$N$ leaves a remainder of $4$ when divided by $33$, what are the possible remainders when $N$ is divided by $55$?
My approach :
Number has to be $33k+4$ Possible remainders will be $(33k+4)/55 = 33k/55 + 4/55 = \text{remainder of $\left(3k/5 + 4/55\right)$} = \text{remainder of $(3k/5)$ + Remainder of $(4/55)$}$
Since, remainder of $3k/5$ will be $1,2,3,4$
And also remainder of $4/55$ will be $4$
So, remainder can be $5,6,7,8$
I think there is some fundamental logical flaw with my approach. Please let me know what it is.