It is currently 17 Oct 2017, 10:31

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
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

29 Apr 2016, 16:13
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

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

### HideShow timer Statistics

If $$\frac{X}{Y}=63^{33}×36^{195}$$, what is the remainder of $$\frac{X}{(10Y)}$$?

A. 3
B. 5
C. 6
D. 8
E. 9
[Reveal] Spoiler: OA

_________________

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

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

### Show Tags

29 Apr 2016, 20:44
1
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...

------------------------------------------------------------------------------------------------------------------------
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
Joined: 09 Sep 2013
Posts: 16762

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

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

### Show Tags

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.
_________________

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