2011 AMC 10A Problem 6

Question

Set

A

has

20

elements, and set

B

has

15

elements. What is the smallest possible number of elements in

A \cup B,

the union of

A

and

B?

5

15

20

35

300

The union must contain all elements of the larger set

Make

B

a subset of

A

to minimize the union

To minimize the number of elements in the union, we want to maximize the overlap between the two sets.

We can then assume that

B

is contained completely within

A,

which means that the union is the same as

A,

which has

20

elements.

Thus, C is the correct answer.

Problem 6 in other years