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

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Current Student
Joined: 21 Aug 2010
Posts: 194
If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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21 Aug 2011, 07:13
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58% (00:39) correct 42% (00:48) wrong based on 168 sessions

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

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

I feel it should be C. But it is not.

(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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-v-and-w-a ... 02599.html
Current Student
Joined: 21 Aug 2010
Posts: 194
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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21 Aug 2011, 07:17
I am sorry. I missed a very important point. Both are different integers.
Manager
Joined: 18 Aug 2011
Posts: 56
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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21 Aug 2011, 11:10
samramandy wrote:
I am sorry. I missed a very important point. Both are different integers.

As you said, you have:

v = 0
or
w-v=0 which is the same as w=v

Since we are told that v and w are different, the second equation doesn't hold and we're left with the first one => v = 0

q.e.d
Manager
Joined: 20 Jul 2011
Posts: 125
GMAT Date: 10-21-2011
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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07 Sep 2011, 02:26
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

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Intern
Joined: 23 Aug 2011
Posts: 36
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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07 Sep 2011, 07:17
+1 for A;can anyone confrim
Intern
Joined: 31 Aug 2011
Posts: 8
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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09 Oct 2011, 16:12
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?
Manager
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GMAT 1: 690 Q47 V37
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Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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10 Oct 2011, 06:02
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
Current Student
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Joined: 29 Jun 2010
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Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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10 Oct 2011, 22:23
samramandy wrote:
If v and w are different integers, does v = 0 ?

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

I feel it should be C. But it is not.

(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.

Using statement A : either v=0 or W=V .but since both are diffrent integers...W should not be equal to V.Hence V=0.

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Math Expert
Joined: 02 Sep 2009
Posts: 45423
Re: If v and w are different integers, does v = 0 ? (1) vw = v^2 [#permalink]

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26 Nov 2017, 23:52
samramandy wrote:
If v and w are different integers, does v = 0 ?

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

I feel it should be C. But it is not.

(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.

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-v-and-w-a ... 02599.html
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Re: If v and w are different integers, does v = 0 ? (1) vw = v^2   [#permalink] 26 Nov 2017, 23:52
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