Question

At Annville Junior High School, $30\%$ of the students in the Math Club are in the Science Club, and $80\%$ of the students in the Science Club are in the Math Club. There are $15$ students in the Science Club. How many students are in the Math Club?

$12$

$15$

$30$

$36$

$40$

Answer: E

Concepts:percentage

Difficulty rating: 1180

Solution:

Since $80\%$ of the $15$ Science Club students are also in the Math Club, the two clubs overlap in $0.8\cdot 15=12$ students. This is $30\%$ of the Math Club, so the Math Club has $\dfrac{12}{0.3}=40$ students.

Thus, the correct answer is E .

1998 AMC 8 Problem 14

Answer: E

Difficulty rating: 1180

Solution:

Problem 14 in Other Years