AMC 10 Daily Practice Round 4
Complete problem set with solutions and individual problem pages
Bertha has daughters and no sons. Some of her daughters have daughters, and the rest have none. Bertha has a total of daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and grand-daughters have no children? (2004 AMC 10A Problems, Problem #6)
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Solution 1: Since Bertha has daughters, she 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. .
Solution 2: Bertha has granddaughters, none of whom have any daughters. The granddaughters are the children of of Bertha's daughters, so the number of women having no daughters is .
Draw a tree diagram and see that the answer can be found in the sum of granddaughters, daughters, and more daughters. Adding them together gives the answer of .
