2004 AMC 12A Problem 4

Problem 4 of 25EasierCombinatorics

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?

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Solution

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.

Tagged: basic counting