2. Caitlin went for a long walk every day in October. Only on the 16 days when rain was expected did she take an umbrella. Of the 31 days in October, the rain forecast was correct on exactly 21 days. Fortunately, Caitlin always had her umbrella with her on the days it rained.

How many days did it not rain?
A) 6
B) 10
C) 16
D) 21
E) 25
A2. E) 25 We create a table of how many days it rains or does not rain, and how many days rain is predicted and Caitlin thus takes an umbrella or not.

|  |  | It rains? |  |
| :---: | :---: | :---: | :---: |
|  | Yes | No |  |
| Rain predicted? | Yes | $a$ | $b$ |
|  | No | 0 | $c$ |

It never happens that it rains but Caitlin does not have an umbrella, which is why there is a 0 in the lower left. For the other three numbers, it holds that $a+b+c=31$ (the number of days in October), $a+b=16$ (the number of days rain was predicted), and $a+c=21$ (the number of days the prediction was correct). We are looking for $b+c$, the number of days it did not rain. From $a+b+c=31$ and $a+b=16$ it follows that $c=15$. Combined with $a+c=21$, this means that $a=6$. Finally, $b+c=31-6=25$.

Alternative solution. On the $31-16=15$ days in October when no rain was expected, the prediction was apparently correct. So of the other 16 days (when rain was expected), the prediction was correct on only $21-15=6$ days. It rained on exactly 6 days, so it did not rain on $31-6=25$ days.