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

BTGmoderatorLU wrote: ↑
Fri May 21, 2021 12:56 pm
Source: GMAT Prep

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

1) \(\textsf{vw} = \textsf{v}^2\)
2) \(\textsf{w} = 2\)

The OA is A

\(v,w =\) different integer
\(v = 0?\)

1) \(v^2 - vw = 0\)
\(v (v - w) = 0 \Longrightarrow v = 0\) or \(w (v=w\) is not possible due to the given constraint\() \Longrightarrow v = 0\) Sufficient. \(\Large{\color{green}\checkmark}\)

2) \(w = 2.\) No info about \(v.\) Not Sufficient \(\Large{\color{red}\chi}\)

Therefore, A

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

by Brent@GMATPrepNow » Fri May 28, 2021 5:31 am

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BTGmoderatorLU wrote: ↑
Fri May 21, 2021 12:56 pm
Source: GMAT Prep

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

1) \(\textsf{vw} = \textsf{v}^2\)
2) \(\textsf{w} = 2\)

The OA is 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

Brent Hanneson - Creator of GMATPrepNow.com