SOLUTION: If N and M are the multiple of 2 which are not divisible by 4 then what will be the reminder when N + M will be divided by 4 A. 0 B. 1 C. 2 D. 3 E. 4

Algebra ->  Divisibility and Prime Numbers  -> Lessons -> SOLUTION: If N and M are the multiple of 2 which are not divisible by 4 then what will be the reminder when N + M will be divided by 4 A. 0 B. 1 C. 2 D. 3 E. 4       Log On


   

Question 461564: If N and M are the multiple of 2 which are not divisible by 4 then what will be the reminder when N + M will be divided by 4
A. 0
B. 1
C. 2
D. 3
E. 4
Found 2 solutions by edjones, richard1234:
Answer by edjones(8007) About Me  (Show Source):
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The first statement implies N and M are congruent to 2 modulo 4. Hence,
N + M ≡ 2 + 2 ≡ 4 ≡ 0 (mod 4), so the remainder is 0.


If you do not know modular arithmetic, you could let N = 4x + 2 and M = 4y + 2, where x and y are integers. Then,
N + M = (4x + 2) + (4y + 2) = 4x + 4y + 4 = 4(x + y + 1)

This is a multiple of 4, so the remainder upon dividing by 4 is 0.

Either way works, it is just a matter of which solution you are most comfortable with. I personally prefer the first solution since it is faster and requires no algebra.