Solution: 2014 Winter Final - 6
Author: Michiel SmidQuestion
In a group of 150 people,
- 30 weigh at least 150 pounds,
- 60 are at least 6 feet tall,
- 70 weigh less than 150 pounds and are less than 6 feet tall.
(a)
10
(b)
30
(c)
20
(d)
40
Solution
Let’s break it down
Let S = All people
Let A = Weigh at least 150 pounds
Let B = At least 6 feet tall
$ |S| = 150 $
$ |A| = 30 $
$ |B| = 60 $
$ |\overline{A \cap B}| = 70 $
$ |A \cup B| = S - |\overline{A \cup B}| = 150 - 70 = 80 $
$ | A \cup B| = |A| + |B| - |A \cap B| $
$ 80 = 30 + 60 - |A \cap B| $
$ 80 - 30 - 60 = -|A \cap B| $
$ -10 = -|A \cap B| $
$ |A \cap B| = 10 $