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GMAT Prep - Inequalities

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Source: — Data Sufficiency |
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by Geva@EconomistGMAT » Wed Aug 31, 2011 5:26 am
bubbliiiiiiii wrote:I understand how statement I is sufficient. Can someone shed some light on how statement 2 is sufficient?
Isolate -2x:

5y-20 = -2x

Plug this into the inequality in the question stem:

5y-20>3y
Isolate y:
2y>20
y>10
And if you know why y>0 is sufficient, then y>10 says the same thing - that y is positive,
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by knight247 » Wed Aug 31, 2011 5:57 am
I like to break down the given inequality into the absolute basics and then solve.
Given that -2x>3y
Solving for x we get,
-x>1.5y
x<-1.5y

If x is less than -1.5 times y then I assume that x=-2y which meets the requirement of the above inequality
(1)y>0 Lets assume y=1 then x=-2. Whichever +ve value of y you try, the value of x will always be -ve
(2)2x+5y=20 We have assumed that x=-2y or 0.5x=-y...Multiply by 5 we get 2.5x=-5y or 5y=-2.5x. Substituting this value, we get
2x-2.5x=20
-0.5x=20
x=-40

Hence D
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