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Does v equal zero?

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Source: — Data Sufficiency |
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by Patrick_GMATFix » Tue Feb 11, 2014 6:25 am
Be careful how you handler statement 1. A common mistake is to divide both sides of an equation by an unknown, without accounting for the possibility that the unknown could equal zero. Doing so can lead to erroneous results. For instance consider xy = y. What is x? If we divide both sides by y, we may think that x=1. But looking at the equation again, notice that x could also = 0. So in fact we don't know whether x=1.

The safer way to solve non-linear equations is to set them to zero and factor them. The full solution below is taken from the GMATFix App.

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by Brent@GMATPrepNow » Tue Feb 11, 2014 7:55 am
BlueDragon2010 wrote:If v and w are different integers, does v = 0?

1) vw = v²
2) w = 2

Target question: Does v = 0?

Given: v and w are different integers

Statement 1: vw = v²
Set equal to zero: v² - vw = 0
Factor to get: v(v - w) = 0
Since this product equals 0, there are two possibilities:
case a: v = 0
case b: v - w = 0 (in other words v = w)
HOWEVER, case b is impossible, because we're told that v and w are different integers
So, we can rule out case b, which means it MUST BE THE CASE that v = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: w = 2
There's no information about v, which means we can't determine whether or not v = 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by [email protected] » Tue Feb 11, 2014 2:33 pm
Hi BlueDragon2010,

Both Brent and Patrick have properly explained this DS question, so I won't rehash that here.

It is worth noting that DS questions are designed to test you on a number of "skills" beyond math skills. Your thoroughness is often tested on DS questions (meaning your ability to see ALL of the possibilities and not just the obvious one). As such, it's important to consider the number 0 when dealing with DS questions. This prompt is literally TELLING you to think about 0, since the question is asking "does v = 0?" Keep that idea in mind any time you're dealing with DS.

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