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

It is currently 20 Aug 2018, 22:59

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

What is the largest prime factor of the expression 3^8 − 2^12?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48074
What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:24
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

44% (01:18) correct 56% (01:29) wrong based on 43 sessions

HideShow timer Statistics

Manager
Manager
avatar
B
Joined: 25 May 2016
Posts: 77
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30
Re: What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:30
If you see it, it is in the (a+b)(a-b) which is = (3^4+2^6)(3^4-2^6) = (81+64)(81-64) = (145)(17)
Therefore, highest prime factor is 17.
_________________

15 Kudos left to unlock next level. Help me by Contributing one for cause :) .. Please

Manick9

If you found my post helpful, kindly press "+1 Kudos" to appreciate

Senior Manager
Senior Manager
User avatar
G
Joined: 31 Oct 2013
Posts: 479
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:32
1
Bunuel wrote:
What is the largest prime factor of the expression \(3^8 − 2^{12}\)?

A. 2
B. 3
C. 5
D. 17
E. 29



Given

\(3^8 − 2^{12}\)

=\((3^4)^2 - (2^6)^2\)

=\(( 3^4 + 2^6) (3^4 - 2^6)\)

= (81 + 64) (81 - 64)

=\((145 ) ( 9^2 - 8^2)\)

= (5 * 29) ( 9 + 8) ( 9- 8)

= 5 * 29 * 17 * 1

The best answer is E.
Manager
Manager
User avatar
G
Joined: 18 Jun 2018
Posts: 110
Premium Member
Re: What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:33
Bunuel wrote:
What is the largest prime factor of the expression 3^8 − 2^12?

A. 2
B. 3
C. 5
D. 17
E. 29


OA:E
\(3^8 − 2^{12} =(3^4)^2 − (2^6)^2 =(3^4-2^6)(3^4+2^6)=(3^2-2^3)(3^2+2^3)(3^4+2^6)=(9-8)(9+8)(81+64)=1*17*145=1*17*5*29\)
Senior Manager
Senior Manager
User avatar
G
Joined: 31 Oct 2013
Posts: 479
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:33
Manick9 wrote:
If you see it, it is in the (a+b)(a-b) which is = (3^4+2^6)(3^4-2^6) = (81+64)(81-64) = (145)(17)
Therefore, highest prime factor is 17.



u can further break down 145

145 = 29 * 5

Hope it's clear.
Manager
Manager
avatar
B
Joined: 25 May 2016
Posts: 77
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 620 Q46 V30
Re: What is the largest prime factor of the expression 3^8 − 2^12?  [#permalink]

Show Tags

New post 10 Aug 2018, 03:59
selim wrote:
Manick9 wrote:
If you see it, it is in the (a+b)(a-b) which is = (3^4+2^6)(3^4-2^6) = (81+64)(81-64) = (145)(17)
Therefore, highest prime factor is 17.



u can further break down 145

145 = 29 * 5

Hope it's clear.


That's right. I missed the last option.
_________________

15 Kudos left to unlock next level. Help me by Contributing one for cause :) .. Please

Manick9

If you found my post helpful, kindly press "+1 Kudos" to appreciate

Re: What is the largest prime factor of the expression 3^8 − 2^12? &nbs [#permalink] 10 Aug 2018, 03:59
Display posts from previous: Sort by

What is the largest prime factor of the expression 3^8 − 2^12?

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

Events & Promotions

PREV
NEXT


cron

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®.