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# 700 level question

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Intern
Joined: 27 Sep 2009
Posts: 41
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Kudos [?]: 85 [0], given: 4

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22 Aug 2010, 21:56
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:26) correct 30% (00:14) wrong based on 33 sessions

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What is the last digit of 3^987 ?

a.1

b.7

c.9

d.2
[Reveal] Spoiler: OA
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 8

Kudos [?]: 211 [0], given: 50

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22 Aug 2010, 22:12
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.

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Manager
Joined: 18 Feb 2010
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Schools: ISB
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Kudos [?]: 208 [0], given: 0

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23 Aug 2010, 02:26
shekar123 wrote:
What is the last digit of 3^987 ?

a.1

b.7

c.9

d.2

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Manager
Joined: 04 Sep 2010
Posts: 51
Followers: 2

Kudos [?]: 2 [0], given: 1

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15 Oct 2010, 09:26
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
Manager
Joined: 25 Jul 2010
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WE 1: 4 years Software Product Development
WE 2: 3 years ERP Consulting
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Kudos [?]: 52 [0], given: 15

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17 Oct 2010, 19:15
B
The last digit for power of 3 is [3,9,7,1]. And 987 = 4k+3
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Manager
Joined: 03 Jun 2010
Posts: 181
Location: United States (MI)
Concentration: Marketing, General Management
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Kudos [?]: 69 [0], given: 40

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18 Oct 2010, 06:23
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, 06:23
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