It is currently 18 Oct 2017, 22:51

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Apr 2014
Posts: 129

Kudos [?]: 63 [0], given: 17

Location: India
Concentration: Strategy, Operations
GMAT 1: 730 Q50 V38
GMAT 2: 750 Q48 V45
GPA: 4
WE: Information Technology (Computer Software)
Re: If n is a positive integer, what is the remainder when [#permalink]

### Show Tags

30 May 2015, 20:57
by the method of exponents break the exp as (3^8n * 3^3) +2
now , we know cyclicity of 3 is 4 that means unit digit is 1 when 3^4 so,3^8n =1 (bcz 8n is divisible by 4)
=> exp becomes 27*3^8n + 2 => 27 *xxxx1 (since n can be any integer)+2 => xxx7+2=> xxx9 and now xxx9/5 leaves rem(5) .

_________________

way to victory .....

Kudos [?]: 63 [0], given: 17

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: If n is a positive integer, what is the remainder when [#permalink]

### Show Tags

04 Jul 2016, 08:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: If n is a positive integer, what is the remainder when [#permalink]

### Show Tags

03 Aug 2017, 10:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 831 [0], given: 5

Re: If n is a positive integer, what is the remainder when [#permalink]

### Show Tags

09 Aug 2017, 12:51
azule45 wrote:
If n is a positive integer, what is the remainder when 3^(8n+3) + 2 is divided by 5?

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

We need to determine the remainder of:

3^8n x 3^3 + 2 when it is divided by 5.

We only need to know the units digit of the above expression to determine the remainder.

Let’s look at the pattern of units digits of powers of 3. Note that we are only concerned with the units digits, so, for example, for 3^3, we concern ourselves only with the units digit of 27, which is 7. Here is the pattern:

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

The repeating pattern is 3-9-7-1. Since the units digit pattern for a base of 3 is 3-9-7-1, we see that whenever 3 is raised to an exponent that is a multiple of 4, the units digit will be 1. Thus:

3^8n x 3^3 = units digit of 1 x units digit of 7 = units digit of 7

So, units digit of 7 + 2 = units digit of 9, and thus 9/5 has a remainder of 4.

_________________

Jeffery Miller

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

Kudos [?]: 831 [0], given: 5

Re: If n is a positive integer, what is the remainder when   [#permalink] 09 Aug 2017, 12:51

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by