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

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Joined: 11 May 2007
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If M and N are positive integers that have remainders of 1 [#permalink] New post 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
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Re: Positive Integers [#permalink] New post 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..
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 [#permalink] New post 16 Nov 2007, 01:04
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
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Re: Positive Integers [#permalink] New post 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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