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If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b

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If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 17 Sep 2010, 17:05
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If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)
(2) \(x > 0 = b\)

The OA is A. I couldn't piece together (1) (I understand it now with the book's explanation), but I had answered B for this one. Why is the answer not D? (2) should be sufficient, because it gives you b = 0, and \(9^x + 9^-^x\) can't possibly be 0. So the answer would be NO and (2) should be sufficient.


PROPER VERSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-is-an-i ... 39874.html
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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 17 Sep 2010, 17:25
TehJay wrote:
If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)
(2) \(x > 0 = b\)

The OA is A. I couldn't piece together (1) (I understand it now with the book's explanation), but I had answered B for this one. Why is the answer not D? (2) should be sufficient, because it gives you b = 0, and \(9^x + 9^-^x\) can't possibly be 0. So the answer would be NO and (2) should be sufficient.


Is \(9^x + 9^{-x} = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\) --> square both sides --> \(9^x+2*3^x*\frac{1}{3^x}+9^{-x}=b+2\) --> \(9^x + 9^{-x} = b\). So answer to the question is YES. Sufficient.

(2) \(x > 0 = b\) --> question becomes: is \(9^x+9^{-x}=0\)? Answer to this question would be NO, as LHS is the sum of two positive values and thus can not equal to zero. So, sufficient.

There must be something wrong with this question. Technically answer would be D, as EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

I guess there is a typo in statement (2) and it should just state \(x>0\) instead of \(x>0=b\) (I've never seen such a notation in official sources).

Hope it helps
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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 18 Sep 2010, 00:39
I have seen this question before. Though I don't remember the exact statement (2) but I am sure there was no ambiguity and that the two statements led to the same answer

As bunuel said it was most likely x>0

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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 18 Sep 2010, 08:24
TehJay wrote:
If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)
(2) \(x > 0 = b\)


In my copy of the OG, Statement 2 simply reads: "x > 0". There may have been a typo in one printing of the OG which has since been corrected; in any case, the second statement should not include the '= b' part.
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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 18 Sep 2010, 08:34
If (2) just said x>0, then what can we answer about the question? What is b? How is the answer still D?

Bunuel wrote:
TehJay wrote:
If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)
(2) \(x > 0 = b\)

The OA is A. I couldn't piece together (1) (I understand it now with the book's explanation), but I had answered B for this one. Why is the answer not D? (2) should be sufficient, because it gives you b = 0, and \(9^x + 9^-^x\) can't possibly be 0. So the answer would be NO and (2) should be sufficient.


Is \(9^x + 9^{-x} = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\) --> square both sides --> \(9^x+2*3^x*\frac{1}{3^x}+9^{-x}=b+2\) --> \(9^x + 9^{-x} = b\). So answer to the question is YES. Sufficient.

(2) \(x > 0 = b\) --> question becomes: is \(9^x+9^{-x}=0\)? Answer to this question would be NO, as LHS is the sum of two positive values and thus can not equal to zero. So, sufficient.

There must be something wrong with this question. Technically answer would be D, as EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

So we can not have answer YES from statement (1) and answer NO from statement (2), as in this case statements would contradict each other.

I guess there is a typo in statement (2) and it should just state \(x>0\) instead of \(x>0=b\) (I've never seen such a notation in official sources).

Hope it helps

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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 18 Sep 2010, 08:38
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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b  [#permalink]

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New post 15 Aug 2017, 05:21
TehJay wrote:
If x is an integer, is \(9^x + 9^-^x = b\)?

(1) \(3^x + 3^-^x = \sqrt{b + 2}\)
(2) \(x > 0 = b\)

The OA is A. I couldn't piece together (1) (I understand it now with the book's explanation), but I had answered B for this one. Why is the answer not D? (2) should be sufficient, because it gives you b = 0, and \(9^x + 9^-^x\) can't possibly be 0. So the answer would be NO and (2) should be sufficient.


PROPER VERSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-is-an-i ... 39874.html
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Re: If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b   [#permalink] 15 Aug 2017, 05:21
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