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If -2x>3y, is x negative

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If -2x>3y, is x negative [#permalink] New post 15 Feb 2010, 13:41
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Could any one please tell me why the second one works? Thanks so much again!
[Reveal] Spoiler: OA

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Re: 700 Algrbra! Need help again. Thanks so much! [#permalink] New post 15 Feb 2010, 14:16
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YTT wrote:
Could any one please tell me why the second one works? Thanks so much again!


(2) 2x+5y-20=0 --> y=4-\frac{2}{5}x, substitute y --> -2x>3(4-\frac{2}{5}x) --> -2x>12-\frac{6}{5}x --> -12>\frac{4}{5}x --> x<-15. Obviously if x<-15 it's negative. Sufficient.

Hope it helps.
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Re: If -2x>3y, is x negative [#permalink] New post 15 Feb 2010, 14:26
Ques x < 0 ?

Given -2x > 3y

S1: y > 0... implies 3y > 0
Therefore -2x > 0.... this can only happen if x < 0.. Hence SUFF

S2: 2x + 5y = 20
5y - 20 = 2x

5y - 20 > 3y
2y > 20
y > 10

Therefore -2x > 30.... this can only be possible if x < 0... Hence SUFF..

Therefore D..
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Re: If -2x>3y, is x negative [#permalink] New post 12 Mar 2010, 03:49
-2x > 3y

stmt1: y>0 if y>0 => 3y>0 => -2x>0 => 2x<0 => x< 0 so suff to answer

stmt2: 2x+5y-20 = 0 => 2x+5y = 20 => 5y = 20 - 2x => y = (20-2x)/5
replace y in first -2x>3y

-2x>3(20-2x)/5
=> -10x>60-6x
=>-4x>60
=>-x>15
=>x<-15 (multiply by -1 both the sides and change the inequalities)
if x<-15 it is sure that x<0 also so suff
hence, both alone can determine the answer
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GMAT PREP (DS) [#permalink] New post 06 May 2010, 11:32
Please explain...
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GMAT PREP (DS)   [#permalink] 06 May 2010, 11:32
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