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If x is an integer, is 9^x + 9^{-x} = b ?

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If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Oct 2012, 04:20
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If x is an integer, is 9^x + 9^{-x} = b ?

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

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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Oct 2012, 04:20
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If x is an integer, 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. No sufficient.

Answer: A.
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Oct 2012, 04:40
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1) 3^x + 3^-^x = \sqrt{b + 2}

square both sides

9^x+2*3^x*\frac{1}{3^x}+9^{-x} = b+2

Therefore, 9^x + 9^{-x} = b.

Sufficient.

2) Tells us nothing about b, but rather that x is a positive number. Insufficient.

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Knowing this, the solution is A - statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Oct 2012, 04:54
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This was tough. I spent at least 3 minutes (during the exam is not possible) :(

We can rephrase the stimulus but I see a lot of options to do. Is not straight (at least for me). Ok better to look at the statements

2) this say nothing about =between the left part of equation and the right part INSUFF

1) square boot sides so we have (3^x + 3^-x)^2=\sqrt{b + 2}^2

Now we 'd have 9^x that is, is the same of 3^2x -------> 9^x + 9^-x + 2 ( 3^x + 3^-x)= b + 2 ---------> 9^x + 2 + 9^-x = b + 2

In the end 9^x + 9^-x = b SUFF

A should be the answer

Note: 2 ( 3^x + 3^-x) is zero because we have 3^ x- x . a number power zero is 1 ---> 2*1 = 2 for me is more than 600 level
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Oct 2012, 19:18
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1) Square both the side & get the same equation as in stem --->Sufficient
2) Insufficient
Answer A
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 04 Oct 2012, 13:44
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SOLUTION

If x is an integer, 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. No sufficient.

Answer: A.

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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 31 Oct 2012, 22:40
Bunuel wrote:
SOLUTION

If x is an integer, 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. No sufficient.

Answer: A.

Kudos points given to everyone with correct solution. Let me know if I missed someone.


Question please: Can we do anything with the 9^x + 9^{-x} = b or simplify any more than what is given? I tried to do something more but could not find anything proper...
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 01 Nov 2012, 06:25
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ikokurin wrote:
Bunuel wrote:
SOLUTION

If x is an integer, 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. No sufficient.

Answer: A.

Kudos points given to everyone with correct solution. Let me know if I missed someone.


Question please: Can we do anything with the 9^x + 9^{-x} = b or simplify any more than what is given? I tried to do something more but could not find anything proper...


I'd say 9^x + 9^{-x} the simplest way of writing this expression and as you can see from the solution we don't even need to manipulate with it further to answer the question.
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 10 Nov 2012, 21:22
bb, I tried navigating below link, but it says "You are not authorised to read this forum". Can you check please?

the-official-guide-for-gmat-review-13th-edition-quant-134495.html
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 11 Nov 2012, 04:42
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bb, I tried navigating below link, but it says "You are not authorised to read this forum". Can you check please?

the-official-guide-for-gmat-review-13th-edition-quant-134495.html


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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 13 Nov 2012, 17:05
why is 3^x * 3^x = 9x? shouldnt it be 9^2x?
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 14 Nov 2012, 01:51
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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink] New post 07 Jan 2014, 07:43
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Re: If x is an integer, is 9^x + 9^{-x} = b ?   [#permalink] 07 Jan 2014, 07:43
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