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GMAT Algebra (Data Sufficiency)
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Author:  questioner [ Sat Jul 10, 2010 5:04 am ]
Post subject:  GMAT Algebra (Data Sufficiency)

If a² = b, is 1 > a > 0?
(1) 1 > b > 0
(2) a > b

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) Statement (1) tells us that b is between 0 and 1, so we also know that a² is between 0 and 1 since b = a². If a is any number between -1 and 1, then a² will be
between 0 and 1, so Statement (1) is insufficient.

Statement (2) tells us that a > b, and since a² = b, we know that a > a². This is only true for
numbers between 0 and 1. The square of any number that is larger than 1 or negative will be larger than the number itself. So Statement (2) is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).
-------------

I think the answer should be letter D. Statement 1 should be sufficient since when I substitute 1/4 for b, it will yield 1/16 for a, so therefore 1>1/16>0.

Author:  Gennadiy [ Sat Jul 10, 2010 5:15 am ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

If you substitute 1/4 for b it gives you two options for a:
1/2 or -1/2.

So we can not definitely say is 1 > a > 0 or not.

Anyway, note, that by picking just one number you can prove that some statement is wrong, but you can not defenitely say that it is right if this number fits Ok. Here is a simple example for you:

Is a > 10 if |a| > 10?
If we pick a = 20 it is true, but it doesn't prove that it is true for any other value of a that satisfies |a| > 10. E.g. it is not true for a = -20 though |-20| > 10.

Author:  questioner [ Fri Feb 24, 2012 5:16 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

I believe the answer to this one should be C.

Author:  Gennadiy [ Fri Feb 24, 2012 5:20 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

questioner wrote:
I believe the answer to this one should be C.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

In the explanation we've proven that statement (2) by itself IS sufficient. Therefore C can NOT be a correct answer.

Author:  rquerub [ Sun Jun 24, 2012 1:57 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

"Statement (2) tells us that a > b and, since a² = b, then we know that a > a²".

Can you explain why you assume that a > a²?

Author:  Gennadiy [ Wed Jun 27, 2012 5:13 am ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

rquerub wrote:
"Statement (2) tells us that a > b and, since a² = b, then we know that a > a²".

Can you explain why you assume that a > a²?
Statement (2) is a > b . The question statement gives us b = a² . So we plug a² instead of b into a > b and get a > a² .

Author:  questioner [ Tue Jun 04, 2013 5:19 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

(1) shows that a is a fraction for a² to be < 1

Author:  Gennadiy [ Tue Jun 04, 2013 5:29 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

questioner wrote:
(1) shows that a is a fraction for a² to be < 1
(1) shows that a is a number between -1 and 1 for a² to be less than 1. It can be -1/2 , for example.

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