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

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If -2x>3y, is x negative [#permalink]

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15 Feb 2010, 14:41
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If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0

Could any one please tell me why the second one works? Thanks so much again!

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2x-3y-is-x-negative-94665.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Jul 2014, 05:38, edited 1 time in total.
Edited the question.
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Re: If -2x>3y, is x negative [#permalink]

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15 Feb 2010, 15:16
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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]

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15 Feb 2010, 15:26
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]

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12 Mar 2010, 04:49
-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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Re: If -2x>3y, is x negative [#permalink]

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06 May 2010, 12:32
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Re: If -2x>3y, is x negative [#permalink]

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17 Jul 2014, 03:57
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Re: If -2x>3y, is x negative [#permalink]

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17 Jul 2014, 05:20
YTT wrote:
Could any one please tell me why the second one works? Thanks so much again!

Statement I is sufficient:

If y is positive and -2x > positive hence x has to be negative

Statement II is sufficient:
2x + 5y = 20

-2x > 3y

-2x > 3(20 - 2x)/5

-10x > 60 - 6x

-4x>60
-x > 15
x<-15

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Re: If -2x>3y, is x negative [#permalink]

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17 Jul 2014, 05:40
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If -2x>3y , is x negative

Given: $$-2x>3y$$.
Question: is $$x<0$$? (Note here that if $$y$$ is any positive number then we would have $$-2x>positive$$, and in order that to be true $$x$$ must be some negative number).

(1) $$y>0$$ --> $$-2x>3y>0$$ --> $$x<0$$. Sufficient.

(2) $$2x+5y-20=0$$ --> $$2x=20-5y$$ --> $$-20+5y>3y$$ --> $$y>10$$. The same as above: $$x<0$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2x-3y-is-x-negative-94665.html
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Re: If -2x>3y, is x negative   [#permalink] 17 Jul 2014, 05:40
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# If -2x>3y, is x negative

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