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# If n and m are positive integers, what is the remainder when 3^(4n+2)

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Director
Joined: 23 Sep 2007
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If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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25 Dec 2007, 00:06
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If n and m are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10 ?

(1) n=2
(2) m=1

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-m-are-positive-integers-what-is-the-remainder-when-105027.html
[Reveal] Spoiler: OA

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SVP
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Schools: CBS, Kellogg
Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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25 Dec 2007, 00:28
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1. insufficient:
2, sufficient. 3^4n+2 + m = 3^4n+2 + 1
3^4n+2 = 3^2.(3^4)^n is a number ending by 9. So, 3^4n+2 + 1 is a number ending by 0 and therefore, devided by 10

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Director
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Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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25 Dec 2007, 01:41
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gmatnub wrote:
if m and n are positive integers, what is the remainder when 3^(4n+2) + m is divided by 10?

1. n = 2
2. m = 1

What is the short cut without plugging in values for n and solve the exponent?

[9^(2n+1)]/10 + m/10

Irrespective of the value of n, the first term will always have an odd power of 9. Thus we know what remainder will be.
But in second term, we need to know the value of m.

So just by knowing the statement (ii), we can solve this.

Therefore, answer is "B"

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VP
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Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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25 Dec 2007, 04:08
interesting...

we know that : [3^(4n+2)+m]/10=q + r/10
where q is the quotient and r is the remainder...if we know that
[3^(4n+2)+m] is a multiple of 10, the remainder would clearly be 0.

if n=2 we don't know anything useful; 1 not suff

3^(4n+2) equals 3^4n * 3^2...3^4n is a number which ends in 1 (i.e. 3^4 is 81). if we multiply this number * 3^2 we have a number ending in 9. let's sum with 1...we got 10, so B is suff

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Manager
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Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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22 Jan 2008, 14:54
B
S1 not suffi & not required since the no will end in 9 for all values of n and the remainder depends on m, which is not given in S1.
S2 is suffi since we get the value for m,

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Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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20 Dec 2014, 09:49
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Re: If n and m are positive integers, what is the remainder when 3^(4n+2) [#permalink]

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20 Dec 2014, 10:39
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-m-are-positive-integers-what-is-the-remainder-when-105027.html
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Re: If n and m are positive integers, what is the remainder when 3^(4n+2)   [#permalink] 20 Dec 2014, 10:39
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# If n and m are positive integers, what is the remainder when 3^(4n+2)

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