Hey thanks for explaining, I still have few doubts..
Sum up A) and B): X-Y+X+Y=5a+1+5b+2 -> 2X=5(a+b)+3: when 2X is divided by 5, the remainder is 3. Then, when X is divided by 5, the remainder is 4, as the only values that satisfy 2X=5(a+b)+3 are 4; 9; 14... etc.
Subtract A) from B): X+Y-X+Y=5b+2-5a-1 -> 2Y=5(b-a)+1: when 2X is divided by 5, the remainder is 1. Then, when Y is divided by 5, the remainder is 3, as the only values that satisfy 2Y=5(b-a)+1 are 3; 8; 13... etc.
Now, knowing that:
- X divided by 5 gives remainder 4, and
- Y divided by 5 gives remainder 3
we can calculate the remainder when is divided by 5, and the answer is C.
So does that mean , you have not considered (a+b) to be even in this case as stated below? why dint I get a remainder of 1.5 in the above case ? I think I understood but you know I am not there yet
2. n is even, i.e. n=2m (m is integer), then , which means, that when X is divided by 5, the "remainder" is 3/2
skpMatcha wrote:
Guys, I just heard about remainder theorm today
can you please explain me this statement ?
Sum up A) and B):
Quote:
X-Y+X+Y=5a+1+5b+2 -> 2X=5(a+b)+3: when 2X is divided by 5, the remainder is 3.
It is clear till above statement. Then part went right above my head, can you please walk me through this...
Quote:
Then, when X is divided by 5, the remainder is 4, as the only values that satisfy 2X=5(a+b)+3 are 4; 9; 14... etc.
Ok, lets just simplify this part. We know, that when 2X is divided by 5, the remainder is 3, i.e. 2X=5n+3 (actually, n=a+b, if we want to link it with the main question, but for simplicity it is better to use only one variable). Now, if we want to know what will be the remainder when X is divided by 5, we can use the equation 2X=5n+3, dividing it by 2. As n is integer, there are 2 possibilities: n is odd or n is even.
1. n is odd, i.e. n=2m+1 (m is integer), then \(X=\frac{2X}{X}=\frac{5n+3}{2}=\frac{5*(2m+1)+3}{2}=\frac{5*2m+5+3}{2}=5m+\frac{8}{2}\), which means, that when X is divided by 5, the remainder is 4, which is the case, considered by
Quote:
Then, when X is divided by 5, the remainder is 4, as the only values that satisfy 2X=5(a+b)+3 are 4; 9; 14... etc.
2. n is even, i.e. n=2m (m is integer), then \(X=\frac{2X}{X}=\frac{5n+3}{2}=\frac{5*2m+3}{2}=5m+\frac{3}{2}\), which means, that when X is divided by 5, the "remainder" is 3/2