Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Oct 2014, 18:18

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If N is a natural integer, what is the remainder when 2 +

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 01 Nov 2007
Posts: 146
Followers: 1

Kudos [?]: 210 [0], given: 0

If N is a natural integer, what is the remainder when 2 + [#permalink] New post 16 Apr 2008, 08:51
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If N is a natural integer, what is the remainder when 2 + 2^(8N+3) is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3571
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 367

Kudos [?]: 1847 [1] , given: 358

GMAT ToolKit User Premium Member
Re: PS Integers [#permalink] New post 16 Apr 2008, 09:32
1
This post received
KUDOS
Expert's post
Actually, we should find an unit digit of the expression.

Consider some powers of 2:

2^0: 1
2^1: 2
2^2: 4
2^3: 8
2^4: 16
2^5: 32
2^6: 64
2^7: 128
2^0: 256
2^0: 512

So, 2^x has a period of 4.

unit digit of 2^(8N+3) = unit digit of 2^(8*0+3) = unit digit of 2^3 = 8

unit digit of (2 + 8) = 0

Therefore, reminder is 0.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Intern
Intern
avatar
Joined: 14 Feb 2007
Posts: 24
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: PS Integers [#permalink] New post 16 Apr 2008, 12:38
Factor out 2:

[2 (1 + 1^(8N+3))] / [5]

1 raised to any power is 1...therefore [2 (1+1)] / [5] = 4/5
Remainder when 4 is divided by 5 is 0. A
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 6

Kudos [?]: 108 [0], given: 0

Re: PS Integers [#permalink] New post 16 Apr 2008, 18:13
JCLEONES wrote:
If N is a natural integer, what is the remainder when 2 + 2^(8N+3) is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4


A

Pick N=1
So you have 2 + 2^11
Knowing that 2^5 has digit of 2, the digit of 2^11 = 8
2+8 = 10
10/5 has remainder=0
CEO
CEO
User avatar
Joined: 17 May 2007
Posts: 2995
Followers: 57

Kudos [?]: 442 [0], given: 210

Re: PS Integers [#permalink] New post 16 Apr 2008, 22:36
You're kidding right ?

Are you sure you can factor out 2 like that ? Also when 4 is divided by 5 , remainder is 4 not zero.

tikpaklong wrote:
Factor out 2:

[2 (1 + 1^(8N+3))] / [5]

1 raised to any power is 1...therefore [2 (1+1)] / [5] = 4/5
Remainder when 4 is divided by 5 is 0. A
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

Re: PS Integers [#permalink] New post 17 Apr 2008, 09:03
bsd*,
Seems like 0 is not natural integer.
Natural integers are 1,2,3.......

Check this one out...
http://physicsmathforums.com/showthread.php?t=100

Have exam in 2 weeks...wonder what else I dont know :evil:
Director
Director
User avatar
Joined: 14 Oct 2007
Posts: 759
Location: Oxford
Schools: Oxford'10
Followers: 13

Kudos [?]: 178 [0], given: 8

Re: PS Integers [#permalink] New post 20 Apr 2008, 09:04
since all the Answer choices are constants , we know that the remainder will be constant for ANY value of N.

so just put N = 1
2+2^11 = 2050 which means that units digit is 0 and therefore remainder has to be 0
CEO
CEO
User avatar
Joined: 17 May 2007
Posts: 2995
Followers: 57

Kudos [?]: 442 [0], given: 210

Re: PS Integers [#permalink] New post 20 Apr 2008, 18:09
Dont worry kyatin - if they ask about natural integer's you'll know that you're looking at 48+ in quant :)
kyatin wrote:
bsd*,
Seems like 0 is not natural integer.
Natural integers are 1,2,3.......

Check this one out...
http://physicsmathforums.com/showthread.php?t=100

Have exam in 2 weeks...wonder what else I dont know :evil:
Re: PS Integers   [#permalink] 20 Apr 2008, 18:09
    Similar topics Author Replies Last post
Similar
Topics:
3 If n is an integer, what is the remainder when (n 3)^2 is PTK 4 31 Mar 2011, 05:40
3 If n is an integer, what is the remainder when n is divided vcbabu 22 31 May 2009, 09:07
1 n is a positive integer. What is the remainder when n is andrehaui 7 09 Apr 2007, 10:59
What is integer n? 1. When divided by 7, remainder is 3 2. alimad 4 27 Sep 2006, 12:35
What is integer n? 1. When divided by 7, remainder is 3 2. vivek123 13 02 Apr 2006, 09:55
Display posts from previous: Sort by

If N is a natural integer, what is the remainder when 2 +

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.