It is currently 17 Oct 2017, 10:31

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

If X/Y=63^33×36^195, what is the remainder of X/(10Y)?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128564 [0], given: 12180

If X/Y=63^33×36^195, what is the remainder of X/(10Y)? [#permalink]

Show Tags

New post 29 Apr 2016, 16:13
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (01:13) correct 35% (02:10) wrong based on 72 sessions

HideShow timer Statistics

Kudos [?]: 128564 [0], given: 12180

1 KUDOS received
Senior Manager
Senior Manager
avatar
B
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 254

Kudos [?]: 127 [1], given: 142

Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
GMAT ToolKit User Reviews Badge
If X/Y=63^33×36^195, what is the remainder of X/(10Y)? [#permalink]

Show Tags

New post 29 Apr 2016, 20:44
1
This post received
KUDOS
3
This post was
BOOKMARKED
Its basically asking the remainder of \(\frac{63^{33}×36^{195}}{10}\)
And it all depends on the unit's digit of \(63^{33}×36^{195}\)

Units digit of \(63^{33}\) depends on cyclicity of 3.
\(63^{1}\) = 3
\(63^{2}\) = 9
\(63^{3}\) = 7
\(63^{4}\) = 1
\(63^{5}\) = 3
.
.
.
\(63^{32}\) = 1
\(63^{33}\) = 3

Hence the units digit would be: 3

On the other hand, the units digit of \(36^{195}\), will depend on cyclicity of 6, which is 1 and the units digit it always 6.

Hence the unit's digit of the expression \(63^{33}×36^{195}\) is \(3x6=18\) =>8

Therefore, the remainder when we divide the above expression by 10 would be 8

Option D
_________________

One Kudos for an everlasting piece of knowledge is not a bad deal at all... :thanks

------------------------------------------------------------------------------------------------------------------------
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.
-Mark Twain

Kudos [?]: 127 [1], given: 142

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16762

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

Premium Member
Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)? [#permalink]

Show Tags

New post 01 Oct 2017, 07:41
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 [?]: 273 [0], given: 0

Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)?   [#permalink] 01 Oct 2017, 07:41
Display posts from previous: Sort by

If X/Y=63^33×36^195, what is the remainder of X/(10Y)?

  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®.