2004 AMC 12A Problems/Problem 4
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- The following problem is from both the 2004 AMC 12A #4 and 2004 AMC 10A #6, so both problems redirect to this page.
Problem
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 grand-daughters have no daughters?
Solution
Since Bertha has 6 daughters, Bertha has 
granddaughters, of which none have daughters. Of Bertha's daughters, 
have daughters, so 
do not have daughters.
Therefore, of Bertha's daughters and granddaughters, 
do not have daughters 
.
OR
Draw a tree diagram and see that the answer can be found in the sum of 6 + 6 granddaughters, 5 + 5 daughters, and 4 more daughters.
See also
| 2004 AMC 12A (Problems) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| 2004 AMC 10A (Problems) | ||
| Preceded by Problem 5 | Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
