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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.

Re: What is the units digit of 18^47 ? [#permalink]
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.

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

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).

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Re: What is the units digit of 18^47 ? [#permalink]
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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