January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Nov 2013
Posts: 88

If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
Updated on: 24 Nov 2016, 07:03
Question Stats:
64% (01:54) correct 36% (02:14) wrong based on 354 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by lalania1 on 24 Nov 2016, 06:57.
Last edited by Bunuel on 24 Nov 2016, 07:03, edited 1 time in total.
Edited the question.



Manager
Joined: 17 Nov 2013
Posts: 88

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



Math Expert
Joined: 02 Sep 2009
Posts: 52218

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
24 Nov 2016, 07:07



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4331
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
24 Nov 2016, 08:21
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, 12:16
Can someone please explain why the answer is not 5B?



Math Expert
Joined: 02 Sep 2009
Posts: 52218

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
26 Feb 2017, 02:37



Manager
Joined: 31 Jan 2017
Posts: 58
Location: India
Concentration: Strategy, Leadership
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, 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
_________________
__________________________________ 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, 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?



Math Expert
Joined: 02 Sep 2009
Posts: 52218

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
01 Dec 2017, 22:58



Senior Manager
Joined: 08 Jun 2015
Posts: 432
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38
GPA: 3.33

Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following
[#permalink]
Show Tags
23 Apr 2018, 06:32
+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^22. Hence option D
_________________
" The few , the fearless "



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4527
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, 10:31
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 Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Status: Studying SC
Joined: 04 Sep 2017
Posts: 118
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, 03:48
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 \(5^x + 5^{–x} = B\): \(25^{x} +2*5^x* 5^{–x}+25^{x} = B^2\); \(25^{x} +2+25^{x} = B^2\); \(25^{x} + 25^{x} = B^22\). Answer: D. 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... \(B^2\) = (\(5^{2x} +5^{xx} +5^{xx} +5^{2x}\)) 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 = \(25^x + 25^{x}\)
_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.
How to sort questions by Topic, Difficulty, and Source: https://gmatclub.com/forum/search.php?view=search_tags



Senior Manager
Joined: 04 Aug 2010
Posts: 320
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, 12:13
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 Click here to learn more 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 longdistance. For more information, please email me at GMATGuruNY@gmail.com.




Re: If for some value of x, 5^x + 5^(–x) = B, then which of the following &nbs
[#permalink]
27 Jun 2018, 12:13






