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Math Expert V
Joined: 02 Sep 2009
Posts: 59039

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Difficulty:   35% (medium)

Question Stats: 58% (00:49) correct 42% (00:50) wrong based on 232 sessions

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Is $$x = 0$$?

(1) $$xy = x$$

(2) $$x+y=x$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 59039

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danjbon wrote:
I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.

If you divide (reduce) xy = x by x, you assume, with no ground for it, that x does not equal to zero thus exclude a possible solution.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

(1) $$xy = x$$. Re-arrange and factor out $$x$$ to get $$x(y-1)=0$$. So, either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). Not sufficient.

(2) $$x+y=x$$. This statemnt implies that $$y=0$$. Not sufficient to answer whether $$x=0$$.

(1)+(2) As from (2) $$y=0\neq{1}$$ then according to (1) $$x=0$$. Sufficient.

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Intern  Joined: 14 Oct 2015
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GMAT 1: 640 Q45 V33 ### Show Tags

I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.
Intern  Joined: 10 Sep 2013
Posts: 2
Location: India
Schools: ISB '18 (A)
GMAT 1: 710 Q50 V37 GPA: 3.5
WE: General Management (Real Estate)

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why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??
Math Expert V
Joined: 02 Sep 2009
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mohitks89 wrote:
why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??

But we have precisely the situation you describe: when we combine the statements we get that x = y = 0.
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Manager  B
Joined: 14 Aug 2012
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GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38 ### Show Tags

What if x = 0 and y = 1 or y = 0 and x = 1
Math Expert V
Joined: 02 Sep 2009
Posts: 59039

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bpdulog wrote:
What if x = 0 and y = 1 or y = 0 and x = 1

Those values do not satisfy given statements.
_________________ Re: M28-05   [#permalink] 15 Oct 2018, 21:05
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# M28-05

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