Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 15 Jul 2019, 23:49

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.

Close

Request Expert Reply

Confirm Cancel

10^k + 5^k =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56238
10^k + 5^k =  [#permalink]

Show Tags

New post 22 Mar 2018, 23:46
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (00:29) correct 24% (00:35) wrong based on 66 sessions

HideShow timer Statistics


Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
Re: 10^k + 5^k =  [#permalink]

Show Tags

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)
_________________
You've got what it takes, but it will take everything you've got
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1074
Re: 10^k + 5^k =  [#permalink]

Show Tags

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.
_________________
Director
Director
avatar
P
Joined: 21 May 2013
Posts: 655
Re: 10^k + 5^k =  [#permalink]

Show Tags

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
Manager
Manager
User avatar
B
Joined: 28 Jan 2018
Posts: 51
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
10^k + 5^k =  [#permalink]

Show Tags

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: \((a*b)^{m} = a^{m} * b^{m}\)

\(10^{k} + 5^{k} = 2^{k}*5^{k} + 5^{k} = 5^{k}*(2^{k} + 1) (B)\)
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: 10^k + 5^k =  [#permalink]

Show Tags

New post 26 Mar 2018, 17:35
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
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: 10^k + 5^k =   [#permalink] 26 Mar 2018, 17:35
Display posts from previous: Sort by

10^k + 5^k =

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne