Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 : GMAT Data Sufficiency (DS)
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2015, 07:24, edited 1 time in total.
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New post 03 Jan 2010, 08:56
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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]

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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]

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New post 02 Sep 2015, 04:48
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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.

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]

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

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New post 03 Sep 2015, 03:35
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.
The answer is A
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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink]

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

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New post 27 Dec 2016, 00:35
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 ? (1) x 0 (2) y = 0 [#permalink]

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New post 04 Jan 2017, 23:45
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.

Answer: A.

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
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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0 [#permalink]

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New post 05 Jan 2017, 02:30
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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New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is xy + z = z, is |x-y| > 0 ? (1) x 0 (2) y = 0   [#permalink] 05 Jan 2017, 02:30
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