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# Is xy + z = z, is |x-y| > 0 ?

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Manager
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Is xy + z = z, is |x-y| > 0 ? [#permalink]

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03 Jan 2010, 09:49
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Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jan 2017, 04:04, edited 2 times in total.
Edited.
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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03 Jan 2010, 09:56
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A...
from eq xy+z=z , we know xy is 0...
for lx-yl>0 x-y ≠ 0...
si) x ≠ 0 so y=0 and x-y will be a -ive or +ive no... suff
sii) y=0... x can be 0 or any other no ...not suff
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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02 Sep 2015, 05:01
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zaarathelab wrote:
Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0

KINDLY EXPLAIN STEP BY STEP
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Please award kudos if you like my explanation.
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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02 Sep 2015, 05:48
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shakticnb wrote:
zaarathelab wrote:
Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0

KINDLY EXPLAIN STEP BY STEP

Is xy + z = z, is |x-y| > 0 ?

xy + z = z;
Cancel z: xy = 0. This implies that either x or y (or both) is 0.

(1) x ≠ 0. Since x is not 0, then y = 0. Thus the question becomes is |x| > 0. The absolute value of a non-zero number (x) is always positive. So, we have a definite YES answer to the question. Sufficient.

(2) y = 0. The question becomes is |x| > 0. If x = 0, then the answer is NO but if x ≠ 0, then the answer is YES. Not sufficient.

Hope it's clear.
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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02 Sep 2015, 23:44
shakticnb wrote:
zaarathelab wrote:
Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0

KINDLY EXPLAIN STEP BY STEP

Given: xy + z = z or xy = 0
Required: |x-y| > 0.

Statement 1: x ≠ 0
Under the given situation, xy = 0 only if y =0
Hence we have |x| > 0

The absolute value of any non zero number is always greater than 0
Hence we can definitely say that |x-y| > 0
SUFFICIENT

Statement 2: y = 0
This leaves us with |x| >0
But by xy = 0 we have either x = 0 or x ≠ 0

So, |x| = 0,
or |x| >0

Not a definitive answer for |x-y|
INSUFFICIENT
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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03 Sep 2015, 04:35
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0

in the original condition we have xy+z=z, xy=0 and the question asks for |x-y|>0?
Since we have 2 variables and 1 equation, in order to match the number of variables and equations we need 1 more equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), y = 0 thus the answer is always yes. Therefore it is sufficient.
In case of 2), x = 2 and y = 0 thus the answer is yes, but if x = 0 and y = 0 the answer is no. Therefore it is not sufficient.
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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08 Oct 2016, 13:15
Hello from the GMAT Club BumpBot!

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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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27 Dec 2016, 01:35
Easy, but the font is so small that the not equal sign was mistaken to be as =
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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05 Jan 2017, 00:45
Bunuel wrote:
shakticnb wrote:
zaarathelab wrote:
Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0
(2) y = 0

KINDLY EXPLAIN STEP BY STEP

Is xy + z = z, is |x-y| > 0 ?

xy + z = z;
Cancel z: xy = 0. This implies that either x or y (or both) is 0.

(1) x ≠ 0. Since x is not 0, then y = 0. Thus the question becomes is |x| > 0. The absolute value of a non-zero number (x) is always positive. So, we have a definite YES answer to the question. Sufficient.

(2) y = 0. The question becomes is |x| > 0. If x = 0, then the answer is NO but if x ≠ 0, then the answer is YES. Not sufficient.

Hope it's clear.

Hi Bunuel..well this analysis is clear and many thanx for it, but i went through a different route..
modulus of any number is always greater than zero...isn't it? so either satement alone could be the answer.

In a recent exapmple this was the approach adopted

the question was something like this (actual number may diifer)Is -7*mod(4x-y)<14??
It was explained that modulus of 4x-y would always be positive and when multiplied by a negative number it will always be negative...and THERE IS NO NEED TO ACTUALLY SOLVE...the inequality...

Why can't we appply this approach here as well?

Desparately need cl;arification
Math Expert
Joined: 02 Sep 2009
Posts: 39683
Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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05 Jan 2017, 03:30
saurabhsavant wrote:
Hi Bunuel..well this analysis is clear and many thanx for it, but i went through a different route..
modulus of any number is always greater than zero...isn't it? so either satement alone could be the answer.

In a recent exapmple this was the approach adopted

the question was something like this (actual number may diifer)Is -7*mod(4x-y)<14??
It was explained that modulus of 4x-y would always be positive and when multiplied by a negative number it will always be negative...and THERE IS NO NEED TO ACTUALLY SOLVE...the inequality...

Why can't we appply this approach here as well?

Desparately need cl;arification

The absolute value of a number is always greater than or equal to 0. What I mean is that |x| = 0, when x = 0.
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Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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23 Jan 2017, 03:57
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The question is typed as Is xy + z = z

Should it not be If xy + z = z

This created confusion for me.
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Joined: 02 Sep 2009
Posts: 39683
Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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23 Jan 2017, 04:05
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Expert's post
malavika1 wrote:
The question is typed as Is xy + z = z

Should it not be If xy + z = z

This created confusion for me.

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Edited. Thank you.
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Posts: 38
Re: Is xy + z = z, is |x-y| > 0 ? [#permalink]

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23 Jan 2017, 08:36
Thanks Bunuel! Now this makes much more sense.
Re: Is xy + z = z, is |x-y| > 0 ?   [#permalink] 23 Jan 2017, 08:36
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