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

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Joined: 02 Sep 2009
Posts: 59095
If X/Y=63^33×36^195, what is the remainder of X/(10Y)?  [#permalink]

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New post 29 Apr 2016, 16:13
1
6
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:39) correct 35% (02:15) wrong based on 191 sessions

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B
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 229
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
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If X/Y=63^33×36^195, what is the remainder of X/(10Y)?  [#permalink]

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New post 29 Apr 2016, 20:44
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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Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)?  [#permalink]

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New post 22 Jan 2019, 14:30
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!
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Re: If X/Y=63^33×36^195, what is the remainder of X/(10Y)?   [#permalink] 22 Jan 2019, 14:30
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