2004 AMC 10A Problem 13

Below is the professionally curated solution for Problem 13 of the 2004 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 10A solutions, or check the answer key.

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Concepts:double counting counting pairs

Difficulty rating: 1190

13.

At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party?

$8$

$12$

$16$

$18$

$24$

Solution:

The number of dancing pairs is $12 \cdot 3 = 36,$ counting from the men's side. Each woman was in exactly $2$ pairs, so the number of women is $\dfrac{36}{2} = 18.$

Thus, the correct answer is D.

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