It is currently 11 Dec 2017, 14:03

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

Events & Promotions in June
Open Detailed Calendar

Cyclicity and remainders

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

Hide Tags

Current Student
avatar
Joined: 23 Jul 2013
Posts: 304

Kudos [?]: 83 [0], given: 71

Cyclicity and remainders [#permalink]

Show Tags

New post 18 Sep 2013, 13:38
1
This post was
BOOKMARKED
Hey guys, and calling for the legend Bunuel!

So I am learning the cyclicity and finding a units digit trick. Very neat. Only thing I am a bit confused on is if the remainder is zero.

For instance, 17^12 is 7^12. 7 has a cyclicity of 4. 12 divided by 4 yields no remainder. So does that mean the unit digit is just the 4th in the cycle, which in this case is 1?

Thanks!

Kudos [?]: 83 [0], given: 71

Expert Post
2 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4545

Kudos [?]: 8936 [2], given: 111

Re: Cyclicity and remainders [#permalink]

Show Tags

New post 18 Sep 2013, 17:04
2
This post received
KUDOS
Expert's post
TheLostOne wrote:
Hey guys, and calling for the legend Bunuel!

So I am learning the cyclicity and finding a units digit trick. Very neat. Only thing I am a bit confused on is if the remainder is zero.

For instance, 17^12 is 7^12. 7 has a cyclicity of 4. 12 divided by 4 yields no remainder. So does that mean the unit digit is just the 4th in the cycle, which in this case is 1?

Thanks!

Dear TheLostOne,
I'm happy to help with this. :-)

First of all, here's a blog you may find informative.
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Let's think about this. The powers of 7 indeed have a cycle of 4 --- this means
7^1 has a units digit of 7
7^2 has a units digit of 9
7^3 has a units digit of 3
7^4 has a units digit of 1
7^5 has a units digit of 7
7^6 has a units digit of 9
7^7 has a units digit of 3
7^8 has a units digit of 1
That's a cycle of 4. Notice, at every exponent that's a multiple of four, the unit digit is 1.

When you divide by 4 and get no remainder, you are at a multiple of four. Therefore, the units digit it 1. Therefore, 7^12 (or 17^12 or 1037^12) would have to have a units digit of 1. You are perfectly correct. :-)

If you think about it, when the power is a multiple of the cycle, the units digit would have to be 1 for any base, because having a units digit of 1 allows the next power to have the same units digit as the base.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8936 [2], given: 111

Current Student
avatar
Joined: 23 Jul 2013
Posts: 304

Kudos [?]: 83 [0], given: 71

Re: Cyclicity and remainders [#permalink]

Show Tags

New post 19 Sep 2013, 06:50
mikemcgarry wrote:
TheLostOne wrote:
Hey guys, and calling for the legend Bunuel!

So I am learning the cyclicity and finding a units digit trick. Very neat. Only thing I am a bit confused on is if the remainder is zero.

For instance, 17^12 is 7^12. 7 has a cyclicity of 4. 12 divided by 4 yields no remainder. So does that mean the unit digit is just the 4th in the cycle, which in this case is 1?

Thanks!

Dear TheLostOne,
I'm happy to help with this. :-)

First of all, here's a blog you may find informative.
http://magoosh.com/gmat/2013/gmat-quant ... questions/

Let's think about this. The powers of 7 indeed have a cycle of 4 --- this means
7^1 has a units digit of 7
7^2 has a units digit of 9
7^3 has a units digit of 3
7^4 has a units digit of 1
7^5 has a units digit of 7
7^6 has a units digit of 9
7^7 has a units digit of 3
7^8 has a units digit of 1
That's a cycle of 4. Notice, at every exponent that's a multiple of four, the unit digit is 1.

When you divide by 4 and get no remainder, you are at a multiple of four. Therefore, the units digit it 1. Therefore, 7^12 (or 17^12 or 1037^12) would have to have a units digit of 1. You are perfectly correct. :-)

If you think about it, when the power is a multiple of the cycle, the units digit would have to be 1 for any base, because having a units digit of 1 allows the next power to have the same units digit as the base.

Does all this make sense?
Mike :-)


Indeed it does!

Thanks.

Kudos [?]: 83 [0], given: 71

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14938

Kudos [?]: 287 [0], given: 0

Premium Member
Re: Cyclicity and remainders [#permalink]

Show Tags

New post 24 Sep 2017, 00:30
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 287 [0], given: 0

Re: Cyclicity and remainders   [#permalink] 24 Sep 2017, 00:30
Display posts from previous: Sort by

Cyclicity and remainders

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


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