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Is there a short-cut method that one can use for these kind

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Senior Manager
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Is there a short-cut method that one can use for these kind [#permalink] New post 07 Aug 2008, 16:52
Is there a short-cut method that one can use for these kind of problems:
What is the unit digit of (758)^23?

Thanks.
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Re: Short-cut method for these type of problems [#permalink] New post 07 Aug 2008, 17:42
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I don't know of any way to start the problem without working through some powers & finding a pattern:

8^1 = 8, 8^2 = 64 , 8^3 = 512 , 8^4 = 4096 , 8^5 = 32768 , 8^6 = units of 4

units pattern is found: 8 , 4, 2, 6, 8, 4, 2, 6....

8^3 has units of 2, so every 4th power higher than that will have units of 2:
8^7, 8^11, 8^15, 8^19, 8^23

As a side note, I'm not sure this is very commonly tested on the GMAT these days.
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Re: Short-cut method for these type of problems [#permalink] New post 07 Aug 2008, 17:42
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Just focus on the last digit.
So question is asking what is unit's digit of 8^23.

Unit's Digits Table for 8
8^0 = 1
8^1 = 8
8^2 = 4
8^3 = 2
8^4 = 6
8^5 = 8 (So again pattern will start repeating from here).

8^23 = (8^4)^5 * 8^3
As 8^4 end in 6 so 6^5 will end in 6.
8^3 ends in 2.

So units digit will end in = 6*2 = 2

Hope it helps.
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Re: Short-cut method for these type of problems [#permalink] New post 07 Aug 2008, 21:50
When I was looking at the problem, I was thinking the way fourier thought (repeating patterns). Splitting the power is a good technique which I used to use it long time ago when I was in high school ( that didn't even strike me now).......

Thanks fourier and Abhijit for the post... (+1) to you both.....
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Re: Short-cut method for these type of problems   [#permalink] 07 Aug 2008, 21:50
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