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# If Sn = 2^n, what is the units digit of S67?

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Intern
Joined: 17 Jun 2014
Posts: 18
If Sn = 2^n, what is the units digit of S67?  [#permalink]

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Updated on: 15 Jul 2014, 01:00
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Question Stats:

90% (00:56) correct 10% (01:23) wrong based on 88 sessions

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If Sn = 2^n, what is the units digit of S67?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

Originally posted by langtuprovn2007 on 14 Jul 2014, 21:43.
Last edited by langtuprovn2007 on 15 Jul 2014, 01:00, edited 1 time in total.
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Joined: 24 Jan 2013
Posts: 36
Re: If Sn = 2^n, what is the units digit of S67?  [#permalink]

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14 Jul 2014, 22:10
Hi.
the cyclicity of 2 is 4 i.e..te numbers 2,4,8,6,2,4 ... repeat after every 4 terms.
In the question 2^67,by cyclicity of 2 we need to find 2^3 as 67/4 because the powers of 2 repeat after 4 terms.
So 2^3= 8 and the answer is 8
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Re: If Sn = 2^n, what is the units digit of S67?  [#permalink]

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14 Jul 2014, 22:11
langtuprovn2007 wrote:
If Sn = 2^n, what is the units digit of S67?
(A) 2 (B) 4 (C) 6 (D) 8 (E) 0
I dont know whether I am right or wrong plz help me :D ! Thnks a lot !

This question tests cyclicity. What is the cyclicity of 2?

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
.....

2, 4, 8, 6, 2, 4, 8, 6, 2 ...
So whenever the power is divisible by 4, the units digit will be 6.

You need the units digit of S67 = $$2^{67}$$
$$2^{64}$$ ends a cycle with units digit of 6.
A new cycle starts at $$2^{65}$$ with units digit of 2.
$$2^{66}$$ will have units digit of 4.
$$2^{67}$$ will have units digit of 8.
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Re: If Sn = 2^n, what is the units digit of S67?  [#permalink]

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15 Jul 2014, 02:14
langtuprovn2007 wrote:
If Sn = 2^n, what is the units digit of S67?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 0

Check similar Units digits, exponents, remainders problems in our Special Questions Directory.

Hope it helps.
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Re: If Sn = 2^n, what is the units digit of S67?  [#permalink]

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15 Jul 2014, 03:31
$$S1 = 2^1 = 2$$

$$S2 = 2^2 = 4$$

$$S3 = 2^3 = 8$$

$$S4 = 2^4 = 16$$

And the series continues with cyclisity 2, 4, 8, 6.........

S64 would have last digit 6

S67 would have last digit 8

Answer = D = 8
Re: If Sn = 2^n, what is the units digit of S67?   [#permalink] 15 Jul 2014, 03:31
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# If Sn = 2^n, what is the units digit of S67?

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