2004 AMC 12A 第 4 题

Question

Bertha 有

6

个女儿，没有儿子。她的一些女儿各有

6

个女儿，其余女儿没有女儿。Bertha 一共有

30

个女儿和外孙女，并且没有曾外孙女。Bertha 的女儿和外孙女中，有多少人没有女儿？

Bertha has

6

daughters and no sons. Some of her daughters have

6

daughters, and the rest have none. Bertha has a total of

30

daughters and granddaughters, and no great-granddaughters. How many of Bertha’s daughters and granddaughters have no daughters?

22

23

24

25

26

先数外孙女，再确定有多少个女儿有孩子。

First count the granddaughters, then determine how many daughters have children

每个有女儿的人都恰好有

6

个女儿。

Every woman with daughters has exactly

6

of them

Bertha 有

30 - 6 = 24

个外孙女，她们都没有女儿。

这些外孙女是 Bertha 的

\frac{24}{6} = 4

个女儿所生，所以恰好有

4

人有女儿。

因此没有女儿的人数是

30 - 4 = 26

。

所以正确答案是 E。

Bertha has

30 - 6 = 24

granddaughters, none of whom have daughters.

These granddaughters are the children of

\frac{24}{6} = 4

of Bertha’s daughters, so exactly

4

women have daughters.

Therefore the number of women with no daughters is

30 - 4 = 26.

Thus, the correct answer is E.

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