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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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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.

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

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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?

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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