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

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) (Show Source): You can put this solution on YOUR website!

Answer by richard1234(7193) (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.
RELATED QUESTIONS
1: sum of all the four digit nos by 0, 1, 2,3 2: two nos. m and n when divided by 6... (answered by CubeyThePenguin)
Prove: If m and n are integers, then 4 is divisible by (m + n)^2 -... (answered by math_tutor2020)
Let n be a three digit number and let m be the number obtained by reversing the order of... (answered by ankor@dixie-net.com,KMST)
Prove the following statement. If n=m^3-m for some integer m, then n is a multiple of... (answered by jsmallt9)
2. Indicate which of the following are valid type int , double , or char constants in C... (answered by ikleyn)
The polynomial 3x^3+mx^2+nx-8 is divisible by 3x-2 where m and n are constants .If the... (answered by josgarithmetic,greenestamps)
Suppose n is divisible by 8 but not by 3. Then which of the following CANNOT be an... (answered by Edwin McCravy,Theo)
Prove: if 3 is not divisible by m * n, then 3 is not divisible by m and 3 is not... (answered by math_tutor2020,ikleyn)
If the integers m and n are chosen at random from 1 to 100, then what is the probability... (answered by MathLover1,ikleyn)