2004 AMC 10A Problem 6

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

Bertha has

30 - 6 = 24

granddaughters, and none of them have daughters

The granddaughters come in groups of

6,

so find how many daughters are mothers

Bertha has

30 - 6 = 24

granddaughters, none of whom have daughters.

These granddaughters belong to

\frac{24}{6} = 4

of Bertha’s daughters. So exactly

4

women have daughters, and the number with no daughters is

30 - 4 = 26.

Thus, the correct answer is E.

Problem 6 in other years