The price of Chrysler stock increased on 30% of the trading days.The price of Ford stock increased on 40% of the trading days over the past year.On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well.On what proportion of the days did neither stock increase in price?
A).82
B).46
C).54
D).30
E).88

Question

Quizplus · Accepted Answer

On 40% of the days, Ford's stock increased. Since Chrysler's stock also increased on 60% of these days, this means 0.6 * 40% = 24% of the days saw both stocks increase. Since Chrysler's stock increased on 30% of the days, and we know 24% of those days overlap with Ford's increases, only 6% of the days saw only Chrysler's stock increase. Therefore, 40% - 24% = 16% of the days saw only Ford's stock increase. Adding the days when neither stock increased, we get 100% - (24% + 6% + 16%) = 54%.

The Price of Chrysler Stock Increased on 30% of the Trading