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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If X/Y=63^33×36^195, what is the remainder of X/(10Y)?  [#permalink]

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29 Apr 2016, 15:13
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:42) correct 35% (02:18) wrong based on 170 sessions

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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

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

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29 Apr 2016, 19:44
2
4
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
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##### General Discussion
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Joined: 12 Sep 2017
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Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)?  [#permalink]

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22 Jan 2019, 13:30
Bunuel wrote:
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

Hello Bunuel !

I am just wondering...

Is it the same approach if in the statement would have been written without the "Y"?

$$\frac{X}{(10)}$$

Thank you so much in advance!
Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)?   [#permalink] 22 Jan 2019, 13:30
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