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# If v and w are different integers, does v = 0?

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Director
Joined: 01 May 2007
Posts: 793
If v and w are different integers, does v = 0? [#permalink]

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14 Jul 2007, 16:28
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Difficulty:

25% (medium)

Question Stats:

57% (01:40) correct 43% (00:36) wrong based on 140 sessions

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If v and w are different integers, does v = 0?

(1) vw = v^2
(2) w = 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-v-and-w-are-different-integers-does-v-0-1-vw-v-102599.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jul 2013, 08:37, edited 1 time in total.
VP
Joined: 10 Jun 2007
Posts: 1439

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14 Jul 2007, 16:39
jimmyjamesdonkey wrote:
If v and w are different integers, does v = 0?

(1) vw = v^2
(2) w = 2

OA to follow.

I got A.

(1) Since v & w are different integers, the only possible solution here is V=0.
Manager
Joined: 17 May 2007
Posts: 170

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14 Jul 2007, 23:20
Since VW = V^2 and V , W are differenet integers V has to be O

Manager
Joined: 05 Mar 2007
Posts: 112

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15 Jul 2007, 06:35
I believe we should get the equation to a simplied form
vw-v^2=0 ; v(w-v) => v=w or v=0

and by the looks of it we have two answers! either v=2 or 0.

Since both are different we have v=0.

FP
Director
Joined: 29 Nov 2012
Posts: 878
Re: If v and w are different integers, does v = 0? (1) vw = v^2 [#permalink]

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02 Jul 2013, 07:10
If v and w are different integers, does v = 0?

Given info V and W are different integers so it can't be equal so (1,1) , (2,2) etc are ruled out

$$(1) vw = v^2$$

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

Since v and w are different integers v must be 0 sufficient!

(2) w = 2

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Math Expert
Joined: 02 Sep 2009
Posts: 39723
Re: If v and w are different integers, does v = 0? [#permalink]

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02 Jul 2013, 08:39
If v and w are different integers, does v = 0?

(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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-v-and-w-are-different-integers-does-v-0-1-vw-v-102599.html [/quote]
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Re: If v and w are different integers, does v = 0?   [#permalink] 02 Jul 2013, 08:39
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