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# If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2

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

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?

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

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?

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

Thank you so much for the clarifications, Chetan!
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

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.

v,w = different int
v = 0?

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

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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
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zerotoinfinite2006 wrote:
If v and w are different integers, does v = 0?

(1) vw = v²
(2) w = 2

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

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

(1) vw = v^2
v(w-v)=0
Since w & v are different integers, w-v is NOT 0; v =0
SUFFICIENT

(2) w = 2
There is no relation between v & w. v can not be known.
NOT SUFFICIENT

IMO A
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
Hello experts, is number testing is possible and could anyone show an example of it? Thanks
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
Kimberly77 wrote:
Hello experts, is number testing is possible and could anyone show an example of it? Thanks

Hi, you can test numbers but for that too you have to understand what $$vw=v^2$$ means
Take any two different values for v and w
2*3=2^2….No
3*5=5^2….No
But till the time you do not realise that only v as 0 will satisfy the equation, you cannot be sure because you cannot check for all pair of different numbers.
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
chetan2u wrote:
Kimberly77 wrote:
Hello experts, is number testing is possible and could anyone show an example of it? Thanks

Hi, you can test numbers but for that too you have to understand what $$vw=v^2$$ means
Take any two different values for v and w
2*3=2^2….No
3*5=5^2….No
But till the time you do not realise that only v as 0 will satisfy the equation, you cannot be sure because you cannot check for all pair of different numbers.

Brilliant thanks chetan2u for your great explanation and crystal clear now. After all algebra way is better in this case then.
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink]
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