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Senior Manager
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06 Nov 2006, 08:03
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I have a vague idea about this and took a guess and got it right. But I'd like to see some other explanations

I basically thought of since its exponent is an odd number, its last digit will always be odd and then tried seeing a pattern and picked 7 coz if you multiple it 7 times, gets you last digit 7......

What is the last digit of 3^(987)?

1) 1
2) 3
3) 6
4) 7
5) 9
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06 Nov 2006, 08:11
You did it right.

3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, 3^5 = 243 and now the ones digit starts repeating. [edit original answer to make more clear]

so the sequence is {3,9,7,1,3,9,7,1,3,9,7,1, ....} so we merely have to find the 987th one in the series. Apparently, each fourth term is a 1 (so term 8 is 1, term 12 is 1, etc..). That means term 984 is a 1, term 985 is a 3, term 986 is a 9, and term 987 is a 7.
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06 Nov 2006, 09:01
Of course an even more straightforward way of doing it is to recognize that 3^987 is simply

829236496921142476706699495492534678333952425419534289892901481209785342961686496112003849816259353947669184786817089357646445909706263355584372003200075313488935570269211950074115956571513326518146197550677383466919154911284033685809943263099187977900655123287740529620125316135462447582745383623592042654361925760199521859891889158161732532817099423444872173084985440322849485291685258736792319114827459947632739061572907631860285305265724594082011214874384364252979387

and then the ones digit becomes clear.
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06 Nov 2006, 09:45
ans = 7

powers of3 go in seq of 1,3,9,7...

quote="uvs_mba"]I have a vague idea about this and took a guess and got it right. But I'd like to see some other explanations

I basically thought of since its exponent is an odd number, its last digit will always be odd and then tried seeing a pattern and picked 7 coz if you multiple it 7 times, gets you last digit 7......

What is the last digit of 3^(987)?

1) 1
2) 3
3) 6
4) 7
5) 9[/quote]
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06 Nov 2006, 10:37
joeydvivre wrote:
Of course an even more straightforward way of doing it is to recognize that 3^987 is simply

829236496921142476706699495492534678333952425419534289892901481209785342961686496112003849816259353947669184786817089357646445909706263355584372003200075313488935570269211950074115956571513326518146197550677383466919154911284033685809943263099187977900655123287740529620125316135462447582745383623592042654361925760199521859891889158161732532817099423444872173084985440322849485291685258736792319114827459947632739061572907631860285305265724594082011214874384364252979387

and then the ones digit becomes clear.

Hahaha this is hilarious. What did you use to get this a calculator. I'll fall asleep doing that lol!

Btw guys thanks for the explanation, looks like was on the right track, just needed that surity and you guys confirmed it.

Thanks a ton
VP
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06 Nov 2006, 21:03
D 7.

it is a repeating sequence of 4. find the remainder of 987/4 and get hte unit digit of 3 to that power.
VP
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Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX)
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07 Nov 2006, 04:01
joeydvivre wrote:
You don't have powers of 3 memorized?

Man - apart from good quant skills you seem to have a perfect wherewithal for some scathing humor!!!
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07 Nov 2006, 22:29
tennis_ball wrote:
D 7.

it is a repeating sequence of 4. find the remainder of 987/4 and get hte unit digit of 3 to that power.

now that is both easy to remember and doable in 2 mins...thanks, tennis_ball!
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07 Nov 2006, 23:29
last digit runs in this order: 3 -> 9 -> 7 -> 1

987/3 = 246.75 --> So is the third in the series - '7'
07 Nov 2006, 23:29
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