NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 12:05 It is currently 28 Apr 2024, 12:05
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If n is an integer,and 5n+5n=62625,how many values of n satisfy the e

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
Afroditee
Manager
Manager
Joined: 13 Aug 2022
Posts: 98
Own Kudos [?]: 151 [5]
Given Kudos: 178
Send PM
If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   11 Oct 2022, 11:50
5
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

55% (01:35) correct 45% (01:39) wrong based on 104 sessions
Hide Show timer Statistics
If n is an integer, and \( 5^{n} + 5^{-n}\)= \(\frac{626}{25}\) , how many values of n satisfy the equation?

A.0

B.1

C.2

D.3

E.4
ShowHide Answer
Official Answer
C
User avatar
G
rajtare
Senior Manager
Senior Manager
Joined: 05 Nov 2014
Posts: 269
Own Kudos [?]: 216 [1]
Given Kudos: 11
Location: India
Concentration: Operations, Leadership
Schools: Sloan '26 Columbia CBS'26 Goizueta '26 Kellogg '26
GPA: 3.99
Send PM
Reviews Badge
Re: If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   11 Oct 2022, 14:34
1
Kudos
Afroditee wrote:
If n is an integer, and \( 5^{n} + 5^{-n}\)= \(\frac{626}{25}\) , how many values of n satisfy the equation?

A.0

B.1

C.2

D.3

E.4


5^n + 5^(-n) = 626/25 ---- 1)
we can simplify this equation considering two conditions n>0, and n<0
if n>0,
5^n + 1/(5^n)
=(5^2n+1)/5^n as per 1)
(5^2n+1)/5^n = 626/25
n=2
if n<0,
1/5^n + 5^n
=(5^2n+1)/5^n = 626/25
n=-2
since two values of n are possible n=2, -2. hence answer will be C
User avatar
B
jonNNNNNy
Intern
Intern
Joined: 09 Jan 2022
Posts: 11
Own Kudos [?]: 0 [0]
Given Kudos: 11
Send PM
Re: If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   12 Oct 2022, 10:57
anyone with another approach plz?
User avatar
B
jai3892
Intern
Intern
Joined: 07 Apr 2020
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 4
Send PM
Re: If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   13 Oct 2022, 10:59
5^n + 1/5^n = (625+1)/25
5^n +1/5^n = 625/25 + 1/25
5^n +1/5^n = 25 + 1/25
5^n +1/5^n = (5)^2 + 1/5^2

Now, N=2
User avatar
B
Afroditee
Manager
Manager
Joined: 13 Aug 2022
Posts: 98
Own Kudos [?]: 151 [0]
Given Kudos: 178
Send PM
If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   10 Dec 2022, 23:28
jai3892 wrote:
5^n + 1/5^n = (625+1)/25
5^n +1/5^n = 625/25 + 1/25
5^n +1/5^n = 25 + 1/25
5^n +1/5^n = (5)^2 + 1/5^2

Now, N=2

I think this is wrong approach. Question stem didn't ask for the value of N, rather it asked for how many values of N satisfy the equation.
According to your result, the answer would be 1. Since you got N=2 only.

It can be modified from the last step, if I am not mistaken.

5^n+5^-n= 5^2 + 5^-2 , thus n has two values (2 and -2)
User avatar
S
Maria240895chile
Manager
Manager
Joined: 23 Apr 2021
Posts: 127
Own Kudos [?]: 41 [0]
Given Kudos: 115
Send PM
If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink] New post   13 Dec 2022, 09:00
jonNNNNNy wrote:
anyone with another approach plz?




\(5^n + 5^{-n}=\frac{625}{25}\)

\(5^n +\frac{ 1}{5^n}=\frac{5^4}{5^2}\)

\(\frac{5^{2n}+1}{5^n}=\frac{5^4}{5^2}\)

cross multiplication \(5^2(5^{2n}+1)=5^4*5^n\)

\(5^{4n}+5^2=5^n*5^4\)

\(\frac{5^{4n}}{5^n*5^4}=-5^2\)

\(\frac{5^{3n}}{5^4}=-5^2\)

\(5^{3n}=5^4*25\)

\(5^{3n}=5^6\)

so we can eliminate the bases having

3n=6

n=2
GMAT Club Bot
gmatclubot
If n is an integer,and 5n+5n=62625,how many values of n satisfy the e [#permalink]
13 Dec 2022, 09:00
Moderators:
Bunuel
Math Expert
92975 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions