M+N is NOT?

Question

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

Answer 1

It's given that M has a remainder of 1 when divided by 6. Thus, M = 6A + 1 for some A.

Similarly, N = 6B + 3 for some B.

Then M + N = (6A + 1) + (6B + 3) = 6(A + B) + 4. So M + N has a remainder of 4 when divided by 6.

All of your choices have a remainder of 4 when divided by 6, except for 86.

Thus, M + N cannot be 86, so the answer is (A).

Answer 2

Let M=6a+1, a E N
N= 6b+3, b E N
So M+N=6(a+b)+4 i.e, M+N should give the remainder 4 when divided by 6. But 86=6*14 +2. So Ans:A

Answer 3

6( )+1=M

6{ }+3=N

6[( )+{ }] +4=M+N
so remainder of the value M+N should be 4.only 86 will not give remainder 4. 86=6*14+2

Answer 4

6( )+1=M

6{ }+3=N

6[( )+{ }] +4=M+N
so remainder of the value M+N should be 4.only 86 will not give remainder 4. 86=6*14+2.

Answer 5

let M=6k+1, N=6m+3. M+N=6[k+m]+4.
k+m is an integer. let k+m=n so M+N=6n+4.
All are in the form of 6n+4 except 86=6*14+2.
so answer is 86.

Answer 6

86 is the answer. since all the remaining numbers give a remainder 4 when divided with 6.86 gives a remainder 2.hence answer is A,86

Answer 7

86

Answer 8

D) 28

Answer 9

let
M = 1 + 6x
N = 3 + 6y
M + N = 4 + 6x + 6y
x + y = (M + N - 4)/6,
so (M + N - 4)mod6 = 0
86 - 4 is not divisible by 6

Answer 10

m=6x+1

n=6x+3

m+n=6x+6y+4
m+n=6(x+y)+4

(ie,)m+n has a reminder 4 when divided by 6

ans=10 (A)(as14 is not divisible by 6)