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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Apr 04, 2014 12:51 am
candygal79 wrote:Is p + pz = p

1) p = 0
2) z = 0
Target question: Is p + pz = p

This is a great candidate for rephrasing the target question.

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take the equation p + pz = p and subtract p from both sides to get pz = 0.
So, we can rephrase the target question as . . .
REPHRASED target question: Does pz = 0

Statement 1: p = 0
If p = 0, then pz definitely equals 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 0
If z = 0, then pz definitely equals 0
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by Brent@GMATPrepNow » Fri Apr 04, 2014 12:52 am
Looks like my response was posted twice.
deleted second response.
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by j_shreyans » Tue Feb 03, 2015 10:12 am
Hi Brent ,
our question is:

p + pz = p

if we take out the p from the above we will have

p(1+z)=p

then 1+z=1

then z=0 so this should be our target question right?

So by the above target question only statement 2 is sufficient.

Please suggest and correct me if i am wrong.

Thanks

Shreyans
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by Brent@GMATPrepNow » Tue Feb 03, 2015 10:43 am
j_shreyans wrote:Hi Brent ,
our question is:

p + pz = p

if we take out the p from the above we will have

p(1+z)=p

then 1+z=1

then z=0 so this should be our target question right?

So by the above target question only statement 2 is sufficient.

Please suggest and correct me if i am wrong.

Thanks

Shreyans
Good idea, Shreyans.
However, there's a slight problem with your conclusion.

We have: p(1+z)=p
If we divide both sides by p, we get: 1+z=1, which means z = 0 is a possible solution
HOWEVER, when we divide both sides by p, we must realize that p might equal 0. Notice that, if p = 0, then p(1+z)=p.
So, p = 0 is another possible solution.

So, we have two possible solutions: z = 0 and p = 0
So if either of these is the solution, then pz = 0

That's why I REPHRASED the target question as: Does pz = 0?

BIG TAKEAWAY, when dividing both sides of an equation by a variable, we must consider the possibility that we may be dividing both sides by ZERO.

Cheers,
Brent
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by [email protected] » Tue Feb 03, 2015 6:29 pm
Hi j_shreyans,

Brent has pointed out an important warning about "dividing out" variables. When 'removing' a variable in this way, you run the risk of removing possible answers to the given question. In DS questions, this will almost certainly lead to an incorrect answer.

You can add/subtract a variable away with no problems, but you have to be careful about multiplying/dividing a variable away.

Here's a basic example:

X^2 = X

How many solutions does this have? How many solutions does it have IF you divide both sides by X?

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