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700 level question

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Intern
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Joined: 27 Sep 2009
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700 level question [#permalink] New post 22 Aug 2010, 20:56
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

68% (01:29) correct 32% (00:16) wrong based on 28 sessions
What is the last digit of 3^987 ?

a.1

b.7

c.9

d.2
[Reveal] Spoiler: OA
Senior Manager
Senior Manager
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Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 411
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
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Re: 700 level question [#permalink] New post 22 Aug 2010, 21:12
shekar123 wrote:
What is the last digit of 3^987 ?

a.1

b.7

c.9

d.2


Numbers 2, 3, 7 and 8 has a cyclicity of 4. Hence every 1st, 5th, 9th and so on power of 2, 3, 7 and 8 has the same unit digit.

Here the power is 987. Divide it by 4, the remainder is 3. Hence the last digit of 3 ^ 987 is the same as 3 ^ 3 -- 7.

Answer is B (7).

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Re: 700 level question [#permalink] New post 23 Aug 2010, 01:26
shekar123 wrote:
What is the last digit of 3^987 ?

a.1

b.7

c.9

d.2



700 level................I doubt...please check...!!!

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Re: 700 level question [#permalink] New post 15 Oct 2010, 08:26
For these types of ques ..just use the cyclicity. i.e 4 for 3..
3
9
7
1
so when power is divided by 4..we get 3 as rem..
so ans will be 7
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Status: ISB, Hyderabad
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WE 1: 4 years Software Product Development
WE 2: 3 years ERP Consulting
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Re: 700 level question [#permalink] New post 17 Oct 2010, 18:15
B
The last digit for power of 3 is [3,9,7,1]. And 987 = 4k+3
So answer is 7.

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Re: 700 level question [#permalink] New post 18 Oct 2010, 05:23
3 has a cyclicity of 4
3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
987/4=246 and rem 3
so we have 7
(B)
Re: 700 level question   [#permalink] 18 Oct 2010, 05:23
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