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 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Tue Dec 14, 2010 12:35 pm 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
Is m²n + mn² = 0?
(1) m + n = 1
(2) mn = 1

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(B) m²n + mn² = mn(m + n)
The formula equals 0 when mn = 0 or m + n = 0.
The statement (1) tells us that m + n = 1. It is not sufficient. If n = 0, m = 1, the equality is TRUE. But if n = 0.5, m = 0.5, it is NOT.

The statement (2) tells us that mn = 1. Therefore the first factor in the formula is not 0. Suppose the second one is. Then m + n = 0
m = -n
mn = -n², which is impossible because mn = 1 > 0. Therefore the second factor can NOT equal 0 and the equality is NEVER true. So the statement (2) is sufficient alone to answer the question.

The correct answer is (B).
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Could you please tell me where I am wrong in the following calculation:

if m²n + mn² = 0
then m²n = -mn²

divide both sides by mn:
m = -n

add n to both sides:
m + n = 0.

So for the initial equation to equal 0, m + n must also = 0

Now consider premise 1: if m + n =1 , then it cannot satisfy m + n = 0 and therefore, (1) BY ITSELF if also sufficient

??

I can follow your workings but I am not sure where my working is flawed.


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 Post subject: Re: math (test 4, question 23): data sufficiency, algebra
PostPosted: Tue Dec 14, 2010 12:48 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
Could you please tell me where I am wrong in the following calculation:

if m²n + mn² = 0
then m²n = -mn²

divide both sides by mn:
m = -n


You can NOT divide by mn if it equals 0. If you do so, you need to consider the situation when m = 0 or n = 0 as well. Or you need to be sure (based on facts), that none of those can equal 0.

In other words, in your reasoning you've "lost" possible values of m and n that make equality m²n + mn² = 0 true.

As the result of this error you got a wrong statement:
Quote:
So for the initial equation to equal 0, m + n must also = 0

The proper statement would be:
"For the initial equation to equal 0, m + n or m or n must equal zero."


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