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# if m and n are positive integers, what is the remainder when

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Director
Joined: 23 Sep 2007
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if m and n are positive integers, what is the remainder when [#permalink]  24 Dec 2007, 23:06
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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?
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SVP
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
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Kudos [?]: 274 [0], given: 1

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
Director
Joined: 03 Sep 2006
Posts: 893
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Kudos [?]: 115 [0], given: 33

Re: DS gmatprep remainder, if m and n are positive integers [#permalink]  25 Dec 2007, 00:41
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.

VP
Joined: 22 Nov 2007
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Re: DS gmatprep remainder, if m and n are positive integers [#permalink]  25 Dec 2007, 03:08
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
Manager
Joined: 04 Jan 2008
Posts: 85
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Kudos [?]: 10 [0], given: 0

Re: DS gmatprep remainder, if m and n are positive integers [#permalink]  22 Jan 2008, 13:54
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,
Re: DS gmatprep remainder, if m and n are positive integers   [#permalink] 22 Jan 2008, 13:54
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