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

 It is currently 21 Feb 2019, 16:06

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53063
If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

### Show Tags

28 Jul 2017, 00:41
00:00

Difficulty:

75% (hard)

Question Stats:

62% (02:48) correct 38% (02:29) wrong based on 83 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.

_________________
Manager
Joined: 14 Oct 2015
Posts: 249
GPA: 3.57
Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

### Show Tags

28 Jul 2017, 01:10
1
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!

Current Student
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

### Show Tags

28 Jul 2017, 01:18
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

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4944
Location: United States (CA)
Re: If n is a positive integer, what is the remainder when 2n is divided  [#permalink]

### Show Tags

15 Dec 2017, 10:55
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.

_________________

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, 10:55
Display posts from previous: Sort by