NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 17:24 It is currently 24 Apr 2024, 17:24
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

15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))=

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
pmklings
Intern
Intern
Joined: 20 May 2014
Posts: 11
Own Kudos [?]: 187 [20]
Given Kudos: 0
Send PM
Reviews Badge
15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   Updated on: 31 May 2017, 20:51
2
Kudos
16
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

75% (01:49) correct 25% (02:28) wrong based on 342 sessions
Hide Show timer Statistics
\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\)

A. 2^7

B. 2^8

C. 2^9

D. 15(2^7)

E. 15 (2^8)
ShowHide Answer
Official Answer
B

Originally posted by pmklings on 18 Sep 2015, 19:33.
Last edited by Bunuel on 31 May 2017, 20:51, edited 1 time in total.
Renamed the topic and edited the question.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618815 [4]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   31 May 2017, 21:06
3
Kudos
1
Bookmarks
Expert Reply
Kp19 wrote:
How did you get (15/8) in the last step? Until that step everything else looks straighforward, I am sure I am missing some silly small step.


Formatted and added few more steps.

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\)

A. 2^7

B. 2^8

C. 2^9

D. 15(2^7)

E. 15 (2^8)

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\frac{15}{2^{-5}+2^{-6}+2^{-7}+2^{-8}}=\)

Factor out 2^(-5) from the denominator:

\(=\frac{15}{2^{-5}(1+2^{-1}+2^{-2}+4^{-3})}=\frac{15*2^5}{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=\frac{15*2^5}{\frac{8}{8}+\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}=\frac{15*2^5}{\frac{15}{8}}=15*2^5*\frac{8}{15}=2^8\).

Answer: B.

Hope it's clear.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618815 [1]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   01 Jun 2017, 07:25
1
Kudos
Expert Reply
csaluja wrote:
Bunuel wrote:
Kp19 wrote:
How did you get (15/8) in the last step? Until that step everything else looks straighforward, I am sure I am missing some silly small step.


Formatted and added few more steps.

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\)

A. 2^7

B. 2^8

C. 2^9

D. 15(2^7)

E. 15 (2^8)

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\frac{15}{2^{-5}+2^{-6}+2^{-7}+2^{-8}}=\)

Factor out 2^(-5) from the denominator:

\(=\frac{15}{2^{-5}(1+2^{-1}+2^{-2}+4^{-3})}=\frac{15*2^5}{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=\frac{15*2^5}{\frac{8}{8}+\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}=\frac{15*2^5}{\frac{15}{8}}=15*2^5*\frac{8}{15}=2^8\).

Answer: B.

Hope it's clear.


Hi Bunuel,

I have a question. I flipped the original equation and made it (2^5+2^6+2^7+2^8)/15 and got 2^5 as my final answer. Could you please help me what exactly I did wrong? Are we not allowed to take reciprocals here at the beginning?


No, this is wrong. \(\frac{1}{2^{-1}+2^{-2}}=\frac{4}{3}\) but \(2^{1}+2^{2}=6\).
User avatar
B
utkarshthapak
Manager
Manager
Joined: 09 Dec 2015
Posts: 96
Own Kudos [?]: 49 [1]
Given Kudos: 48
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36
GPA: 3.5
WE:Engineering (Consumer Products)
Send PM
Reviews Badge
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   05 Jun 2017, 03:19
1
Kudos
Easiest way as per me, change 2^-5 to 1/2^5 which is 1/32, do the same to other terms as we so we'll get,

15/ (1/32+1/64+1/128+1/256) = 15/ [(8+4+2+1)/256] = 15/15/256 = 256 = 2^8.

Took only 48 sec to get the answer by this method. Option B is correct.

Kudos if you like my method. Thanks :)
avatar
B
OptimusPrepJanielle
SVP
SVP
Joined: 06 Nov 2014
Posts: 1798
Own Kudos [?]: 1367 [0]
Given Kudos: 23
Send PM
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   18 Sep 2015, 20:38
Expert Reply
I think you are asking the value of

\(15/(2^{-5}+2^{-6}+2^{-7}+4^{-4})\)

We can write it as

\(15 / (2^{-5}+2^{-6}+2^{-7}+2^{-8})\) = \(15/ 2^-{5}*(1 + 2^{-1} + 2^{-2} + 2^{-3})\) = \(15*2^5 /(15/8)\)
On simplification, we get \(2^5*2^3\)

Hence the answer\(2^8\)

Please make sure that you type the question properly.
avatar
pmklings
Intern
Intern
Joined: 20 May 2014
Posts: 11
Own Kudos [?]: 187 [0]
Given Kudos: 0
Send PM
Reviews Badge
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   18 Sep 2015, 21:09
you said there was a problem with the way i wrote the question. i am trying to see how it is wrong.
avatar
Kp19
Intern
Intern
Joined: 31 May 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   31 May 2017, 20:46
How did you get (15/8) in the last step? Until that step everything else looks straighforward, I am sure I am missing some silly small step.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618815 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   31 May 2017, 20:54
Expert Reply
pmklings wrote:
you said there was a problem with the way i wrote the question. i am trying to see how it is wrong.


You wrote like this 15/(2^-5+2^-6+2^-7+4^-4)=, which mathematically is wrong. The correct way is as follows: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))=


Edited.
User avatar
P
JS1290
Manager
Manager
Joined: 27 Dec 2016
Posts: 241
Own Kudos [?]: 238 [0]
Given Kudos: 1103
Send PM
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   01 Jun 2017, 07:17
Bunuel wrote:
Kp19 wrote:
How did you get (15/8) in the last step? Until that step everything else looks straighforward, I am sure I am missing some silly small step.


Formatted and added few more steps.

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\)

A. 2^7

B. 2^8

C. 2^9

D. 15(2^7)

E. 15 (2^8)

\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\frac{15}{2^{-5}+2^{-6}+2^{-7}+2^{-8}}=\)

Factor out 2^(-5) from the denominator:

\(=\frac{15}{2^{-5}(1+2^{-1}+2^{-2}+4^{-3})}=\frac{15*2^5}{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=\frac{15*2^5}{\frac{8}{8}+\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}=\frac{15*2^5}{\frac{15}{8}}=15*2^5*\frac{8}{15}=2^8\).

Answer: B.

Hope it's clear.


Hi Bunuel,

I have a question. I flipped the original equation and made it (2^5+2^6+2^7+2^8)/15 and got 2^5 as my final answer. Could you please help me what exactly I did wrong? Are we not allowed to take reciprocals here at the beginning?
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: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   06 Jun 2017, 16:41
Expert Reply
pmklings wrote:
\(\frac{15}{2^{-5}+2^{-6}+2^{-7}+4^{-4}}=\)

A. 2^7

B. 2^8

C. 2^9

D. 15(2^7)

E. 15 (2^8)


Let’s first simplify the denominator of the fraction:

2^-5 + 2^-6 + 2^-7 + 4^-4

1/2^5 + 1/2^6 + 1/2^7 + 1/4^4

1/32 + 1/64 + 1/128 + 1/256

8/256 + 4/256 + 2/256 + 1/256 = 15/256

So, we have:

15/(15/256) = 256 = 2^8.

Alternative Solution:

Let’s multiply the numerator and the denominator of the fraction by 2^8:

(2^8 * 15)/(2^8 * (2^-5 + 2^-6 + 2^-7 + 2^-8)

(2^8 * 15)/(2^3 + 2^2 + 2^1 + 2^0)

(2^8 * 15)/(8 + 4 + 2 + 1)

(2^8 * 15)/15 = 2^8

Answer: B
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32655
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink] New post   07 Apr 2024, 02:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: 15/(2^(-5)+2^(-6)+2^(-7)+4^(-4))= [#permalink]
07 Apr 2024, 02:08
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