GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Nov 2018, 18:34

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is

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

Hide Tags

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 21 Nov 2014, 00:42
4
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:01) correct 39% (02:07) wrong based on 157 sessions

HideShow timer Statistics

The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)

_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
User avatar
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 118
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
GMAT ToolKit User
The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post Updated on: 24 Nov 2014, 20:17
[quote="PareshGmat"]The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)[/quo

Originally posted by Ashishmathew01081987 on 21 Nov 2014, 06:52.
Last edited by Ashishmathew01081987 on 24 Nov 2014, 20:17, edited 1 time in total.
Manager
Manager
User avatar
Joined: 11 May 2013
Posts: 80
Concentration: Finance, Strategy
GMAT 1: 710 Q48 V39
GPA: 3.94
WE: Accounting (Accounting)
The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 21 Nov 2014, 08:22
Let's simplify both expressions first:

\((3^13+3^10)=3^13(3^3+1)=3^10*28=3^10*2*2*7\)
\((3^13-3^10)=3^13(3^3-1)=3^10*26=3^10*2*13\)

Clearly, the common factor is \(3^10*2\), but none of the answer choices matches it. So, we need to try to simplify the answer choices. Once we get to D, we get \(3^11-9^5=3^11-3^10=3^10(3-1)=3^10*2\)

Sorry for my formulas being off - new to this formatting thing.
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 276
Premium Member
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 21 Nov 2014, 11:56
2
Ashishmathew01081987 wrote:

\(3^{13} + 9^5 = 3^{13} + 3^{10} = 3^{23}\)
\(3^{13} - 9^5 = 3^{13} - 3^{10} = 3^3\)


hi this is incorrect

\(a^{b} . a^{c} = a^{b+c}\)

\(also,\) \(a^{b}. a^{-c} = a^{b-c}\)

PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)


\((3^{13} + 9^5)\) = \(3^{13} + 3^{10}\)
\(=3^{10} (3^{3} +1 )
=3^{10}28
= 2^{2}. 7 . 3^{10}\) -------------------------1)
\((3^{13} - 9^5)\) = \(3^{13} - 3^{10}\)
\(= 3^{10} (3^{3} - 1 )
=3^{10}26
=2 . 13 . 3^{10}\) -----------------------------2)

as can be seen the highest common factor of 1 and 2 is \(2 . 3^{10}\)

option D = \(3^{11} - 9^5\)
\(= 3^{11} - 3^{10}

=3^{10} (3-1)

= 2 . 3^{10}\)

hence answer is D
Manager
Manager
User avatar
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 118
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
GMAT ToolKit User
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 23 Nov 2014, 20:53
manpreetsingh86 wrote:
Ashishmathew01081987 wrote:

\(3^{13} + 9^5 = 3^{13} + 3^{10} = 3^{23}\)
\(3^{13} - 9^5 = 3^{13} - 3^{10} = 3^3\)


hi this is incorrect

\(a^{b} . a^{c} = a^{b+c}\)

\(also,\) \(a^{b}. a^{-c} = a^{b-c}\)

PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)


\((3^{13} + 9^5)\) = \(3^{13} + 3^{10}\)
\(=3^{10} (3^{3} +1 )
=3^{10}28
= 2^{2}. 7 . 3^{10}\) -------------------------1)
\((3^{13} - 9^5)\) = \(3^{13} - 3^{10}\)
\(= 3^{10} (3^{3} - 1 )
=3^{10}26
=2 . 13 . 3^{10}\) -----------------------------2)

as can be seen the highest common factor of 1 and 2 is \(2 . 3^{10}\)

option D = \(3^{11} - 9^5\)
\(= 3^{11} - 3^{10}

=3^{10} (3-1)

= 2 . 3^{10}\)

hence answer is D



Thanks for pointing out my mistake. That was a careless error :oops: +1 Kudos for identifying it :lol:
Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 109
GMAT ToolKit User
The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 25 Nov 2014, 10:51
PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)



It is D. Factor out 3^10 from both expressions and solve. one expression gives you 28, and the other gives you 26. GCD of these two is 2.
Therefore 3^10 *2.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7039
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 01 Apr 2016, 23:44
PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)


Hi,
Since we are to find HCF, we will have to simplify the terms..
\((3^{13} + 9^5)\) = \((3^{13} + 3^{10})\)
=>\(3^{10}*(3^3 + 1)\) =\(3^{10}*28\)


\((3^{13} - 9^5)\) = \((3^{13} - 3^{10})\)
=>\(3^{10}*(3^3 - 1)\) =\(3^{10}*26\)

so HCF = 3^{10}*2

Let see the choices..


A: \(3^{13}\)... Eliminate

B: \(3^{12} - 9^5\)..simplify

C: \(2*3^{12}\).. . Eliminate

D: \(3^{11} - 9^5\)..simplify

E: \(3^{11}\)... Eliminate

lets see B and D


B: \(3^{12} - 9^5\)

\((3^{13} - 9^5)\) = \((3^{12} - 3^{10})\)
=>\(3^{10}*(3^2 - 1)\) =\(3^{10}*8\).. eliminate

D.
\((3^{11} - 9^5)\) = \((3^{11} - 3^{10})\)
=>\(3^{10}*(3 - 1)\) =\(3^{10}*2\)

ans D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 632
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 18 Jul 2017, 23:54
PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)


\((3^{13} + 9^5)\)
= \((3^{13} + 3^{10})\)
= \(3^{10}(3^{3} + 1)\)
= \(3^{10}(3^{3} + 1)\)
= \(3^{10}(7*4)\)

\((3^{13} - 9^5)\)
= \((3^{13} - 3^{10})\)
= \(3^{10}(3^{3} - 1)\)
= \(3^{10}(3^{3} - 1)\)
= \(3^{10}(13*2)\)

Highest common factor = \(2*3^{10}\)


Here most difficult part s that the options are not clear and the highest common factor has been hidden in the complex form.
Lets now start analyzing the options.

OPTION A : \(3^{13}\)
OPTION B : \(3^{12} - 9^5\) = \(3^{10}(3^{2} - 1\) = \(8*3^{10}\)
OPTION C :\(2*3^{12}\)
OPTION D : \(3^{11} - 9^5\) = \(3^{10}(3 - 1)\) = \(2*3^{10}\)
OPTION E : \(3^{11}\)


Answer D

_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is  [#permalink]

Show Tags

New post 31 Oct 2018, 17:23
PareshGmat wrote:
The highest common factor of \((3^{13} + 9^5)\) and \((3^{13} - 9^5)\) is

A: \(3^{13}\)

B: \(3^{12} - 9^5\)

C: \(2*3^{12}\)

D: \(3^{11} - 9^5\)

E: \(3^{11}\)


Let’s first simplify each of the numbers whose GCF we wish to determine:

3^13 + 9^5 = 3^13 + 3^10 = 3^10(3^3 + 1) = 3^10 x 28 = 2^2 x 3^10 x 7^1

3^13 - 9^5 = 3^13 - 3^10 = 3^10(3^3 - 1) = 3^10 x 26 = 2^1 x 3^10 x 13^1

The GCF is 2^1 x 3^10. We can easily eliminate answer choices A, C, and E. Simplifying answer choice D, we have:

3^11 - 9^5 = 3^11 - 3^10 = 3^10(3 - 1) = 3^10 x 2^1

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

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

GMAT Club Bot
Re: The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is &nbs [#permalink] 31 Oct 2018, 17:23
Display posts from previous: Sort by

The highest common factor of (3^13 + 9^5) and (3^13 - 9^5) is

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.