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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]  10 Oct 2010, 08:36
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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: DS - OG10 - 259 [#permalink]  10 Oct 2010, 08:44
Expert's post
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]  10 Oct 2010, 08:45
Expert's post
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]  11 Oct 2010, 01:15
(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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Re: v = 0? [#permalink]  21 Mar 2012, 14:02
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]  03 Jul 2013, 00:17
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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]  04 Jul 2013, 07:27
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]  21 Sep 2015, 21:24
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Re: If v and w are different integers, does v=0? (1) vw = v^2   [#permalink] 21 Sep 2015, 21:24
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