A5. Frank has a drawer filled with loose socks. There are 10 red socks in it, and the rest of the socks are blue. He is going to blindly pick a number of socks from the drawer and wants to end up with two socks of a certain color. To be sure of having at least two red socks, he needs to pick twice as many socks as to be sure of having at least two blue socks. How many socks are there in total in the drawer?
A) 14
B) 18
C) 26
D) 32
E) 40
A5. D) 32 The number of blue socks in the drawer we call $b$. To be sure that he has two blue socks, Frank has to take 12 socks. In the worst case, he first picks the ten red socks. To be sure that he has two red socks, he has to take $b+2$ socks. In the worst case, he first picks the $b$ blue socks. It is given that this second number is twice as large as the first, so $b+2=2 \times 12=24$. From this it follows that $b=22$. The total number of socks is then $22+10=32$.