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

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If -2x > 3y, is x negative? [#permalink]  22 May 2010, 23:35
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If -2x > 3y, is x negative?

(1) y > 0
(2) 2x + 5y - 20 = 0
[Reveal] Spoiler: OA

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If -2x > 3y, is x negative? [#permalink]  23 May 2010, 01:49
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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.

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Re: If -2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y - 20 = 0 [#permalink]  29 Jun 2013, 06:45
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fozzzy wrote:

In statement 2 we can write the equation 2x+3y+2y = 20 we know 2x+3y is positive and we get y = 10 hence same as statement 1 is this approach correct?

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

(1) y > 0
-2x > +ve number, hence x is negative.
Sufficient

(2) 2x + 5y - 20 = 0
The area defined by -2x > 3y is the area under the red line. If we know that $$2x + 5y - 20 = 0$$ (blue line) (given the initial condition) we can say that x is negative because they intersect when x is negative. (refer to the image)
Sufficient

Your approach is correct. We know that 2x+3y is negative (typo I think), so $$2x + 3y +2y= 20$$ can be seen as $$-ve +2y=20$$ so y is positive for sure as $$2y=20+(+ve)$$
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Re: is X negative [#permalink]  23 May 2010, 08:54
Bunuel wrote:
dimitri92 wrote:
If -2x>3y , is X negative

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

Given: $$-2x>3y$$. Q: is $$x<0$$? (Note here that if $$y$$ is any positive number than 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) $$2x+5y-20=0$$ --> $$2x=20-5y$$ --> $$-20+5y>3y$$ --> $$y>10$$. Same as above: $$x<0$$. Sufficient.

Can you please explain stmt. 2 again.
Unable to understand the following stmt---

$$-20+5y>3y$$
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Re: is X negative [#permalink]  23 May 2010, 09:08
Expert's post
onedayill wrote:
Bunuel wrote:
dimitri92 wrote:
If -2x>3y , is X negative

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

Given: $$-2x>3y$$. Q: 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) $$2x+5y-20=0$$ --> $$2x=20-5y$$ --> $$-20+5y>3y$$ --> $$y>10$$. Same as above: $$x<0$$. Sufficient.

Can you please explain stmt. 2 again.
Unable to understand the following stmt---

$$-20+5y>3y$$

(2) $$2x+5y-20=0$$ --> $$2x=20-5y$$ --> given $$-2x>3y$$, substitute $$2x$$ --> $$-(20-5y)>3y$$ --> $$-20+5y>3y$$ --> $$y>10$$ --> $$y=positive$$, as discussed above if $$y$$ is any positive number then $$x$$ must be some negative number: $$x<0$$. Sufficient.

Hope it's clear.
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Re: If -2x > 3y, is x negative [#permalink]  24 Aug 2013, 23:04
SUNGMAT710 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

-2x > 3y
2x + 3y<0 -----(1)

Statement 1
If y>0
& 2x + 3y<0

Then x must be Negative.
Sufficient

Statement 2
2x + 5y - 20 = 0
2x + 5y = 20
(2x + 3y) + 2y=20
We can write
2y + some negative no = 20
2y = 20 + some Positiveno
y = 10 + some Positiveno/2
This mean that y>10

2x + 3y<0
2x< -3y
x < -1.5 (Positive no) because y is positive

Then x must be Negative.
Sufficient

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Re: If -2x > 3y, is x negative [#permalink]  24 Aug 2013, 23:06
Expert's post
SUNGMAT710 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

From F.S 1, we know that -2x>0. Thus, x<0. Sufficient.

From F.S 2, we know that $$y = \frac{20-2x}{5}$$ , replacing this value , $$-2x>3*\frac{20-2x}{5} \to$$$$-10x>60-6x \to -4x>60$$. Again, x<0.

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Re: If -2x > 3y, is x negative? [#permalink]  09 Apr 2015, 13:57
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GMAT Prep DS [#permalink]  10 Jul 2015, 18:51
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0
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Re: If -2x > 3y, is x negative? [#permalink]  11 Jul 2015, 01:23
Expert's post
janani28 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Merging topics.

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Re: If -2x > 3y, is x negative?   [#permalink] 11 Jul 2015, 01:23
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# If -2x > 3y, is x negative?

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