Question

A is a set of even integers, while B is a set of integers that are multiples of $3$. There are $16$ integers in set A, $22$ integers in set B, and $7$ integers in both sets. How many integers are in exactly one of the two sets?

• A. $22$
• B. $24$
• C. $27$
• D. $26$

Answer 1

Answer: (B)

$24$

Use a Double-Set Matrix to solve this problem. First, fill in the numbers given in the problem: $16$ integers in set A (first column total) and $22$ integers in set B (first row total). There are $7$ integers in both sets (first row, first column). Next, use subtraction to figure out that there are $9$ integers in set A but not in set B and $15$ integers in set B but not in set A. Finally, add those two numbers: $9+15=24$.

Set A NOT Set A Total

Set B $7$ $15$ $22$

Not Set B $9$

Total $16$