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# If M and N are positive integers that have remainders of 1

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Director
Joined: 09 Aug 2006
Posts: 525
Followers: 2

Kudos [?]: 39 [0], given: 0

If M and N are positive integers that have remainders of 1 [#permalink]  18 May 2007, 21:50
19. If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10
Current Student
Joined: 22 Apr 2007
Posts: 1097
Followers: 5

Kudos [?]: 21 [0], given: 0

M = 6m + 1
N = 6n + 3

M+N = 6(m+n) + 4

Only 86 - 4 = 82 not a multiple of 6. So, A
Intern
Joined: 16 Mar 2007
Posts: 7
Followers: 0

Kudos [?]: 5 [0], given: 0

Do the following
M=6k+1
N=6k'+3

M+N=6(k+k')+4=6K+4

Now check which answer choice does not confer to the above expression.

86=6*14+2
52=6*8+4
34=6*5+4
28=6*4+4
10=6+4

So clearly the first choice does not confer to the expression so ans is A.
Director
Joined: 26 Feb 2006
Posts: 905
Followers: 4

Kudos [?]: 52 [0], given: 0

Re: Numbers... [#permalink]  18 May 2007, 22:18
Amit05 wrote:
19. If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10

any integer that doesnot fit to an expression: 6n+4.
so A. 86
Re: Numbers...   [#permalink] 18 May 2007, 22:18
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