jmc

We know that every third whole number starting from one must be removed from the list. Since the greatest multiple of $3$ less than $100$ is $3\cdot 33=99$, this gives us a total of $33$ such numbers. We then consider the multiples of four. Every fourth whole number starting from one is a multiple of four and since $4\cdot 25=100$, this gives us $25$ such numbers. However, we also have to account for the numbers that are multiples of both $3$ and $4$ which we counted twice. These are the multiples of $12$ (the least common multiple of $3$ and $4$). Since $100÷12=8\text{ R}4$, we know that there are $8$ multiples of both $3$ and $4$. Thus, we have $33+25-8=50$ numbers that we removed from the list. Since there were $100$ whole numbers total, this leaves us with $100-50=\boxed{50}$ whole numbers.