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

It is currently 08 Dec 2019, 01:49

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

If n and m are positive integers, what is the remainder when 3^(4n+2)

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 12 Jul 2006
Posts: 97
If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post Updated on: 05 Jun 2019, 03:15
1
28
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:23) correct 30% (01:40) wrong based on 489 sessions

HideShow timer Statistics

If n and m are positive integers, what is the remainder when \(3^{(4n+2)} + m\) is divided by 10?

(1) n = 2
(2) m = 1

Originally posted by wshaffer on 12 Nov 2006, 14:38.
Last edited by Bunuel on 05 Jun 2019, 03:15, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 18 Nov 2010, 07:58
14
1
14
Geronimo wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10 ?
(1) n=2
(2) m=1


When considering the remainder when a number is divided by 10, focus on the last digit of the number. That will be the remainder. e.g. 85/10, remainder 5. 39 divided by 10, remainder 9 etc...

The last digit of powers of 3 have a cyclicity of 4. Look at the example below:
3^1 = 3
3^2 = 9
3^ 3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
and so on.. notice the last digits 3, 9, 7, 1, 3, 9,....
thats the pattern they follow.
So 3^(4n + 2) will end with 9. (If you are not comfortable with cyclicity, check out its theory. You can also check out this post where I have discussed cyclicity of some other numbers in detail: http://gmatclub.com/forum/cyclicity-of-103262.html#p803511)


Now, we just need to know what m is. If m = 1, 3^(4n + 2) + m will end in 0. So remainder will be 0.
Answer (B).
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
General Discussion
CEO
CEO
avatar
Joined: 15 Dec 2003
Posts: 3352
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 12 Nov 2006, 15:17
1
3
Given that n and m are positive integers, knowing n is useless because the expression (4n+2) will always give an answer which is 4 units apart. What we need to know is what m is for it will determine the remainder of the expression when divided by 10.
Notice that for any exponent of 3, the unit digit is repeating in cycles of 4:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
____________________________
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6561
____________________________
Notice the cycle: 3-9-7-1
Hence, knowing that m is 1, we know that the whole expression (4n+2)+m will give an exponent of 7, 11, 15, etc.
This ensures that the remainder will ALWAYS be 7 and B is sufficient.

:btw do not provide the answer before it is answered, nobody may attempt it. Give it a maximum of 2 days and provide the answer thereafter.
Manager
Manager
avatar
Joined: 01 Feb 2010
Posts: 174
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 06 Apr 2010, 21:31
2
1
mads wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10?
1. n=2
2. m=1


1: not enough as we do not know what is m hence impossible to answer remainder.

2: 3 has a cylicity of 4 i.e
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
hence cyclicity of 4
for any +ve value of n (1,2,3,.....) the unit digit of 3^(4n+2) will be 9 hence adding m=1 into it will give unit digit as 0 which is divisible by 10 hence sufficient to answer.
Its B
Manager
Manager
avatar
Joined: 26 May 2005
Posts: 155
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 06 Apr 2010, 22:48
1
mads wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10?
1. n=2
2. m=1

st 1) n=2, dont know about m. Not sufficient
st 2) m=1

3^(4n+2) + m = 3^[2 * (2n+1)] + m = 9 ^(2n+1) + m
2n+1 is always odd . so the units digit of 9^(2n+1) is 9 and m is 1, so the remainder will be 0

B
Manager
Manager
User avatar
Joined: 07 Jan 2010
Posts: 103
Location: So. CA
WE 1: 2 IT
WE 2: 4 Software Analyst
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 20 Nov 2010, 19:38
VeritasPrepKarishma wrote:
Geronimo wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10 ?
(1) n=2
(2) m=1


When considering the remainder when a number is divided by 10, focus on the last digit of the number. That will be the remainder. e.g. 85/10, remainder 5. 39 divided by 10, remainder 9 etc...

The last digit of powers of 3 have a cyclicity of 4. Look at the example below:
3^1 = 3
3^2 = 9
3^ 3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
and so on.. notice the last digits 3, 9, 7, 1, 3, 9,....
thats the pattern they follow.
So 3^(4n + 2) will end with 9. (If you are not comfortable with cyclicity, check out its theory. You can also check out this post where I have discussed cyclicity of some other numbers in detail: http://gmatclub.com/forum/cyclicity-of-103262.html#p803511)


Now, we just need to know what m is. If m = 1, 3^(4n + 2) + m will end in 0. So remainder will be 0.
Answer (B).


if m=1 wouldn't it end in 7? I'm not sure how you got 0.
3^(4n + 2) + 1 = 3^(4n + 3) and based on the cyclicity pattern from above, it would be the next one over which will end in 7?

maybe i'm not understanding this correctly, please correct me. thanks!
Intern
Intern
avatar
B
Joined: 15 May 2015
Posts: 10
GPA: 3.5
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 28 Nov 2019, 11:11
VeritasKarishma wrote:
Geronimo wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10 ?
(1) n=2
(2) m=1


When considering the remainder when a number is divided by 10, focus on the last digit of the number. That will be the remainder. e.g. 85/10, remainder 5. 39 divided by 10, remainder 9 etc...

The last digit of powers of 3 have a cyclicity of 4. Look at the example below:
3^1 = 3
3^2 = 9
3^ 3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
and so on.. notice the last digits 3, 9, 7, 1, 3, 9,....
thats the pattern they follow.
So 3^(4n + 2) will end with 9. (If you are not comfortable with cyclicity, check out its theory. You can also check out this post where I have discussed cyclicity of some other numbers in detail: http://gmatclub.com/forum/cyclicity-of-103262.html#p803511)


Now, we just need to know what m is. If m = 1, 3^(4n + 2) + m will end in 0. So remainder will be 0.
Answer (B).


I have a tough time with this not being C. Hear me out:

We will not know what the exponent will be unless we know the value of N. Exponents change the value of the integer (obviously), and thus the final digit...

3
9
27
81
243

We will not know the remainder if we don't know what N is...

what am I missing
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 01 Dec 2019, 21:31
esonrev wrote:
VeritasKarishma wrote:
Geronimo wrote:
If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10 ?
(1) n=2
(2) m=1


When considering the remainder when a number is divided by 10, focus on the last digit of the number. That will be the remainder. e.g. 85/10, remainder 5. 39 divided by 10, remainder 9 etc...

The last digit of powers of 3 have a cyclicity of 4. Look at the example below:
3^1 = 3
3^2 = 9
3^ 3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
and so on.. notice the last digits 3, 9, 7, 1, 3, 9,....
thats the pattern they follow.
So 3^(4n + 2) will end with 9. (If you are not comfortable with cyclicity, check out its theory. You can also check out this post where I have discussed cyclicity of some other numbers in detail: http://gmatclub.com/forum/cyclicity-of-103262.html#p803511)


Now, we just need to know what m is. If m = 1, 3^(4n + 2) + m will end in 0. So remainder will be 0.
Answer (B).


I have a tough time with this not being C. Hear me out:

We will not know what the exponent will be unless we know the value of N. Exponents change the value of the integer (obviously), and thus the final digit...

3
9
27
81
243

We will not know the remainder if we don't know what N is...

what am I missing


The actual value of n is irrelevant.

Say n = 1
3^(4n + 2) = 3^6 - The units digit here will be 9

Say n = 2
3^(4n + 2) = 3^10 - The units digit here will be 9

Say n = 3
3^(4n + 2) = 3^14 - The units digit here will be 9

and so on...

The exponent of 3 will always be of the form 4n + 2. So it will start a new cycle and end at the second term. So the units digit will always be 9. Even without the actual value of n, you know what you need to know - the units digit of 3^(4n + 2) is 9.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
G
Joined: 28 Feb 2014
Posts: 205
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)
If n and m are positive integers, what is the remainder when 3^(4n+2)  [#permalink]

Show Tags

New post 01 Dec 2019, 22:20
wshaffer wrote:
If n and m are positive integers, what is the remainder when \(3^{(4n+2)} + m\) is divided by 10?

(1) n = 2
(2) m = 1

To find remainder when the expression is divided by 10, calculate the unit digit of the given expression
3^(4n+2) + m = 3^4n * 3^2 + m
Unit digit of 3^4n is 1
unit digit of 3^2 is 9
Require value of m to find unit digit of the expression

(1) Insufficient
(2) Sufficient

B is correct.
GMAT Club Bot
If n and m are positive integers, what is the remainder when 3^(4n+2)   [#permalink] 01 Dec 2019, 22:20
Display posts from previous: Sort by

If n and m are positive integers, what is the remainder when 3^(4n+2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne