When $67$ is divided by a number $x$, a remainder of $3$ is obtained. If $x<50$, then the largest value of $x$ is:

If $67$ divided by $x$ leaves a remainder of $3$, then $(67-3)=64$ must be exactly divisible by $x$.Thus $x$ must be a factor of $64$.Factors of $64$ are: $1,2,4,8,16,32,64$.Since $x<50$, the possible values are $\{1,2,4,8,16,32\}$.The largest of these values is $32$.