It is currently 22 Feb 2018, 16:45

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

2^1 + 2^2 + 2^3 + 2^4 + 2^5=

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43867
2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 05 Nov 2017, 01:42
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (01:06) correct 18% (00:57) wrong based on 135 sessions

HideShow timer Statistics

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2068
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 05 Nov 2017, 02:02
Bunuel wrote:
\(2^1 + 2^2 + 2^3 + 2^4 + 2^5=\)

(A) 2^14
(B) 2^15
(C) 2^9 + 2^5
(D) 2^7 – 2
(E) 2^6 – 2


\(2^1 + 2^2 + 2^3 + 2^4 + 2^5\) =\(2(1 + 2) + 2^3 + 2^4 + 2^5\) =\(2(3 + 2^2) + 2^4 + 2^5\) =\(2(7 + 2^3) + 2^5\)

=\(2(15) + 2^5\) =\(2(15 + 2^4)\) =\(2(31) = 62 = 2^6 - 2\) (Option E)
_________________

Stay hungry, Stay foolish

2017-2018 MBA Deadlines

Class of 2020: Rotman Thread | Schulich Thread
Class of 2019: Sauder Thread

Senior Manager
Senior Manager
avatar
S
Joined: 31 Jul 2017
Posts: 298
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 05 Nov 2017, 02:40
It's a GP series with r=2, a = 2.. Sum =a(r^n - 1)/r-1

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Intern
avatar
B
Joined: 07 Jul 2015
Posts: 48
Location: India
Concentration: Operations, General Management
GMAT 1: 660 Q47 V35
GMAT 2: 740 Q50 V40
GPA: 3.7
WE: Operations (Manufacturing)
Reviews Badge
Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 05 Nov 2017, 02:46
2+4+8+16+32=62

2^6-2=62

Ans:E
Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5660
2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 05 Nov 2017, 03:02
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
\(2^1 + 2^2 + 2^3 + 2^4 + 2^5=\)

(A) 2^14
(B) 2^15
(C) 2^9 + 2^5
(D) 2^7 – 2
(E) 2^6 – 2



HI...

a different way and a point to remember.....
\(2^1 + 2^2 + 2^3 .........+ 2^{n-1} + 2^n=2^{n+1}-2\)

and this is WHY?
\(2^1+2^1=2^2.......2^1=2^2-2^1\)....

substitute this value in equation below

\((2^1 )+ 2^2 + 2^3 .........+ 2^{n-1} + 2^n=(2^2-2^1) + 2^2 + 2^3 .........+ 2^{n-1} + 2^n\)..

\(2^2-2^1 + 2^2 + 2^3 .........+ 2^{n-1} + 2^n=2^2 + 2^2 + 2^3 .........+ 2^{n-1} + 2^n-2^1\).....

\(2* 2^2 + 2^3 .........+ 2^{n-1} + 2^n-2^1= 2^3 + 2^3 .........+ 2^{n-1} + 2^n-2^1=2*2^3 .........+ 2^{n-1} + 2^n-2^1\)

and so on till \(2* 2^{n-1} + 2^n-2^1=2^n+2^n-2=2^{n+1}-2\)

so \(2^1+2^2+2^3+2^4+2^5=2^{5+1}-2=2^6-2\)

E

Bunuel, may be the choices could be put in ascending or descending order. choice A and B could be interchanged
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Manager
Manager
User avatar
S
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 97
Schools: Rotman '21
WE: Marketing (Consulting)
Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 07 Nov 2017, 00:44
Bunuel wrote:
\(2^1 + 2^2 + 2^3 + 2^4 + 2^5=\)

(A) 2^14
(B) 2^15
(C) 2^9 + 2^5
(D) 2^7 – 2
(E) 2^6 – 2


\(2^1 + 2^2 + 2^3 + 2^4 + 2^5=
2(1+2+2^2+2^3+2^4)=
2(3+4+8+16)=
2(31)=62\)

\(16*4=2^4*2^2=2^6=64\)

Therefore, E is the correct answer \(2^6-2\)
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
YouTube sessions by GMATNinja: https://gmatclub.com/forum/verbal-live-with-gmat-ninja-sc-pronouns-that-parallelism-250568.html#p1936104
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2008
Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5= [#permalink]

Show Tags

New post 08 Nov 2017, 16:43
Bunuel wrote:
\(2^1 + 2^2 + 2^3 + 2^4 + 2^5=\)

(A) 2^14
(B) 2^15
(C) 2^9 + 2^5
(D) 2^7 – 2
(E) 2^6 – 2


We can evaluate the given equation:

2^1 + 2^2 + 2^3 + 2^4 + 2^5

2 + 4 + 8 + 16 + 32 = 62

We see that 62 = 64 - 2, which is 2^6 - 2.

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

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

Re: 2^1 + 2^2 + 2^3 + 2^4 + 2^5=   [#permalink] 08 Nov 2017, 16:43
Display posts from previous: Sort by

2^1 + 2^2 + 2^3 + 2^4 + 2^5=

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.