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

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07 Sep 2011, 01:26

Quote:

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

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

Statement 1 vw-v^2=0 v(w-v)=0 ---> since v and w are different integers, (w-v) cannot be zero. So, it has to be that v=0. Sufficient.

Statement 2 Not helpful. Insufficient.

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

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09 Oct 2011, 15:12

Hi,

For st 1, the question doesn't specify that it is only positive integers, so couldn't v=-2 and w=2 and stmt 1 would be satisfied. This would not only make v=0 a possibility, but also -2, so then, wouldn't this be insufficient?

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

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10 Oct 2011, 05:02

1) vw = v^2 vw - v^2 = 0 v(w-v) = 0 Either v = 0 or w-v = 0, Therefore v = o or v = w. 2) says nothg about v. insufficient. Since the question stem states v is not equal to w. V=o Sufficient

(1) vw = v^2 vw - v^2 = 0 v(w-v) = 0 Either v = 0 or w-v = 0 So we cannot say anything about v whether it's 0 or not.

2. w = 2

This statement tells us nothing about v.

Combining both If w= 2 then w = v so v should also be 2.

So that means v is not 0 by using both the statements.

So the answer should be C which is not.

Please guide.

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.