It is currently 18 Nov 2017, 14:58

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

Events & Promotions in June
Open Detailed Calendar

What will be the remainder when 13^7+14^7+15^7+16^7 is div..

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

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 28 Jan 2011
Posts: 22

Kudos [?]: 17 [1], given: 15

What will be the remainder when 13^7+14^7+15^7+16^7 is div.. [#permalink]

Show Tags

New post 06 Sep 2013, 13:10
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (00:41) correct 44% (01:39) wrong based on 41 sessions

HideShow timer Statistics

What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided by 58?

a) 57
b) 1
c) 30
d) 0
e) 28


[Reveal] Spoiler:
Not quite sure how to go about this problem - does the fact that 13 + 14 + 15 + 16 add up to 58 have anything to do with the solution?
[Reveal] Spoiler: OA

Kudos [?]: 17 [1], given: 15

Manager
Manager
avatar
Joined: 04 Apr 2013
Posts: 149

Kudos [?]: 58 [0], given: 36

Re: What will be the remainder when 13^7+14^7+15^7+16^7 is div.. [#permalink]

Show Tags

New post 06 Sep 2013, 17:25
salsal wrote:
What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided by 58?

a) 57
b) 1
c) 30
d) 0
e) 28


[Reveal] Spoiler:
Not quite sure how to go about this problem - does the fact that 13 + 14 + 15 + 16 add up to 58 have anything to do with the solution?


salsal,

probably this is not the appropriate way (though correct) to solve this problem, but it helped me to solve this under 20 sec :)


a^n + b^n + c^n will always be divisible by a+b+c is n is odd. ex:- a^3 + b^3 = (a + b) (a^2 + b^2 - ab)

a^n - b^n will be divisible by a+b if n is even. ex: - a^2 - b^2 = (a-b)(a+b)

Experts might provide you with a better way to solve this problem.
_________________

Maadhu

MGMAT1 - 540 ( Trying to improve )

Kudos [?]: 58 [0], given: 36

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 740 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: What will be the remainder when 13^7+14^7+15^7+16^7 is div.. [#permalink]

Show Tags

New post 02 Dec 2013, 08:59
salsal wrote:
What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided by 58?

a) 57
b) 1
c) 30
d) 0
e) 28


[Reveal] Spoiler:
Not quite sure how to go about this problem - does the fact that 13 + 14 + 15 + 16 add up to 58 have anything to do with the solution?


a^n - b^n is always divisible by a-b
a^n-b^n is always divisible by a+b whenever 'n' is even
a^n + b^n is always divisible by a+b whenever 'n' is odd and not divisible by a+b if 'n' is even

Therefore D is the correct answer
Hope this helps
Cheers
J

Last edited by jlgdr on 17 Feb 2014, 07:36, edited 1 time in total.

Kudos [?]: 740 [0], given: 355

Manager
Manager
avatar
Joined: 04 Sep 2012
Posts: 139

Kudos [?]: 42 [0], given: 17

Location: United States
GMAT 1: 760 Q50 V42
GPA: 3.3
Re: What will be the remainder when 13^7+14^7+15^7+16^7 is div.. [#permalink]

Show Tags

New post 02 Dec 2013, 10:38
Tough problem.

If you're unable to determine that the sum of the exponent bases is a factor (ie, a+b+c+d is a factor), you can at least bring the odds to your favor.

The equation can also be expressed as odd + even + odd + even = even, so we know that the remainder should be even. This eliminates two of the choices, and gives you much better odds.

Kudos [?]: 42 [0], given: 17

Re: What will be the remainder when 13^7+14^7+15^7+16^7 is div..   [#permalink] 02 Dec 2013, 10:38
Display posts from previous: Sort by

What will be the remainder when 13^7+14^7+15^7+16^7 is div..

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


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