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

 It is currently 20 Oct 2019, 22:04

### 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

# If n is a positive integer, what is the remainder when 3^n is divided

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58443
If n is a positive integer, what is the remainder when 3^n is divided  [#permalink]

### Show Tags

21 Aug 2017, 06:15
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:10) correct 24% (01:27) wrong based on 133 sessions

### HideShow timer Statistics

If n is a positive integer, what is the remainder when 3^n is divided by 10?

(1) n is a multiple of 8
(2) n is a multiple of 12

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
If n is a positive integer, what is the remainder when 3^n is divided  [#permalink]

### Show Tags

21 Aug 2017, 07:42
1
3^1(3) divided by 10 gives us a remainder of 3
3^2(9) divided by 10 gives us a remainder of 9
3^3(27) divided by 10 gives us a remainder of 7
3^4(81) divided by 10 gives us a remainder of 1
3^5(243) divided by 10 gives us a remainder of 3
3^6(729) divided by 10 gives us a remainder of 9
If you look there is a pattern of remainders for the different numbers 3,9,7,1,3,9.....

1. n is a multiple of 8
n can be 8,16,24.... and so on
The remainder will be the same when 3^n is divided by 10 if the values of n are evenly spaced.
Hence, this statement alone is sufficient

2. n is a multiple of 12
n can be 12,24,36.... and so on
The remainder will be the same when 3^n is divided by 10 if the values of n are evenly spaced.
Hence, this statement alone is sufficient(Option D)
_________________
You've got what it takes, but it will take everything you've got
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
If n is a positive integer, what is the remainder when 3^n is divided  [#permalink]

### Show Tags

21 Aug 2017, 08:16
2
Bunuel wrote:
If n is a positive integer, what is the remainder when 3^n is divided by 10?

(1) n is a multiple of 8
(2) n is a multiple of 12

The question asks what is the value, so we need to know whether a definite value is possible here.

The remainder when any number is divided by 10 will be its Units Digit. So we need to find the unit's digit of integer $$3^n$$

Statement 1: Let $$n = 8k$$. so $$3^n = 3^{8k} = (3^4)^{2k}$$
$$3^4 = 81$$, so units digit will $$1$$ and $$1$$ raised to any power will be $$1$$. So the unit's digit of $$3^n$$ will $$1$$, hence the remainder when divided by $$10$$ will be $$1$$. Sufficient

Statement : Let $$n = 12q$$. so $$3^n = 3^{12q} = (3^4)^{3q}$$
$$3^4 = 81$$, so units digit will $$1$$ and $$1$$ raised to any power will be $$1$$. So the unit's digit of $$3^n$$ will $$1$$, hence the remainder when divided by $$10$$ will be $$1$$. Sufficient

Option $$D$$
Non-Human User
Joined: 09 Sep 2013
Posts: 13320
Re: If n is a positive integer, what is the remainder when 3^n is divided  [#permalink]

### Show Tags

18 Oct 2018, 09:38
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.
_________________
Re: If n is a positive integer, what is the remainder when 3^n is divided   [#permalink] 18 Oct 2018, 09:38
Display posts from previous: Sort by