What is the units digit of 18^47 ? : GMAT Problem Solving (PS)
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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]

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New post 21 Oct 2010, 16:40
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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]

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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]

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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]

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New post 13 Jul 2012, 10:18
what is the difficulty level of this question?
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Re: unit digit [#permalink]

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New post 14 Jul 2012, 03:03
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Re: What is the units digit of 18^47 ? [#permalink]

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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]

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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]

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New post 10 Dec 2014, 12:46
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Re: What is the units digit of 18^47 ? [#permalink]

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New post 06 Jan 2015, 02:44
Hi,

Just sharing a thought. I haven't managed to understand how the difficulty of the questions is decided - not by you in the GMATCLUB, but by GMAC.

This one for example is very very difficult, if you don't know the simple trick of the cyclicity of the powers. If you do know it however, it becomes ridiculously easy...

So, in fact, it requires very little reasoning and quite a bit of either math knowledge or GMAT tricks knowledge... At least for me, a psychologist that wants to do a psychology PhD in a marketing department that requires the GMAT, I didn't reason at all while solving this one.. Just increased the powers of 8 until the same last digit came up and counted...
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Re: What is the units digit of 18^47 ? [#permalink]

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New post 19 Jan 2015, 05:23
The unit digit will be the unit digit of 8x7
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Re: What is the units digit of 18^47 ? [#permalink]

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New post 19 Jan 2015, 05:27
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Re: What is the units digit of 18^47 ? [#permalink]

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New post 19 Jan 2015, 05:28
Bunuel wrote:
ugurozturk wrote:
The unit digit will be the unit digit of 8x7


That't not correct. It's 18^47, not 18*47.


Whops, yes, my bad!
Re: What is the units digit of 18^47 ?   [#permalink] 19 Jan 2015, 05:28
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