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TehJay
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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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17 Sep 2010, 16:05
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25% (medium)

Question Stats:

77% (01:14) correct 23% (01:44) wrong based on 35 sessions

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

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

Show Spoiler
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: if-x-is-an-integer-is-9-x-9-x-b-139874.html

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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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17 Sep 2010, 16:25
TehJay
If x is an integer, is \(9^x + 9^-^x = b\)?

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

Show Spoiler
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.
Show more

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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If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b
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17 Sep 2010, 23:39
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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If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b
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18 Sep 2010, 07:24
TehJay
If x is an integer, is \(9^x + 9^-^x = b\)?

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

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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If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b
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18 Sep 2010, 07:34
If (2) just said x>0, then what can we answer about the question? What is b? How is the answer still D?

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

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

Show Spoiler
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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Bunuel
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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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18 Sep 2010, 07:38
mainhoon
If (2) just said x>0, then what can we answer about the question? What is b? How is the answer still D?
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If (2) just says \(x>0\) then answer is A, not D.

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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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15 Aug 2017, 04:21
TehJay
If x is an integer, is \(9^x + 9^-^x = b\)?

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

Show Spoiler
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.
Show more

PROPER VERSION OF THIS QUESTION IS HERE: if-x-is-an-integer-is-9-x-9-x-b-139874.html

This Question is Locked Due to Poor Quality
Hi there,
The question you've reached has been archived due to not meeting our community quality standards. No more replies are possible here.
Looking for better-quality questions? Check out the 'Similar Questions' block below for a list of similar but high-quality questions.
Want to join other relevant Problem Solving discussions? Visit our Data Sufficiency (DS) Forum for the most recent and top-quality discussions.
Thank you for understanding, and happy exploring!

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