If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 5, which of the following could NOT be a possible value of M+N?  Choose the correct choice from the following answers.
A) 84  B) 52  C) 34  D) 29  E) 14
M=5p+1   N=5q+3   We need M+N=5p+1+5q+3=5(p+q)+4   Pick numbers for pq   Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),   we just need to choose values so that we get integer multiples of 5 so   p+q=0 ; M+n = 4   p+q=1 ; M+N = 9   P+q=2 ; M+N = 14   and so on, so basically you get something like - 4,9,14,19,24,29,34,..... all the other options were turning up.   Then I directly tried p+q=10 because it was closer to 52 for the first option, i got 54, .   So Answer 52.
<result>B</result>
If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 5, which of the following could NOT be a possible value of M+N?