NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 13:24 It is currently 26 Apr 2024, 13:24
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

3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
Ekland
Senior Manager
Senior Manager
Joined: 15 Oct 2015
Posts: 375
Own Kudos [?]: 1551 [36]
Given Kudos: 342
Concentration: Finance, Strategy
Schools: Fordham '18 Schulich Jan '18 Desautels '19 Haskayne(Calgary) Alberta"19 Jindal '19 Owen '19 Olin '19 (I) Queens"18
GPA: 3.93
WE:Account Management (Education)
Send PM
GMAT ToolKit User
3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   Updated on: 15 Feb 2016, 07:22
3
Kudos
33
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

77% (02:41) correct 23% (02:39) wrong based on 457 sessions
Hide Show timer Statistics
\((\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})\) is how many times \(3^{-14}\) ?

A. 1/3
B. 21
C. 65/4
D. 24
E. 251/6
ShowHide Answer
Official Answer
C

Originally posted by Ekland on 15 Feb 2016, 07:02.
Last edited by Bunuel on 15 Feb 2016, 07:22, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [10]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   15 Feb 2016, 07:39
8
Kudos
2
Bookmarks
Expert Reply
Nez wrote:
\((\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})\) is how many times \(3^{-14}\) ?

A. 1/3
B. 21
C. 65/4
D. 24
E. 251/6


\(\frac{(\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})}{3^{-14}}=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{3}{6})=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{1}{2})=\)

\(=(\frac{2*3^{3}}{4}) + (\frac{3^{2}}{4}) + (\frac{2}{4})=\frac{65}{4}\)

Answer: C.
General Discussion
User avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2362
Own Kudos [?]: 3626 [4]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Send PM
GMAT ToolKit User Reviews Badge
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   15 Feb 2016, 07:35
1
Kudos
3
Bookmarks
Nez wrote:
\((\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})\) is how many times \(3^{-14}\) ?

A. 1/3
B. 21
C. 65/4
D. 24
E. 251/6



You are asked for the value of x such that \(x*3^{-14} = (\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})\)

In order to find x, lets focus on\((\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})= (\frac{2*3^{-10}+3^{-11}+2*3^{-13}}{12}) = \frac{3^{-14}*195}{12} = \frac{3^{-14}*65}{4}\)

Thus, \(x = \frac {65}{4}\)

C is thus the correct answer.

Hope this helps.
avatar
shukiPortal12
Intern
Intern
Joined: 21 Dec 2016
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   Updated on: 21 Dec 2016, 10:55
Can you please explain how did you get from (\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6}) to (\frac{2*3^{-10}+3^{-11}+2*3^{-13}}{12})

Originally posted by shukiPortal12 on 21 Dec 2016, 10:22.
Last edited by shukiPortal12 on 21 Dec 2016, 10:55, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   21 Dec 2016, 10:33
Expert Reply
shukiPortal12 wrote:
Can you please how did you get from (\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6}) to (\frac{2*3^{-10}+3^{-11}+2*3^{-13}}{12})


There are TWO steps between those two equations, which one is unclear?

\(\frac{(\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})}{3^{-14}}=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{3}{6})=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{1}{2})=\)

\(=(\frac{2*3^{3}}{4}) + (\frac{3^{2}}{4}) + (\frac{2}{4})=\frac{65}{4}\)


Also, please format properly so that it's clear what you mean: rules-for-posting-please-read-this-before-posting-133935.html#p1096628
avatar
shukiPortal12
Intern
Intern
Joined: 21 Dec 2016
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   21 Dec 2016, 11:00
from the 1st, (3−112)+(3−124)+(3−136)3−14=(3−112)+(3−124)+(3−136)3−14
to
(332)+(324)+(36)

I never get to understand whether there's a way to add distinct powers with distinct bases (such as 3^7 + 2^11)

Sorry about my English. It's not so good...
avatar
B
mcrimmin
Intern
Intern
Joined: 26 Oct 2016
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   21 Dec 2016, 15:30
Dumb question but how do we go from (3^-11)/2 to (3^3)/2? That's not totally clear to me.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619229 [3]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   22 Dec 2016, 02:05
2
Kudos
1
Bookmarks
Expert Reply
shukiPortal12 wrote:
from the 1st, (3−112)+(3−124)+(3−136)3−14=(3−112)+(3−124)+(3−136)3−14
to
(332)+(324)+(36)

I never get to understand whether there's a way to add distinct powers with distinct bases (such as 3^7 + 2^11)

Sorry about my English. It's not so good...


Added few more steps:

\(\frac{(\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})}{3^{-14}}=\)

\(=\frac{3^{-11}}{2*3^{-14}} + \frac{3^{-12}}{4*3^{-14}} + \frac{3^{-13}}{6*3^{-14}}=\)

\(=\frac{3^{-11-(-14)}}{2} + \frac{3^{-12-(-14)}}{4} + \frac{3^{-13-(-14)}}{6}=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{3}{6})=\)

\(=(\frac{3^{3}}{2}) + (\frac{3^{2}}{4}) + (\frac{1}{2})=\)

\(=(\frac{2*3^{3}}{4}) + (\frac{3^{2}}{4}) + (\frac{2}{4})=\frac{65}{4}\).

Hope it's clear.
avatar
shukiPortal12
Intern
Intern
Joined: 21 Dec 2016
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   22 Dec 2016, 07:28
Very clear. Thank you very much.
User avatar
S
Nunuboy1994
Director
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 118 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   12 Apr 2017, 19:52
1
Bookmarks
In order to solve this question we need to set up an algebraic expression:

3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6= x (3^-14)

Trick* if remember that any fraction divided by a number is that fraction multiplied by the reciprocal of that number ( e.x (1/2)/3=(1/2) * (1/3)) then we can rewrite the expression as so:

3^(-11)/2(3^-14) + 3^(-12)/4(3^-14) + 3^(-13)/6(3^-14)= x
3^3/2 + 3^2/2^2 + 3/6=
27/2 + 9/4 + 3/6 = 65/4
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 965
Own Kudos [?]: 223 [1]
Given Kudos: 434
Location: United States
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   22 Nov 2020, 12:01
1
Kudos
Ekland wrote:
\((\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})\) is how many times \(3^{-14}\) ?

A. 1/3
B. 21
C. 65/4
D. 24
E. 251/6


= \(\frac{(\frac{3^{-11}}{2}) + (\frac{3^{-12}}{4}) + (\frac{3^{-13}}{6})}{3^{-14}}=\)

= \(\frac{3^{11-(-14)}}{2} + \frac{3^{-12-(-14)}}{4} + \frac{3^{-12-(-14)}}{6}\)

= \(\frac{3^3}{2} + \frac{3^2}{4} + \frac{3}{6}\)

= \(\frac{65}{4}\)
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32689
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink] New post   18 Mar 2023, 09:22
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: 3^(-11)/2 + 3^(-12)/4 + 3^(-13)/6 is how many times 3^(-14) ? [#permalink]
18 Mar 2023, 09:22
Moderators:
Bunuel
Math Expert
92948 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