18. There are 66 cats in my street. I don't like 21 of them because they catch mice. Of the rest, 32 have stripes and 27 have one black ear. The number of cats with both stripes and one black ear is as small as it could possibly be. How many cats have both stripes and one black ear?
A 5
B 8
C 11
D 13
E 14
SOLUTION
$\mathbf{E}$

The information in the question tells us that the number of cats in my street that don't catch mice is $66-21=45$. Of these 45 , let the number of cats with both stripes and one black ear be $X$ and let the number of cats with neither stripes nor one black ear be $Y$. Since 32 cats have stripes and 27 have one black ear, we have $32+27-X+Y=45$ and hence that $14+Y=X$. We are told that the number of cats with both stripes and one black ear is as small as possible and hence that number is 14 with no cats having neither stripes nor one black ear.