AMC10 2004 A

AMC10 2004 A · Q13

AMC10 2004 A · Q13. It mainly tests Counting & probability misc.

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?

在一次派对上，每个男人与恰好三个女人跳舞，每个女人与恰好两个男人跳舞。有12个男人参加派对。有多少女人参加派对？

(A) 8 8

(B) 12 12

(D) 18 18

(E) 24 24

Answer

Correct choice: (D)

正确答案：（D）

Solution

Because each man danced with exactly three women, there were $(12)(3) = 36$ pairs of men and women who danced together. Each woman had two partners, so the number of women who attended is $36/2 = 18$.

因为每个男人与恰好三个女人跳舞，所以有$(12)(3)=36$对男人和女人的舞伴对。每个女人有两个舞伴，因此参加的女人数量是$36/2=18$。

Topics

CP.015 Counting & probability misc