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If for some value of x, 5^x + 5^(–x) = B, then which of the following

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If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 24 Nov 2016, 06:57
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If for some value of x, 5^x + 5^(–x) = B, then which of the following is equal to 25^x + 25^(–x)?

A) 5B
B) 5B - 10
C) B^2
D) B^2 - 2
E) B^2 - 10
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Nov 2016, 07:03, edited 1 time in total.
Edited the question.

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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 24 Nov 2016, 06:59
Hi all,

5^–x = 5 to the -x exponent. I was not able to find the right way to express it. Feel free to edit with a fix if you have it.

Looking forward to your answers on this question

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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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lalania1 wrote:
If for some value of x, 5^x + 5^(–x) = B, then which of the following is equal to 25^x + 25^(–x)?

A) 5B
B) 5B - 10
C) B^2
D) B^2 - 2
E) B^2 - 10


Square \(5^x + 5^{–x} = B\):

\(25^{x} +2*5^x* 5^{–x}+25^{-x} = B^2\);

\(25^{x} +2+25^{-x} = B^2\);

\(25^{x} + 25^{-x} = B^2-2\).

Answer: D.
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 24 Nov 2016, 08:21
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lalania1 wrote:
If for some value of x, 5^x + 5^(–x) = B, then which of the following is equal to 25^x + 25^(–x)?

A) 5B
B) 5B - 10
C) B^2
D) B^2 - 2
E) B^2 - 10


Let x = 1

\(5^x + 5^{–x} = \ B \ = 5 + \frac{1}{5}\) = \(\frac{26}{5}\)

Let x = 2

\(5^x + 5^{–x} = 5^2 + \frac{1}{5^2}\) = 25 + \(\frac{1}{25}\) = \(\frac{626}{25}\)

From the above options (A) and (B) can straightaway be rejected...

(C) \(B^2 = \frac{676}{25}\) Rejected...

(D) \(B^2 - 2 = \frac{( 676 - 50 )}{25}\) = \(\frac{626}{25}\)

Hence, answer must be (D) \(\frac{626}{25}\)
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 25 Feb 2017, 12:16
Can someone please explain why the answer is not 5B?

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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 26 Feb 2017, 06:42
Answer: D

Given, 5^x + 1/ (5^x) = B
Substitute 5^x = a
a + 1/a = B

Needed = 25^x + 25^(–x) = (5^x)^2 + 1 / (5^x)2 = a^2 +1/ a^2 = (a^4 + 1) / a^2

a + 1/a = B
a^2+ 1 = a * B
a^4 + 1 + 2*(a^2) = (a^2) * (B^2) [squaring both sides]
a^4 + 1 = (a^2) * (B^2) - 2*(a^2)
(a^4 + 1) / a^2 = (B^2) - 2
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 01 Dec 2017, 18:11
Can someone please advise where I went wrong?

I approached the question in the following manner:

Given: \(5^x+5^{-x} = B\)

Simplify: \(25^x+25^{-x} = 5^{2x}+5^{-2x} = 5(5^x+5^{-x}) = 5(B)\)

Why can't I approach like this?

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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

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New post 01 Dec 2017, 22:58
nicoeddy wrote:
Can someone please advise where I went wrong?

I approached the question in the following manner:

Given: \(5^x+5^{-x} = B\)

Simplify: \(25^x+25^{-x} = 5^{2x}+5^{-2x} = 5(5^x+5^{-x}) = 5(B)\)

Why can't I approach like this?


If you factor 5 from \(5^{2x}+5^{-2x}\) you get \(5(5^{2x-1}+5^{-2x-1})\), not \(5(5^x+5^{-x})\).

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8. Exponents and Roots of Numbers



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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following   [#permalink] 01 Dec 2017, 22:58
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