duongthang wrote:M=6x+1
N=6y+3

M+N=6(x+y)+ 4

x+y must be bigger than 2, M+N must bigger than 16

E is the right answer

This starts out well, but there is no reason why x+y must be larger than 2. There is nothing wrong with having a quotient of 0 in division: when you divide 5 by 6, for example, the quotient is 0 and the remainder is 5. x and y are the quotients here, and they can certainly be equal to 0.

That said, your approach is good to begin with. We know

M+N = 6(x+y) + 4

That means that M+N must be 4 larger than a multiple of 6, or in other words, that the remainder must be 4 when you divide M+N by 6. This is essentially what niraj found above by picking numbers. A is the only answer that gives a remainder different from 4 when you divide by 6.

yvichman wrote:Can't you just divide each of the answer choices given, by 6 to find out if they give a remainder of 4 (3+1 as stated in the question). The one that does not have a remainder of 4 would give you the correct answer.

Is this an approach that would not work all the time?

Yes, that's perfect. My post above is identical in method- I just wanted to demonstrate why the remainder needs to be equal to 4.