2012-06-15 09:00:17

A certain club cannot accept all members and uses a process to sort potential members.  ¼ of all applicants are rejected in the first step of this process, which eliminates applicants randomly. Of the remaining number of applicants, 2/3 are eliminated after someone reads through their applications. In the final stage of the process, a committee of three members meets with individual applicants and uses those meetings to eliminate ¾ of all remaining applicants. Those who survive all three rounds are granted membership. Last year, the club accepted 225 members. How many applicants did it have?

The correct choice is 3600

Explanation: Take this problem step-by-step, starting from the final step. 225 members is ¼ of those who met with the committee. Thus, there were 4 times as many applicants as were accepted at that stage. This means that there were 900 applicants who met with the committee. 900 is 1/3 of the number of applicants who got to round two (since 2/3 of those applicants were rejected), meaning there were 2700 applicants who survived the initial random purge. 2700 represents ¾ of the total applicants, since ¼ of the total applicants were rejected randomly. This means there were 3600 total applicants, since ¾ of 3600 is 2700.