2011 AMC 10A Problem 6 — Solution | LIVE by Po-Shen Loh

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2011 AMC 10A Problem 6

Below is the professionally curated solution for Problem 6 of the 2011 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10A solutions, or check the answer key.

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Concepts:Venn Diagram bounding to limit cases

Difficulty rating: 660

6.

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 $B?$

$5$

$15$

$20$

$35$

$300$

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 $B$ 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.

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Problem 6 in Other Years

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