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Is x negative?

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dvinoth86
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Is x negative? [#permalink] New post   19 Feb 2012, 20:05
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Is x negative?

(1) y + x = -22
(2) y – x < -22
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C
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GMATPASSION
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Re: DS: Inequalities [#permalink] New post   19 Feb 2012, 20:23
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dvinoth86 wrote:
Is x negative? (1) y + x = -22 (2) y – x < -22


1) NS. Take x=-10 & y=-12. & take x= 10 & y=-32

2) NS. Check different values.

Together. Sufficient. Just put the value y=-22-x into 2nd statement. U will get x>0.
So the answer is no. Sufficient.
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Re: DS: Inequalities [#permalink] New post   Updated on: 19 Feb 2012, 22:57
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Answer should be C. Here is how:

Question: Is \(x\) negative?

Statement A: \(y + x = -22\)

\(x=-22-y\) so let \(y\) be \(-30\), then \(x=8\) so \(x>0\) , Let \(y=30\), then \(x=-52\) so \(x<0\) , Two different answers Hence Insufficient.

Statement B: \(y-x<{-22}\)

Rearranging, \(x>y+22\) , Let \(y=8\) , then \(x>30\) & \(x=+ve\) , let \(y=-30\), then \(x=-8\) & \(x=-ve\) , Two different answers Hence Insufficient.

Combined (Statements A & B):

We know that \(y=-22-x\) , lets substitute this in Statement B:

so \((-22-x)-x<-22\) so \(-2x<0\) which boils down to \(x>0\) (\(x\) has to be \(+ve\) for it to multiply with \(-2\) and result in a \(-ve\) number).

Hence Sufficient. Answer C.

Originally posted by omerrauf on 19 Feb 2012, 20:25.
Last edited by omerrauf on 19 Feb 2012, 22:57, edited 1 time in total.
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Re: Is x negative? (1) y + x = -22 (2) y – x < -22 [#permalink] New post   19 Feb 2012, 21:20
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Is x negative?

(1) y + x = -22. Clearly insufficient: the sum of two numbers is negative: either both are negative or just one of them, but we don't know which one, since no info about y.

(2) y – x < -22. Also insufficient: no info about y.

(1)+(2) Substitute \(y=-x-22\) from (1) into (2): \((-x-22)-x<-22\) --> rearrange and cancel -22 on both sides: \(2x>0\) --> \(x>0\), hence the answer to the question whether \(x\) negative is NO. Sufficient.

Answer: C.

Hope it's clear.
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Re: Is x negative? [#permalink] New post   23 Feb 2014, 06:08
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Bumping for review and further discussion.
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kinjiGC
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Re: Is x negative? [#permalink] New post   17 Jul 2014, 09:11
dvinoth86 wrote:
Is x negative?

(1) y + x = -22
(2) y – x < -22


Statement 1) x depends on y and value of y is not specified -> So Insufficient.
Statement 2) x depends on y and value of y is not specified -> So Insufficient

Adding both the equations
2y < -44 => y < -22

As per the 1st equation, x > 0 to make the equation correct.
Sufficient.
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Re: Is x negative? [#permalink] New post   13 Mar 2016, 08:39
Nice question...
Combining the two statements we can say that X>0
hence C
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Re: Is x negative? [#permalink] New post   31 Oct 2020, 05:07
Is x negative?

(1) y + x = -22

Can't determine x or y individually. INSUFFICIENT.

(2) y – x < -22

Can't determine x or y individually. INSUFFICIENT.

(1&2)
y - x = -22
y - x < -22

Lets say x was 0.
y - 0 = -22
y - 0 < -22?
For y to be less than -22, x has to be > 0. SUFFICIENT.

Answer is C.
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OjhaShishir
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Re: Is x negative? [#permalink] New post   31 Oct 2020, 06:50
kinjiGC wrote:
Adding both the equations
2y < -44 => y < -22

I am confused here. Can we add the two like this? One is equation and second is inequality.
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Re: Is x negative? [#permalink] New post   08 Mar 2023, 07:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is x negative? [#permalink]
08 Mar 2023, 07:56
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