NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 14:10 It is currently 23 Apr 2024, 14:10
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

1/2^10 + 1/2^11 + 1/2^12 + 1/2^12

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618584 [27]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   22 May 2020, 08:46
1
Kudos
25
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:17) correct 18% (01:31) wrong based on 468 sessions
Hide Show timer Statistics
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)


A. \(\frac{1}{2^7}\)

B. \(\frac{1}{2^8}\)

C. \(\frac{1}{2^9}\)

D. \(\frac{1}{2^{13}}\)

E. \(\frac{1}{2^{45}}\)


PS21160
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29893 [7]
Given Kudos: 799
Location: Canada
Send PM
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   22 May 2020, 08:56
4
Kudos
3
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)


A. \(\frac{1}{2^7}\)

B. \(\frac{1}{2^8}\)

C. \(\frac{1}{2^9}\)

D. \(\frac{1}{2^{13}}\)

E. \(\frac{1}{2^{45}}\)


21160


Key property: \(\frac{1}{x^n} = x^{-n}\)
For example, \(\frac{1}{5^8} = 5^{-8}\)


So, we can rewrite our sum as follows: \(2^{-10} + 2^{-11} + 2^{-12} + 2^{-12}\)

Factor out \(2^{-12}\) to get: \(2^{-12}(2^2 + 2^1 + 1 + 1)\)

Evaluate to get: \(2^{-12}(4 + 2 + 1 + 1)\)

Simplify: \(2^{-12}(8)\)

Rewrite as follows: \((2^{-12})(2^3)\)

Apply the product law to get: \(2^{-9}\)

Rewrite as: \(\frac{1}{2^{9}}\)

Answer: C

Cheers,
Brent
General Discussion
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [0]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   22 May 2020, 08:51
=> (1/2^10)+(1/2^11)+(1/2^12)+(1/2^12)
Using LCM
=> (1*4/2^10*4)+(1*2/2^11*2)+(1/2^12)+(1/2^12)
=> (4/2^12)+(2/2^12)+(1/2^12)+(1/2^12)
=> (4+2+1+1)/(2^12)
=> 8/2^12
=> 2^3/2^12
=> 1/2^9

Answer is C

Posted from my mobile device
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13376 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge CAT Tests Forum Quiz Mode
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   22 May 2020, 08:52
Expert Reply
Bunuel wrote:
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)


A. \(\frac{1}{2^7}\)

B. \(\frac{1}{2^8}\)

C. \(\frac{1}{2^9}\)

D. \(\frac{1}{2^{13}}\)

E. \(\frac{1}{2^{45}}\)


21160


\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}} = \frac{1}{2^{10}}*[1+1/2 + 1/4 + 1/8]\)

i.e. \(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}} = \frac{1}{2^{10}}*[15/8] ≈ \frac{1}{2^{9}}\)
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Own Kudos [?]: 4095 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   22 May 2020, 09:19
1
Bookmarks
given
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)
can be written as
1/2^10 * ( 1+1/2+1/4+1/4 )
or say
1/2^10 * 8/4 ; 1/2^10 * 2 ;
1/2^9
OPTION C


Bunuel wrote:
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)


A. \(\frac{1}{2^7}\)

B. \(\frac{1}{2^8}\)

C. \(\frac{1}{2^9}\)

D. \(\frac{1}{2^{13}}\)

E. \(\frac{1}{2^{45}}\)


21160
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18753
Own Kudos [?]: 22041 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   25 May 2020, 12:05
Expert Reply
Bunuel wrote:
\(\frac{1}{2^{10}} + \frac{1}{2^{11}} + \frac{1}{2^{12}} + \frac{1}{2^{12}}\)


A. \(\frac{1}{2^7}\)

B. \(\frac{1}{2^8}\)

C. \(\frac{1}{2^9}\)

D. \(\frac{1}{2^{13}}\)

E. \(\frac{1}{2^{45}}\)




First, let’s obtain the common denominator of 2^12. We obtain:

(2^2/2^2)(1/2^10) + (2/2)1/2^11) + 1/2^12 + 1/2^12

2^2/2^12 + 2/2^12 + 1/2^12 + 1/2^12 = 8/2^12 = 2^3/2^12 = 1/2^9

Answer: C
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Own Kudos [?]: 7624 [0]
Given Kudos: 215
Location: India
Send PM
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   24 Aug 2021, 08:28
Top Contributor
Let try another approach:
The max value in the series is 1/2^10 and the rest of the terms are less than 1/2^10.

since there are 4 terms , we can say that SUM < 4 * 1/2^10
i.e. SUM < 1/2^8

The min value in the series is 1/2^12 and the rest of the terms are greater than 1/2^10.
SUM > 4 * 1/2^12
SUM > 1/2^10


We can conclude that 1/2^10 < SUM < 1/2^8

When we analyze the options, we can see that all options are in decreasing order and only 1/2^9 is in our range.

Option C is the right answer.

Thanks,
Clifin J Francis
GMAT SME
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32627
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink] New post   04 Dec 2023, 17:37
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: 1/2^10 + 1/2^11 + 1/2^12 + 1/2^12 [#permalink]
04 Dec 2023, 17:37
Moderators:
Bunuel
Math Expert
92883 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