Last year 100 adult cats, half of whom were female, were brought into the Smallville Animal Shelter. Half of the adult female cats were accompanied by a litter of kittens. The average number of kittens per litter was 4. What was the total number of cats and kittens received by the shelter last year?
$\textbf{(A)}\ 150\qquad\textbf{(B)}\ 200\qquad\textbf{(C)}\ 250\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 400$
Half of the 100 adult cats are female, so there are $\frac{100}{2}$ = $50$ female cats.  Half of those female adult cats have a litter of kittens, so there would be $\frac{50}{2}$ = $25$ litters.  Since the average number of kittens per litter is 4, this implies that there are $25 \times 4$ = $100$ kittens.  So the total number of cats and kittens would be $100 + 100$ = $\boxed{\textbf{(B)}\ 200}$