It is currently 19 Sep 2017, 06:51

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 is the remainder ?

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 23 Sep 2008
Posts: 8

Kudos [?]: 6 [0], given: 1

what is the remainder ? [#permalink]

Show Tags

New post 23 Apr 2009, 09:57
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Could someone pls elaborate whats the approach for these questions ??

Kudos [?]: 6 [0], given: 1

Manager
Manager
User avatar
Joined: 15 Dec 2008
Posts: 52

Kudos [?]: 114 [0], given: 1

Schools: HBS(08) - Ding. HBS, Stanford, Kellogg, Tuck, Stern, all dings. Yale - Withdrew App. Emory Executive -- Accepted, Matriculated, Withdrewed (yes, I spelled it wrong on purpose). ROSS -- GO BLUE 2011.
Re: what is the remainder ? [#permalink]

Show Tags

New post 23 Apr 2009, 12:19
mavesum 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

Could someone pls elaborate whats the approach for these questions ??



13+14+15+16=58

the whole mess (13^7+....) will be divisable by 58, since all of them have the same exponent.

1^x + 2^x will always be divisible by 3 for interger x>0

same thing for any combination of foolishness they give you.


remainder is 0.

Kudos [?]: 114 [0], given: 1

Expert Post
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1341

Kudos [?]: 1907 [0], given: 6

Re: what is the remainder ? [#permalink]

Show Tags

New post 23 Apr 2009, 17:50
RahlowJenkins wrote:
1^x + 2^x will always be divisible by 3 for interger x>0


No, that's not true - 1^2 + 2^2 is not divisible by 3, for example. What you're saying is true when x is odd, and not true when x is even.

I responded to the question in the original post on BTG by rearranging terms and factoring, but I can give a different solution here, using mathematics you definitely don't need to know for the test. But since modular arithmetic will be familiar to some people here, I'll use it on the above question.

Here the \(\equiv\) symbol means "has the same remainder as" and "mod 29" means "when dividing by 29". Modular arithmetic establishes that, if you're interested in finding the remainder of a sum, product, or difference, you can replace one number in that sum, product or difference with any other number that gives the same remainder).

\(13^7 + 14^7 + 15^7 + 16^7 \equiv 13^7 + 14^7 + (-14)^7 + (-13)^7 \equiv 0 \text{ mod 29}\)

So the sum is divisible by 29. Since it's even, it must also be divisible by 58.

Here I'm using the fact that 15 and -14 both have the same remainder when divided by 29, since they're both 15 more than a multiple of 29 (-14 = -29 + 15). Similarly, 16 and -13 have the same remainder when divided by 29.

You certainly don't ever need modular arithmetic on the GMAT, however, and the above question is not a realistic test question.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1907 [0], given: 6

Intern
Intern
avatar
Joined: 24 Mar 2009
Posts: 6

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

Re: what is the remainder ? [#permalink]

Show Tags

New post 23 Apr 2009, 22:23
I cannot agree that this is unrealistic question, 2 days ago I took my GMAT and I encountered with very similar problem, to which I still do not know a quick solution, it was something like this:

2+2^1+2+^2+2^3+2^4+2^5+2^6 =?

Aswers were all in similar form (but I dont remembe the precicely):

2^11
2^15
2^7
or something like that.

Can anyone help?

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

Expert Post
GMAT Tutor
avatar
B
Joined: 24 Jun 2008
Posts: 1341

Kudos [?]: 1907 [0], given: 6

Re: what is the remainder ? [#permalink]

Show Tags

New post 24 Apr 2009, 03:31
yns, those are very different questions, and the mathematics needed to solve them is entirely separate. If you're referring to a question you saw on a real GMAT, you should not be posting it here. There is, however, a GMATPrep question that asks:

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

If you notice that 2 + 2 = 2^2, and 2^2 + 2^2 = 2^3, etc, you can see that

2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ... = 2^9
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1907 [0], given: 6

Senior Manager
Senior Manager
User avatar
Joined: 05 Apr 2007
Posts: 255

Kudos [?]: 92 [0], given: 1

Re: what is the remainder ? [#permalink]

Show Tags

New post 24 Apr 2009, 12:32
Adding all the numbers, the result is 7 * 58. So the remainder, on dividing by 58 will be O.
_________________

Choose Life

Kudos [?]: 92 [0], given: 1

Re: what is the remainder ?   [#permalink] 24 Apr 2009, 12:32
Display posts from previous: Sort by

what is the remainder ?

  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®.