It is currently 20 Apr 2018, 22:47

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

If n is a positive integer, what is the remainder when 2n is divided

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44588
If n is a positive integer, what is the remainder when 2n is divided [#permalink]

Show Tags

New post 28 Jul 2017, 01:41
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (01:48) correct 44% (01:33) wrong based on 73 sessions

HideShow timer Statistics

If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
avatar
P
Joined: 14 Oct 2015
Posts: 239
GPA: 3.57
Reviews Badge
Re: If n is a positive integer, what is the remainder when 2n is divided [#permalink]

Show Tags

New post 28 Jul 2017, 02:10
1
This post received
KUDOS
Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


It should be E

Statement 1: Insufficient

\(n = 6q + 5\)

This set has values \(5, 11, 17, 23\)... These have remainder of \(5, 3, 1, 7\) respectively when divided by 8. If we multiply them by \(2\), we get \(10,22,34,46,\) remainder when divided by 8 is 2,6,2,6 so not a singular value.

Statement 2: Insufficient

3n = 6r + 3

This set has values \(3, 9, 15, 21, 27\) and so on. Since this is \(3n\), n would be \(1,3,5,7,9,11,13,15,17\) and so on. \(2n\) would be \(2,6,10,14,18,22\) and so on. Remainder when \(2n\) is divided by \(9\) is, \(2, 6, 2, 6\).

Statement 1+2:

In both set of values of n from statements 1 and 2, we see \(5,11,17,23\) as common. \(2n\) would be \(10,22,34\) and \(46\). However remainder when divided by 8 is again not a singular value.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 631
GMAT ToolKit User Premium Member Reviews Badge
Re: If n is a positive integer, what is the remainder when 2n is divided [#permalink]

Show Tags

New post 28 Jul 2017, 02:18
Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


2n = 8x + r ..r?

(1) n can take 5, 11, 17, 23, 29.....
2n becomes 10, 22, 34, 46, 58
when divided by 8 r is 2, 6, 2, 6, 2

Not sufficient

(2) 3n takes 3, 9, 15, 21, 27, 33, 39, 45
n becomes 1, 3, 5, 7, 9, 11, 13, 15
2n becomes 2, 6, 10, 14, 18, 22, 26, 30
when divided by 8 r is 2, 6, 2, 6, 2, 6, 2
Not sufficient

On combining also we have two value of r (2 and 6)

Not Sufficient
E
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)
Re: If n is a positive integer, what is the remainder when 2n is divided [#permalink]

Show Tags

New post 15 Dec 2017, 11:55
Bunuel wrote:
If n is a positive integer, what is the remainder when 2n is divided by 8?

(1) n, when divided by 6, leaves remainder 5.
(2) 3n, when divided by 6, leaves remainder 3.


We need to determine the remainder when 2n is divided by 8.

Statement One Alone:

n, when divided by 6, leaves remainder 5.

Thus, we see n can be a number such as 5, 11, 16, 21, 26, 31, 35, etc.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

3n, when divided by 6, leaves remainder 3.

Thus, we see that 3n can be a number such as 3, 9, 15, 21, 28, etc.

When 3n is 3, n is 1; when 3n is 9, n is 3; when 3n is 15, n is 5; etc.

In other words n will always be an odd number: 1, 3, 5, 7, ...

When 2(1) = 2 is divided by 8, the remainder is 2.

When 2(3) = 6 is divided by 8, the remainder is 6.

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using our two statements, we see the first value for n that satisfies both statements is 5. We also see that in statement two, n can be any odd number. So, another number that would match is n = 11.

When 2(5) = 10 is divided by 8, the remainder is 2.

When 2(11) = 22 is divided by 8, the remainder is 6.

We see that the statements together are still not sufficient to answer the question.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: If n is a positive integer, what is the remainder when 2n is divided   [#permalink] 15 Dec 2017, 11:55
Display posts from previous: Sort by

If n is a positive integer, what is the remainder when 2n is divided

  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®.