2016 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

Gaby lists the numbers $3, 4, 5, 6, 7, 8, \text{and} 9$ . In her list, the ratio of the number of prime numbers to the number of composite numbers is

$\textbf{(A)}\ 3:4 \qquad\textbf{(B)}\ 5:2 \qquad\textbf{(C)}\ 2:5 \qquad\textbf{(D)}\ 3:7 \qquad\textbf{(E)}\ 1:6$

First, we can list all of the numbers that are prime and then list all of the numbers are composite.

$3, 5, 7$ are the prime numbers

$4, 6, 8, 9$ are the composite numbers

Next, we can count how many numbers are prime and how many are composite. We see that $3$ are prime, while $4$ are composite.

Using this, the ratio of the number of prime numbers in the list to the number of composite numbers in the list is $\boxed {\textbf {(A) } 3:4}$

~anabel.disher