GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jul 2018, 11:22

### 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

# 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: 132
If for some value of x, 5^x + 5^(–x) = B, then which of the following  [#permalink]

### Show Tags

Updated on: 24 Nov 2016, 08:03
12
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:36) correct 38% (01:34) wrong based on 329 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

Originally posted by lalania1 on 24 Nov 2016, 07:57.
Last edited by Bunuel on 24 Nov 2016, 08:03, edited 1 time in total.
Edited the question.
Manager
Joined: 17 Nov 2013
Posts: 132
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: 47183
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
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: 3655
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
1
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: 47183
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: 58
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: 47183
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.
_________________
Director
Joined: 08 Jun 2015
Posts: 517
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following  [#permalink]

### Show Tags

23 Apr 2018, 07:32
+1 for option D.

Use (a+b)^2=a^2+b^2+2ab.

(5^x+5^-x)^2=25^x+25^-x+2=b^2 ; The required qty is b^2-2.

Hence option D
_________________

" The few , the fearless "

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2973
Location: United States (CA)
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following  [#permalink]

### Show Tags

24 Apr 2018, 11:31
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

Squaring both sides of the equation, we have:

[5^x + 5^(–x)]^2 = B^2

(5^2)^x + (5^2)^-x + 2(5^x)(5^-x) = B^2

25^x + 25^-x + 2(5^0) = B^2

25^x + 25^-x + 2 = B^2

25^x + 25^-x = B^2 - 2

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Status: Studying Quant
Joined: 04 Sep 2017
Posts: 45
GPA: 3.6
WE: Sales (Computer Software)
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following  [#permalink]

### Show Tags

27 Jun 2018, 04:48
1
Bunuel wrote:
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 $$5^x + 5^{–x} = B$$:

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

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

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

Okay I had a question, but as I typed this out I got the answer... Here is a detailed step by step of Bunuel's solution. Thanks Bunuel.

I was confused how he got the 2 $$* 5^x * 5^{-x}$$, but now I see that's just $$5^0 + 5^0$$

Square $$5^x + 5^{–x} = B$$

$$B^2$$= ($$5^x + 5^{-x}$$)($$5^x + 5^{-x}$$). Foil method...

$$B^2$$ = ($$5^{2x} +5^{x-x} +5^{x-x} +5^{-2x}$$) Which then would lead to

$$B^2$$ = ($$5^{2x} + 5^0 + 5^0 + 5^{-2x}$$) We know $$5^0$$ = 1

$$B^2$$ = ($$5^{2x} + 2 + 5^{-2x}$$) Subtract the 2 to move it over to LHS. $$5^{2x} +5^{-2x} = 25^x + 25^{-x}$$

$$B^2$$ -2 = $$25^x + 25^{-x}$$
Manager
Joined: 04 Aug 2010
Posts: 198
Schools: Dartmouth College
Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following  [#permalink]

### Show Tags

27 Jun 2018, 13:13
2
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=0.

$$B = 5^x + 5¯^x = 5^0 + 5^0 = 1 + 1 = 2.$$
$$25^x + 25¯^x = 25^0 + 25^0 = 1 + 1 =$$ $$2$$.

When B=2 is plugged into the answer choices, the result must be the value in blue.
Only D works:
$$B^2 - 2 = 2^2 - 2 = 4 - 2 = 2$$.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following &nbs [#permalink] 27 Jun 2018, 13:13
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.