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# 3^n is divided by 10, what's the remainder?

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Intern
Joined: 05 Nov 2010
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3^n is divided by 10, what's the remainder? [#permalink]

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07 Nov 2010, 13:56
00:00

Difficulty:

55% (hard)

Question Stats:

50% (00:23) correct 50% (00:58) wrong based on 9 sessions

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3^n is divided by 10, what's the remainder?

(1) n is a multiple of 8
(2) n is a multiple of 12
[Reveal] Spoiler: OA

Kudos [?]: 28 [0], given: 0

Intern
Joined: 07 Nov 2010
Posts: 1

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Re: 3^n is divided by 10, what's the remainder? [#permalink]

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07 Nov 2010, 16:46
Let us understand the question stem :

3^n is divided by 10, what's the remainder? ---> what will be the unit digit for 3^n. Now let us try to observe a pattern of unit digit

3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^n=729
3^n=2187
3^n=6581

You can see the unit place digit (3,9,7,1) repeats itself after an interval of 4 .

Now let us come back to question again

1. n is a multiple of 8 --implies n will be divisible by 4 .Hence unit digit 1 Sufficient
2. n is a multiple of 12 --implies n will be divisible by 4 .Hence unit digit 1 Sufficient

Hence Ans - D

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Re: 3^n is divided by 10, what's the remainder? [#permalink]

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07 Nov 2010, 16:50
Creeper300 wrote:
3^n is divided by 10, what's the remainder?

1. n is a multiple of 8
2. n is a multiple of 12

Lets observe the cyclicity in the last digits of the powers of 3 :

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

.. after this the pattern repeats

(1) n is a multiple of 8 ---> Implies n is a multiple of 4 ---> Implies last digit is 1 : Sufficient

(2) n is a multiple of 12 --> Implies n is a multiple of 4 ---> Implies last digit is 1 : Sufficient

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Kudos [?]: 1211 [0], given: 25

Intern
Joined: 05 Nov 2010
Posts: 22

Kudos [?]: 28 [0], given: 0

Re: 3^n is divided by 10, what's the remainder? [#permalink]

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08 Nov 2010, 20:22
well done, D looks correct

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Re: 3^n is divided by 10, what's the remainder?   [#permalink] 08 Nov 2010, 20:22
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