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

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Senior Manager
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If -2x > 3y, is x negative? [#permalink]

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23 May 2010, 00:35
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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]

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23 May 2010, 02:49
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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: is X negative [#permalink]

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23 May 2010, 09:54
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]

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23 May 2010, 10:08
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? (1) y > 0 (2) 2x + 5y - 20 = 0 [#permalink]

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29 Jun 2013, 07:45
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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: If -2x > 3y, is x negative [#permalink]

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25 Aug 2013, 00:04
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]

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25 Aug 2013, 00:06
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.

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

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

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10 Jan 2016, 05:17
We are given
-2x > 3y
need to find if x is negative?

(1) y > 0
x has to be negative to ensure that -2x > 3y
Suff

(2) 2x + 5y - 20 = 0
substituting y = (20-2x)/5
gives
x>15
Suff

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

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10 Jan 2016, 05:18
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

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

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10 Jan 2016, 05:58
chetan2u wrote:
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D

how can you say
2x+3y<0?
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Re: If -2x > 3y, is x negative? [#permalink]

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10 Jan 2016, 06:20
paidlukkha wrote:
chetan2u wrote:
NoHalfMeasures wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Hi,
-2x > 3y...
(a)If y<0, x can be both +ive and -ive..
(b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..
(1) y > 0
If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0..
this can be written as 2x+3y + 2y -20=0..
now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

ans D

how can you say
2x+3y<0?

Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps
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If -2x > 3y, is x negative? [#permalink]

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10 Jan 2016, 06:29
Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps[/quote]

Aye, it does!
Thanks

Also, if I understand, <> sign changes in multiplication only!

Btw,
St2 gives me x as +ve
What am I doing wrong?
(2) 2x + 5y - 20 = 0
substituting y = (20-2x)/5
gives
x>15
Suff
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Re: If -2x > 3y, is x negative? [#permalink]

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10 Jan 2016, 06:32
paidlukkha wrote:
Hi,
2x + 3y <0 comes from -2x>3y..
-2x>3y..
add 2x to both sides..
2x-2x>3y+2x..
0>2x+3y...
hope it helps

Aye, it does!
Thanks

Also, if I understand, <> sign changes in multiplication only![/quote]

hi,
yes you are right , whenever you multiply two sides on either side of equality with a -ive sign or -ive quantity, you are required to change the greater/lesser than sign..
-2x>3y..
2x<-3y..
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If -2x > 3y, is x negative? [#permalink]

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13 Jan 2016, 07:02
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0
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If -2x > 3y, is x negative? [#permalink]

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13 Jan 2016, 07:42
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Given that -2x > 3 y---> x<-1.5 y and the question asks whether x<0.

Per statement 1, y>0 ---> from this statement and the fact that x<-1.5y, clearly we can see that x must be <0. Sufficient.

Per statement 2, 2x + 5y - 20 = 0 ---> y = (20-2x)/5 and from the given fact, y<-2x/3 ---> x < -15. Again sufficient to answer the question asked.

Hence both statements are sufficient to answer the question asked. D is thus the correct answer.

Hope this helps.
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If -2x > 3y, is x negative? [#permalink]

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13 Jan 2016, 07:59
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

It is clear that if x negative, -2x > 0, so we will wish to see whether 3y >0, if so -2x > 3y > 0.

(1) y >0 => clearly, -2x > 3y > 0 => x negative

(2) 2x + 5y - 20 = 0. => 2x + 5y =20
Because -2x > 3y => 2x < -3y
=> 2x + 5y < -3y + 5y =2y
or 20 < 2y => 10<y => -2x > 3y > 30 => x negative

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

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13 Jan 2016, 08:32
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Please search before posting. Thank you.
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Re: If -2x > 3y, is x negative? [#permalink]

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13 Jan 2016, 08:50
Bunuel wrote:
Sash143 wrote:
If -2x > 3y, is x negative?
(1) y > 0
(2) 2x + 5y - 20 = 0

Please search before posting. Thank you.

Bunuel I did search before posting but couldn't find one! Anyway my bad
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Re: If -2x > 3y, is x negative? [#permalink]

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13 Jan 2016, 09:29
Bunuel wrote:
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.

we have 2 equation and two variables so we can calculate . so answer is D.
Re: If -2x > 3y, is x negative?   [#permalink] 13 Jan 2016, 09:29

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