2004 AMC 12A Problem 4

Question

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

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

Every woman with daughters has exactly

6

of them

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.

Problem 4 in other years