2009 10:38 am, edited 1 time in total.
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by DanaJ » Thu Mar 26, 2009 10:37 am
So you get that -2x > 3y.

1. y > 0 means that 3y > 0. Since -2x > 3y > 0, then you get that -2x > 0. Divide by -2 on each side to get that x < 0. So 1 is sufficient.

2. 2x + 5y - 20 = 0 makes 2x = 20 - 5y. This means that -2x = 5y - 20. Replace this in your initial inequality to get:
5y - 20 > 3y
2y - 20 > 0
y > 10 > 0, meaning that y > 0, so you're back at stmt 1. This is why 2 is sufficient as well.
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