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

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

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26 Aug 2006, 16:28
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If M and N are positive integers that have remainders of 1 and 4, respectively, when divided by 6, which of the following could not be a possible value of M + N?

86
52
34
28
10
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26 Aug 2006, 18:32
10 - If Iâ€™m not missing something.

Least possible values of M and N that satisfy the question:

M: 7 --> 7/6, reminder of 1
N: 10 --> 10/6, reminder of 4

So, 7+10=/=10....
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26 Aug 2006, 18:43
M = 6q1 + 1
N = 6q2 + 4

M + N = 6q1 + 6q2 + 5 = 6(q1 + q2) + 5

for 10: 10 -5 = 6(q1 + q2); 5= 6(q1 + q2) which cannot be..

However, none of the other answers seem to be a multiple of 6 either..
Can someone verify my logic?
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