15. Talulah plants 60 tulip bulbs. When they flower, she notes that half are yellow; one third of those which are not yellow are red; and one quarter of those which are neither yellow nor red are pink. The remainder are white. What fraction of the tulips are white?
A $\frac{1}{24}$
B $\frac{1}{12}$
C $\frac{1}{6}$
D $\frac{1}{5}$
E $\frac{1}{4}$
Solution: $\mathbf{E}$
Since half the 60 bulbs are yellow, 30 are yellow and 30 are not yellow. One third of the 30 bulbs that are not yellow are red, So 10 are red and 20 are neither yellow nor red. One quarter of the 20 that are neither yellow nor red, are pink. So 5 bulbs are pink. This leaves 15 bulbs which are neither yellow, nor red nor pink. So there are 15 white bulbs. Therefore the fraction of bulbs that are white is $\frac{15}{60}$, that is, $\frac{1}{4}$.