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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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.

Answer: A.
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(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

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

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


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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.

Answer: A

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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Thank you for your reply, Chetan!

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?

Thank you for your help!

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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Great!

Thank you so much for the clarifications, Chetan!

v,w = different int
v = 0?

Start with stmt 2 since it's easier
2) w = 2. No info about v. => Not Sufficient

1) v^2 - vw = 0
v (v - w) = 0 => v = 0 or w (v=w is not possible due to the given constraint) => v = 0 => Sufficient

ANSWER: A

Given: v and w are different integers

Target question: Does v = 0?

Statement 1: vw = v²
Subtract v² from both sides of the equation: vw - v² = 0
Factor: v(w - v) = 0
So, EITHER v = 0 OR w - v = 0
Important: If w - v = 0, then that means w = v, and the question tells us that v and w are different integers.
This means w - v cannot equal 0, which means v = 0
So, the answer to the target question is YES, v = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: w = 2
Since statement to provides no information about v, we can’t answer the target question with certainty
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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