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# If v and w are different integers, does v=0? (1) vw = v^2

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If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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10 Oct 2010, 09:36
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If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

[Reveal] Spoiler: OA
A.

I am confused that why OA is "A", in option A, we got v = w and both v and w are different integer. Please explain this point.
[Reveal] Spoiler: OA

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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Jun 2016, 04:44
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iliavko wrote:

So if we just cancel a V on each side and get V=W, it's like we are forgetting a possible solution (that also V=0), am I correct?

Yes, you are absolutely correct on this point...
Unless we know that V is non-zero, we cannot cancel out..

As a rule never cancel out or Cross-multiply a variable....Bring to one side and then simplify
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Re: DS - OG10 - 259 [#permalink]

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10 Oct 2010, 09:44
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zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

From Statement 1, we have:

vw = v^2
vw - v^2 = 0
v(w - v) = 0

and for this equation to be true, one of the factors on the left side must be equal to zero, so either v = 0, or v = w. Since we know that v does *not* equal w, the only remaining possibility is that v = 0, and Statement 1 is sufficient. Since Statement 2 is clearly insufficient, the answer is A.
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Re: DS - OG10 - 259 [#permalink]

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10 Oct 2010, 09:45
Expert's post
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zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

[Reveal] Spoiler: OA
A.

I am confused that why OA is "A", in option A, we got v = w and both v and w are different integer. Please explain this point.

(1) $$vw = v^2$$ --> $$vw-v^2=0$$ --> $$v(w-v)=0$$: either $$v=0$$ or $$v=w$$, but as we are told that $$v$$ and $$w$$ are different integers then this case is out, so $$v=0$$. Sufficient.

(2) $$w = 2$$. Clearly not sufficient.

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Re: DS - OG10 - 259 [#permalink]

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11 Oct 2010, 02:15
(1) vw = v^2

vw = v^2 possible only if v = w or v
v= 0
since v and w are 2 diff integers, definately its v = 0
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21 Mar 2012, 15:02
Bloody hell.. i got it wrong and then it dawned me.. Hate it when that happens

1)
OK so wv = v^2

thus wv -v^2 = 0
or v(w-v)=0

so v = 0 or v = w but we know that v doesnt equal w

thus sufficient

2) tells us nothing new insufficient
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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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03 Jul 2013, 01:17
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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04 Jul 2013, 08:27
Statement 1: Can be rewritten as v(w-v) = 0. Since v and w are not the same v must = 0. Sufficient.
Statement 2: Doesn't tell us anything about v.

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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Sep 2015, 22:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Jun 2016, 04:11
Hi everyone,

A question on algebra here.

If we do V*W=V^2 can we cancel a V on each side to get V=W? It would contradict the question stem, so obviously it's wrong, but it seems to make mathematical sense. What if the question didn't say that V and W are distinct integers? Would V=W be acceptable? Or is this operation illegal under any circumstances?

Thank you!
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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Jun 2016, 04:16
iliavko wrote:
Hi everyone,

A question on algebra here.

If we do V*W=V^2 can we cancel a V on each side to get V=W? It would contradict the question stem, so obviously it's wrong, but it seems to make mathematical sense. What if the question didn't say that V and W are distinct integers? Would V=W be acceptable? Or is this operation illegal under any circumstances?

Thank you!

Hi,

in these Qs, always take the TERMS on same side..
so here $$V*W = V^2....... V*W-V*V = 0....$$
so V(V-W)=0...
so either V=0 or V-W=0.....V=W..

But if you cancel out, you are left with only V=W...
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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: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Jun 2016, 04:39

So if we just cancel a V on each side and get V=W, it's like we are forgetting a possible solution (that also V=0), am I correct?

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Re: If v and w are different integers, does v=0? (1) vw = v^2 [#permalink]

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21 Jun 2016, 04:49
Great!

Thank you so much for the clarifications, Chetan!
Re: If v and w are different integers, does v=0? (1) vw = v^2   [#permalink] 21 Jun 2016, 04:49
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