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

Question

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.

IanStewart · Answer

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.

Bunuel · Answer

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.

vitamingmat · Answer

(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

AbeinOhio · Answer

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

Bunuel · Answer

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sambam · Answer

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

iliavko · Answer

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!

chetan2u · Answer

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...

iliavko · Answer

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!

chetan2u · Answer

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

iliavko · Answer

Great!

Thank you so much for the clarifications, Chetan!

dabaobao · Answer

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

BrentGMATPrepNow · Answer

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

Kinshook · Answer

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

Kimberly77 · Answer

Hello experts, is number testing is possible and could anyone show an example of it? Thanks

chetan2u · Answer

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.

Kimberly77 · Answer

Brilliant thanks  chetan2u  for your great explanation and crystal clear now. After all algebra way is better in this case then.

bumpbot · Answer

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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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