It is currently 21 Mar 2018, 15:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 17 Nov 2013
Posts: 171
If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

24 Nov 2016, 07:57
6
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:38) correct 40% (01:40) wrong based on 199 sessions

### HideShow timer Statistics

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, 08:03, edited 1 time in total.
Edited the question.
Manager
Joined: 17 Nov 2013
Posts: 171
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

24 Nov 2016, 07:59
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.

Math Expert
Joined: 02 Sep 2009
Posts: 44388
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

24 Nov 2016, 08:07
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 $$5^x + 5^{–x} = B$$:

$$25^{x} +2*5^x* 5^{–x}+25^{-x} = B^2$$;

$$25^{x} +2+25^{-x} = B^2$$;

$$25^{x} + 25^{-x} = B^2-2$$.

_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3366
Location: India
GPA: 3.5
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

24 Nov 2016, 09:21
1
This post was
BOOKMARKED
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) $$\frac{626}{25}$$
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Joined: 15 Feb 2017
Posts: 2
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

25 Feb 2017, 13:16
Math Expert
Joined: 02 Sep 2009
Posts: 44388
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

26 Feb 2017, 03:37
Tylcleaner wrote:

There are TWO solutions above:
https://gmatclub.com/forum/if-for-some- ... l#p1767286
https://gmatclub.com/forum/if-for-some- ... l#p1767321
_________________
Manager
Joined: 31 Jan 2017
Posts: 59
Location: India
GMAT 1: 680 Q49 V34
GPA: 4
WE: Project Management (Energy and Utilities)
If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

26 Feb 2017, 07:42

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
_________________

__________________________________
Kindly press "+1 Kudos" if the post helped

Intern
Joined: 12 Oct 2014
Posts: 6
N: E
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

01 Dec 2017, 19:11

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?
Math Expert
Joined: 02 Sep 2009
Posts: 44388
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following [#permalink]

### Show Tags

01 Dec 2017, 23:58
nicoeddy wrote:

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 $$5(5^x+5^{-x})$$.

Check below:

8. Exponents and Roots of Numbers

Check below for more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
_________________
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following   [#permalink] 01 Dec 2017, 23:58
Display posts from previous: Sort by