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# If n is a positive number, what is the remainder when

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Manager
Joined: 04 Jan 2008
Posts: 118
If n is a positive number, what is the remainder when [#permalink]

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05 Sep 2008, 23:43
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If n is a positive number, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
SVP
Joined: 29 Aug 2007
Posts: 2467
Re: Zumit PS 003 [#permalink]

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05 Sep 2008, 23:53
dancinggeometry wrote:
If n is a positive number, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

A. 0.

look for the pattren of 3's power.
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VP
Joined: 05 Jul 2008
Posts: 1401
Re: Zumit PS 003 [#permalink]

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06 Sep 2008, 10:54
3 power (8n+3) is some thing like 3 ^ 11 , 3 ^ 19, 3 ^ 27 for n =1,2 ,3

All of these end in 7 just like 3 ^ 3

units digit of 3 ^ (8n+3) + 2 will be 9 && remainder will be 4.
Manager
Joined: 04 Jan 2008
Posts: 118
Re: Zumit PS 003 [#permalink]

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06 Sep 2008, 22:45
OA is E. Bin 3 problem.
Retired Moderator
Joined: 18 Jul 2008
Posts: 959
Re: Zumit PS 003 [#permalink]

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07 Sep 2008, 10:15
How did you go about to find out that 3^11 ends in 7?

icandy wrote:
3 power (8n+3) is some thing like 3 ^ 11 , 3 ^ 19, 3 ^ 27 for n =1,2 ,3

All of these end in 7 just like 3 ^ 3

units digit of 3 ^ (8n+3) + 2 will be 9 && remainder will be 4.
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York
Re: Zumit PS 003 [#permalink]

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07 Sep 2008, 12:35
dancinggeometry wrote:
If n is a positive number, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

3^(8n+3) + 2 = 3^8n* 27+2

when n=0 3^0=1
when n=1 3^8= ends with 1

3^1=3
3^2 =9
3^3=27
3^4=81
.
.
3^8= xxx1 last digit is 1

similarly 3^16 last digit is 1

so 3^8n* 27+2 = xxxxxxx9
when you divide with 5 remainder is always 4
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Joined: 29 Aug 2007
Posts: 2467
Re: Zumit PS 003 [#permalink]

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07 Sep 2008, 15:00
GMAT TIGER wrote:
dancinggeometry wrote:
If n is a positive number, what is the remainder when 3^(8n+3) + 2 is divided by 5 ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

A. 0.

look for the pattren of 3's power.

huh... another silly mistake.
_________________

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Re: Zumit PS 003   [#permalink] 07 Sep 2008, 15:00
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# If n is a positive number, what is the remainder when

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