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# If n is a positive integer, what is the remainder When

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Intern
Joined: 08 Nov 2008
Posts: 38
If n is a positive integer, what is the remainder When [#permalink]

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17 Nov 2008, 09:00
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If n is a positive integer, what is the remainder
When (7^(4n+3))(6^n) is divided by 10?
F. 1
G. 2
H. 4
I. 6
J. 8
Intern
Joined: 03 Oct 2008
Posts: 17

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17 Nov 2008, 09:08
ans should be 2..
the remainder..
Manager
Joined: 08 Aug 2008
Posts: 229

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17 Nov 2008, 09:15

7 repeats itself every 5th power.
so $$7^(4n+3)$$ always end with 3.
$$6^n$$ always ends in 6.

so $$3*6=18$$...remainder is 8.
Intern
Joined: 03 Oct 2008
Posts: 17

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17 Nov 2008, 09:24
7 (4n+3) will always end up with 7..

we can take
7^(4n) * 7^(3)

7^(4n) ends up with 9
7^(3) ends up with 3.

which makes it 7 in end.
Current Student
Joined: 28 Dec 2004
Posts: 3317
Location: New York City
Schools: Wharton'11 HBS'12

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17 Nov 2008, 09:28
bindrakaran001 wrote:
7 (4n+3) will always end up with 7..

we can take
7^(4n) * 7^(3)

7^(4n) ends up with 9
7^(3) ends up with 3.

which makes it 7 in end.

you are forgetting to multiply by 6^n in other words its 6*3=18

remainder will be 8
Intern
Joined: 03 Oct 2008
Posts: 17

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17 Nov 2008, 09:32
7^(4n) ends with 9
7 ^(3) ends with 3
6^(n)ends with 6..

last digit when multiply will be 2.

so remainder 2.

is it not this..
Manager
Joined: 08 Aug 2008
Posts: 229

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17 Nov 2008, 09:40
7^4n ends with 1....
bindrakaran001 wrote:
7^(4n) ends with 9
7 ^(3) ends with 3
6^(n)ends with 6..

last digit when multiply will be 2.

so remainder 2.

is it not this..
Intern
Joined: 03 Oct 2008
Posts: 17

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17 Nov 2008, 09:43
ohhhhhh..
wat a silly mistake..

thanx sir..
Re: interger--25   [#permalink] 17 Nov 2008, 09:43
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# If n is a positive integer, what is the remainder When

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