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2011 AMC 10A Problem 6

Problem 6 of 25EasierAlgebraCounting & Probability

Set AA has 2020 elements, and set BB has 1515 elements. What is the smallest possible number of elements in AB,A \cup B, the union of AA and B?B?

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Solution

To minimize the number of elements in the union, we want to maximize the overlap between the two sets. We can then assume that BB is contained completely within A,A, which means that the union is the same as A,A, which has 2020 elements. Thus, C is the correct answer.

More practice

Concepts: Venn Diagram · bounding to limit cases

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.