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M28-05

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Bunuel
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M28-05 [#permalink] New post   16 Sep 2014, 01:28
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45% (medium)

Question Stats:

60% (01:13) correct 40% (01:10) wrong based on 172 sessions
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Is \(x = 0\)?


(1) \(xy = x\)

(2) \(x+y=x\)
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C
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Bunuel
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Re M28-05 [#permalink] New post   16 Sep 2014, 01:28
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Official Solution:


Is \(x = 0\)?

(1) \(xy = x\).

Rearrange and factor out \(x\) to get \(x(y - 1) = 0\). This implies that 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 statement implies that \(y = 0\). However, it is not sufficient to answer whether \(x = 0\).

(1) + (2) From statement (2), we know that \(y = 0 \neq 1\). Therefore, according to statement (1), \(x = 0\). Sufficient.


Answer: C
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Re: M28-05 [#permalink] New post   17 Oct 2015, 14:04
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.
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M28-05 [#permalink] New post   18 Oct 2015, 11:27
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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.



Note that we cannot divide xy = x by x because x can be 0 and division by zero is not allowed. By dividing by x, you would be incorrectly assuming that x does not equal zero, potentially excluding a valid solution (observe that x = 0 satisfies the equation).

As a rule, never reduce an equation by a variable (or by an expression containing a variable) if you are not certain that the variable (or expression with the variable) does not equal zero. Remember, we cannot divide by zero.
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Re: M28-05 [#permalink] New post   08 May 2023, 05:45
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M28-05 [#permalink] New post   07 Jun 2023, 14:42
just starting my gmat journey and first post on here, tough but positive road ahead.

explanation a little bit confusing with solution with respect to xy=x.

I solved it this way by dividing both side of xy and x by x to get y=1. This translates to x could be anything so eliminate AD. Did I do this incorrectly compared to how it was solved on here?
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M28-05 [#permalink] New post   07 Jun 2023, 14:53
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toxtimmy wrote:
just starting my gmat journey and first post on here, tough but positive road ahead.

explanation a little bit confusing with solution with respect to xy=x.

I solved it this way by dividing both side of xy and x by x to get y=1. This translates to x could be anything so eliminate AD. Did I do this incorrectly compared to how it was solved on here?


Welcome. I think this method works that you have used as long as you realize that it means X can be anything. As long as you arrive to that, it works.

It’s a different approach with parentheses and a bit more advanced and helpful since you still have both variables. This approach will help you plug-in numbers in other questions.

Posted from my mobile device
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Re: M28-05 [#permalink] New post   07 Jun 2023, 23:38
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toxtimmy wrote:
just starting my gmat journey and first post on here, tough but positive road ahead.

explanation a little bit confusing with solution with respect to xy=x.

I solved it this way by dividing both side of xy and x by x to get y=1. This translates to x could be anything so eliminate AD. Did I do this incorrectly compared to how it was solved on here?


The reason you cannot divide by x is given just two posts above yours: https://gmatclub.com/forum/m28-184503.html#p1588423

Hope it helps.
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Re: M28-05 [#permalink]
07 Jun 2023, 23:38
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