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Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink]
01 Oct 2012, 04:54

2

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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 _________________

Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink]
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...

Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink]
01 Nov 2012, 06:25

Expert's post

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. _________________

Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink]
07 Jan 2014, 07:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x is an integer, is 9^x + 9^{-x} = b ? [#permalink]
17 Nov 2014, 14:24

As was noted earlier in this post, this question uses the formula (x+y)^2=x^2+2xy+y^2. In this question xy=1 because x^0=1. This allows for the 2's to cancel out.

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