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What is the units digit of 18^47 ?

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What is the units digit of 18^47 ? [#permalink] New post 21 Oct 2010, 16:40
00:00
A
B
C
D
E

Difficulty:

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Question Stats:

68% (01:31) correct 32% (00:32) wrong based on 96 sessions
What is the units digit of 18^47 ?

A. 0
B. 2
C. 4
D. 6
E. 8
[Reveal] Spoiler: OA

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Re: unit digit [#permalink] New post 21 Oct 2010, 17:03
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shrive555 wrote:
What is the units digit of 18^47 ? (18 power 47 )

0
2
4
6
8


The last digit of 18^47 is the same as the last digit of 8^47.

8^1=8;
8^2=64;
8^3=...2;
8^4=...6;
8^5=...8;
...

So the last digit of 8 in power repeats a pattern of 4 numbers: 8-4-2-6 --> 47=11*4+3, which means that the last digit of 8^47 will be the same as that of 8^3 (the third from the pattern), which is 2.

Answer: B.

Check Number Theory chapter of Math Book for more: math-number-theory-88376.html

Hope it helps.
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Re: unit digit [#permalink] New post 21 Oct 2010, 17:38
47/4 remainder = 3

18^3. The unit digit is 2. hence answer is B
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Re: unit digit [#permalink] New post 13 Jul 2012, 10:18
what is the difficulty level of this question?
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Re: unit digit [#permalink] New post 14 Jul 2012, 03:03
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Re: What is the units digit of 18^47 ? [#permalink] New post 25 Jul 2012, 01:35
B) 2

18^47 = (3^47) * (3^47) * (2^47)

Solving for units digit individually, we get unit's digit for 3^47 as 7 and of 2^47 as 8 (as 47/4 has remainder 3). Therefore, 7*7*8 has unit's digit 2.
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Re: What is the units digit of 18^47 ? [#permalink] New post 25 Jul 2012, 20:38
Hi,

18^{47}, considering the unit digits only,
=8^{46}*8

=4^{23}*8

=4^{22}*4*8

=6^{11}*2

=6*2

=2

Answer (B)

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Re: What is the units digit of 18^47 ?   [#permalink] 25 Jul 2012, 20:38
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