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

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Manager
Joined: 11 May 2007
Posts: 107
Followers: 1

Kudos [?]: 12 [0], given: 0

If M and N are positive integers that have remainders of 1 [#permalink]  15 Nov 2007, 13:03
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
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 577 [0], given: 19

Re: Positive Integers [#permalink]  15 Nov 2007, 13:13
yogachgolf wrote:
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

A. any integer that fits to the expression (6k+4) is not the answer. 86 = 6k+2, so it is the required answer..
SVP
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 126 [0], given: 39

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

m= 6k+1 , N = 6x+3

m+n = 6k+6x+4 = 2(3k+3x+2)

devide given by 2 ( 43-26-17-14-5)

now subtract 2 from each and see which is not a multiple of 3

(41 - 24 - 15 - 12 - 3)

41 is out , ie: answer is A
Manager
Joined: 20 Sep 2006
Posts: 58
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: Positive Integers [#permalink]  16 Nov 2007, 03:12
yogachgolf wrote:
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

Ok my theory is that in this case when M+N is divided by 6 the remainder has to be 3+1=4

Only 86 does not satisfy this condition hence Ans is A).
Re: Positive Integers   [#permalink] 16 Nov 2007, 03:12
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