CAT 2023 Slot 2 Solved Paper

It is given that k divides m+2n and 3m+4n.
Since k divides (m+2n), it implies k will also divide 3(m+2n). Therefore, k divides 3m+6n.
Similarly, we know that k divides 3m+4n.
We know that if two numbers a, and b both are divisible by c, then their difference (a-b) is also divisible by c.
By the same logic, we can say that {(3m+6n)−(3m+4n)} is divisible by k. Hence, 2n is also divisible by k.
Now, (m+2n) is divisible by k, it implies 2(m+2n)=2m+4n is also divisible by k.
Hence, {(3m+4n)−(2m+4n)}=m is also divisible by k.
Therefore, m, and 2n are also divisible by k.
The correct option is C