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

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Senior Manager
Joined: 05 Oct 2005
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If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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27 Oct 2005, 17:59
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Aug 2014, 03:19, edited 1 time in total.
Edited the question and added the OA.
VP
Joined: 22 Aug 2005
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Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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27 Oct 2005, 18:11
A.

3^x + 3^(-x) = sqrt(b+2)
squaring both sides

3^2x + 3^-2x + 2 * 3^0 = b+2

(3^2)^x + (3^2)^-x + 2 = b+2
9^x + 9^-x = b

wondering if any of the above steps require x to be > 0 (stmt 2)
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Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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27 Oct 2005, 18:37
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yb wrote:
If x is an integer, is 9^x + 9^(-x) = b ?

1) 3^x + 3^(-x) = sqrt(b+2)

2) x>0

(1) 3^x + 3^(-x) = sqrt(b+2) = [3^x + 3^(-x)]^2 = b+2
[3^x + 3^(-x)] [3^x + 3^(-x)] = [3^2x + 3^0 + 3^0 + 3^-2x]= b+2
3^2x + 1 + 1 + 3^-2x = b+2
9^x + 2 + 9^-x = b+2
9^x + 9^-x = b - Thus (1) is sufficient

(2) Reveals nothing about b. Insufficient.

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

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19 Aug 2014, 22:35
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yb wrote:
If x is an integer, is 9^x + 9^(-x) = b ?

1) 3^x + 3^(-x) = sqrt(b+2)

2) x>0

Note that 9^x is the square of 3^x so we know that we should try to square stmnt 1.

1) $$3^x + 3^{-x} = \sqrt{(b+2)}$$
$$3^{2x} + 3^{-2x} + 2*3^x*3^{-x} = \sqrt{(b+2)}^2$$
$$9^x + 9^{-x} = b + 2 - 2 = b$$

We answer with 'Yes' and hence this statement alone is sufficient.

2) x > 0
Obviously not sufficient.

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Joined: 21 Mar 2014
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Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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05 Dec 2015, 12:56
Bunuel , what is x=0 ?
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Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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06 Dec 2015, 10:31
saroshgilani wrote:
Bunuel , what is x=0 ?

If x = 0, then the questions asks whether b = 2.

(1) gives $$2 = \sqrt{b+2}$$ --> b = 2. Sufficient.

Hope it's clear.
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If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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16 Sep 2016, 16:33

(1) 3^x + 3^(-x) = sqrt(b+2)
= [3^x + 3^(-x)]^2 = [sqrt(b+2)]^2 (square both sides)
= 3^(2x) + 3^(-2x) = b+2
= 9^x + 9^(-x) = b+2

SUFFICIENT

(2) x > 0

NOT SUFFICIENT (this statement doesn't provide any information we can use to verify the statement)
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Re: If x is an integer, is 9^x + 9^(-x) = b ? [#permalink]

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05 Nov 2017, 06:25
Hello from the GMAT Club BumpBot!

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Re: If x is an integer, is 9^x + 9^(-x) = b ?   [#permalink] 05 Nov 2017, 06:25
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