NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 00:23 It is currently 25 Apr 2024, 00:23
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

10^k + 5^k =

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618867 [1]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
10^k + 5^k = [#permalink] New post   22 Mar 2018, 23:46
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

79% (00:31) correct 21% (00:56) wrong based on 82 sessions
Hide Show timer Statistics
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)
ShowHide Answer
Official Answer
B
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5205 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: 10^k + 5^k = [#permalink] New post   23 Mar 2018, 00:00
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)



Formula used: \((a*b)^m = a^m * b^m\)

\(10^k + 5^k = (5*2)^k + 5^k = 5^k*2^k + 5^k = 5^k(2^k + 1)\) (Option B)
User avatar
P
DavidTutorexamPAL
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Own Kudos [?]: 1777 [0]
Given Kudos: 26
Send PM
Re: 10^k + 5^k = [#permalink] New post   23 Mar 2018, 00:04
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


We'll show two approaches to solution:

The first relies on simplification and is a Precise approach.
Since 10^k = (5*2)^k = (5^k)(2^k) then we can extract a common factor of 5^k
from the original equation to get (5^k)(2^k+1).

If we don't feel too confident with the algebraic manipulations, we can instead just pick easy numbers.
This is an Alternative approach.

Say k = 2 then 10^k + 5^k = 100 + 25 = 125.
A. 5(4 + 1) = 25 NO
B. 25(4 + 1) = 125 Maybe, let's check the others.
C. 25*9 = 225 NO
D. 15^2 = 225 NO
E. 15^4 definitely not.

Either way, (B) is our answer.
User avatar
P
KS15
Director
Director
Joined: 21 May 2013
Posts: 540
Own Kudos [?]: 225 [0]
Given Kudos: 608
Send PM
Re: 10^k + 5^k = [#permalink] New post   23 Mar 2018, 05:39
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


=5^k(2^k+1)
Answer B
User avatar
B
hoang221
Intern
Intern
Joined: 28 Jan 2018
Posts: 46
Own Kudos [?]: 16 [0]
Given Kudos: 23
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Send PM
10^k + 5^k = [#permalink] New post   23 Mar 2018, 09:54
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


Key formula to use: \((a*b)^{m} = a^{m} * b^{m}\)

\(10^{k} + 5^{k} = 2^{k}*5^{k} + 5^{k} = 5^{k}*(2^{k} + 1) (B)\)
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6272 [0]
Given Kudos: 1646
Send PM
Re: 10^k + 5^k = [#permalink] New post   26 Mar 2018, 17:35
Expert Reply
Bunuel wrote:
\(10^k + 5^k =\)


A. \(5(2^k + 1)\)

B. \(5^k(2^k + 1)\)

C. \(5^k*3^k\)

D. \(15^k\)

E. \(15^{2k}\)


10^k + 5^k = 2^k * 5^k + 5^k = 5^k(2^k + 1)

Answer: B
GMAT Club Bot
gmatclubot
Re: 10^k + 5^k = [#permalink]
26 Mar 2018, 17:35
Moderators:
Bunuel
Math Expert
92900 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