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

It is currently 12 Dec 2018, 18:43

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

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

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

Hide Tags

Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 117
Reviews Badge
If n is a positive integer, what is the remainder when  [#permalink]

Show Tags

New post 23 Jun 2010, 11:35
2
10
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

80% (00:40) correct 20% (01:08) wrong based on 418 sessions

HideShow timer Statistics

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: PS Questions from SET 1-Need detail solution  [#permalink]

Show Tags

New post 23 Jun 2010, 13:40
1
1
udaymathapati wrote:
Some difficult PS Questions from SET1. Please help me with resolving them...OAs have mentioned at the end.

Q13:
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


3 in power has cyclicity of 4:
1. 3^1=3 (last digit is 3)
2. 3^2=9 (last digit is 9)
3. 3^3=27 (last digit is 7)
4. 3^4=81 (last digit is 1)

5. 3^5=243 (last digit is 3 again!)
...

To find the last digit of \(3^{8n+3}\), divide the power (which is \(8n+3\)) by cyclicity # ( which is \(4\)) and look at the remainder --> \(\frac{8n+3}{4}\) --> \(remainder=3\), which means that the last digit of \(3^{8n+3}\) will be the same as the last digit of \(3^3=27\) (last digit is 7). (Side note: If the remainder were 0, then last digit would be the same as the las digit of \(3^4\)).

Now, last digit of \(3^{8n+3}+2\) will be \(7+2=9\). Any integer with last digit 9 upon division by 5 yields remainder of 4.

Answer: E.

Hope it's clear.
_________________

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

Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 117
Reviews Badge
Re: PS Questions from SET 1-Need detail solution  [#permalink]

Show Tags

New post 23 Jun 2010, 20:35
Bunuel wrote:
udaymathapati wrote:
Some difficult PS Questions from SET1. Please help me with resolving them...OAs have mentioned at the end.

Q13:
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


3 in power has cyclicity of 4:
1. 3^1=3 (last digit is 3)
2. 3^2=9 (last digit is 9)
3. 3^3=27 (last digit is 7)
4. 3^4=81 (last digit is 1)

5. 3^5=243 (last digit is 3 again!)
...

To find the last digit of \(3^{8n+3}\), divide the power (which is \(8n+3\)) by cyclicity # ( which is \(4\)) and look at the remainder --> \(\frac{8n+3}{4}\) --> \(remainder=3\), which means that the last digit of \(3^{8n+3}\) will be the same as the last digit of \(3^3=27\) (last digit is 7). (Side note: If the remainder were 0, then last digit would be the same as the las digit of \(3^4\)).

Now, last digit of \(3^{8n+3}+2\) will be \(7+2=9\). Any integer with last digit 9 upon division by 5 yields remainder of 4.

Answer: E.

Hope it's clear.


Bunuel, : If the remainder were 0, then last digit would be the same as the las digit of 3^4=81 means 1.
shouldn't it be 3^0=1 instead?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: PS Questions from SET 1-Need detail solution  [#permalink]

Show Tags

New post 23 Jun 2010, 21:01
1
udaymathapati wrote:

Bunuel, : If the remainder were 0, then last digit would be the same as the las digit of 3^4=81 means 1.
shouldn't it be 3^0=1 instead?


No, as in this case all numbers in power which is multiple of cyclicity would have the last digit of 1.

When power is divisible by cyclicity # (remainder 0), then the last digit is the same as the last digit of number in the power of cyclicity #.

For example:
Cyclicity of 2 is 4, so \(2^{4n}\) (where \(n\) is a positive integer) will have the same last digit as \(2^4\), which is 6.

OR:

Cyclicity of 4 is 2, so \(4^{2n}\) (where \(n\) is a positive integer) will have the same last digit as \(4^2\), which is 6.

Hope it's clear.
_________________

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

Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 117
Reviews Badge
Re: PS Questions from SET 1-Need detail solution  [#permalink]

Show Tags

New post 24 Jun 2010, 11:08
1
Bunuel wrote:
udaymathapati wrote:

Bunuel, : If the remainder were 0, then last digit would be the same as the las digit of 3^4=81 means 1.
shouldn't it be 3^0=1 instead?


No, as in this case all numbers in power which is multiple of cyclicity would have the last digit of 1.

When power is divisible by cyclicity # (remainder 0), then the last digit is the same as the last digit of number in the power of cyclicity #.

For example:
Cyclicity of 2 is 4, so \(2^{4n}\) (where \(n\) is a positive integer) will have the same last digit as \(2^4\), which is 6.

OR:

Cyclicity of 4 is 2, so \(4^{2n}\) (where \(n\) is a positive integer) will have the same last digit as \(4^2\), which is 6.

Hope it's clear.


Thanks bunuel. It's clear for me.
Intern
Intern
avatar
Joined: 22 Jun 2010
Posts: 2
Re: PS Questions from SET 1-Need detail solution  [#permalink]

Show Tags

New post 25 Jun 2010, 20:03
Ok, beautiful solution, but to time consuming...
It´s a problem solving question, so, there is just one answer right?
Just to n = 1 and make the calculation...
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
Re: If n is a positive integer, what is the remainder when  [#permalink]

Show Tags

New post 09 Mar 2014, 12:09
Intern
Intern
User avatar
B
Joined: 09 Mar 2017
Posts: 49
Location: India
GMAT 1: 650 Q45 V31
GPA: 4
WE: Marketing (Advertising and PR)
Reviews Badge
Re: If n is a positive integer, what is the remainder when  [#permalink]

Show Tags

New post 21 Aug 2017, 09:57
600 Level Question.
Took me 1 minute to solve.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1128
If n is a positive integer, what is the remainder when  [#permalink]

Show Tags

New post 21 Aug 2017, 11:36
udaymathapati 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


let n=1
check the units digits of 3,9,27,81
3^11, or 3^3+4+4, falls into the 3rd position in a cycle of 4, giving a units digit of 7
7+2=9
9/5 gives a remainder of 4
E
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 509
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User CAT Tests
If n is a positive integer, what is the remainder when  [#permalink]

Show Tags

New post 27 Sep 2018, 23:57
3^(8n+3) this means it will always be the third cycle.

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81 and the cycle repeats.

Since we know 3^(8n+3) will have a units digit like the one in 3^3

Then we can do 7+2 = 9/5 = 1 4/5

Or similarly we can take 27+2 = 29/5 = 5 4/5

Answer choice E

Posted from my mobile device
GMAT Club Bot
If n is a positive integer, what is the remainder when &nbs [#permalink] 27 Sep 2018, 23:57
Display posts from previous: Sort by

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

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.