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Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0

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Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink] New post 03 Jan 2010, 08:49
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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 27 Jul 2015, 07:24, edited 1 time in total.
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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink] New post 03 Jan 2010, 08:56
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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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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink] New post 02 Sep 2015, 04:01
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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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink] New post 02 Sep 2015, 04:48
Expert's post
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.

Answer: A.

Hope it's clear.
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Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink] New post 02 Sep 2015, 22:44
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 ? (1) x 0 (2) y = 0 [#permalink] New post 03 Sep 2015, 03:35
Expert's post
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.
The answer is A
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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0   [#permalink] 03 Sep 2015, 03:35
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