smclean23 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
Another solution is to look for the pattern in the choices.
We're looking for something related to cycles of 6, so let's use that to our advantage and play the Sesame Street favourite "one of these things is not like the others".
10... 28.... 34.... 52... 86
If we look at the gaps:
18.. 6... 18... 34
Well hey! 18, 6 and 18 are all multiples of 6, so 10, 28, 34 and 52 will all fit in the same place in the multiples/remainders of 6 cycle. 86 is at a different place in the cycle, so it MUST be the right answer to the question.
There are other ways we could look at the choices as well. 10, 28, 34 and 52 all give a remainder of 4 when divided by 6, while 86 gives a remainder of 2. Even if we're not sure why we need a remainder of 4, we can deduce that 86 is the oddball and must be correct.
