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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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zerotoinfinite2006
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If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  10 Oct 2010, 09:36
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If v and w are different integers, does v = 0?

(1) vw = v^2

(2) w = 2


Show SpoilerOA
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.
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IanStewart
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  10 Oct 2010, 09:44
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zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2



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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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  10 Oct 2010, 09:45
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zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

Show SpoilerOA
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.


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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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  11 Oct 2010, 02:15
(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] New post  21 Mar 2012, 15:02
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] New post  03 Jul 2013, 01:17
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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] New post  04 Jul 2013, 08:27
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
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  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?

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] New post  21 Jun 2016, 04:16
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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] New post  21 Jun 2016, 04:39
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!
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  21 Jun 2016, 04:44
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iliavko wrote:
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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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  21 Jun 2016, 04:49
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] New post  19 Aug 2019, 03:18
zerotoinfinite2006 wrote:
If v and w are different integers, does v=0?

(1) vw = v^2

(2) w = 2

Show SpoilerOA
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?

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
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  28 May 2021, 06:31
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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

Answer: A

Cheers,
Brent
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Re: If v and w are different integers, does v = 0? (1) vw = v^2 (2) w = 2 [#permalink] New post  11 Jul 2022, 23:06
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] New post  08 Oct 2022, 07:15
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] New post  08 Oct 2022, 09:57
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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] New post  08 Oct 2022, 13:17
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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