How many prime numbers are there between 10 and 30 ?
(A) 4
(B) 7
(C) 6
(D) 3
(E) 5
Each prime number is divisible by exactly two numbers, 1 and itself.

Each of the even numbers $\{12,14,16,18,20,22,24,26,28\}$ is divisible by 1 and itself and also

by 2 .

Therefore the numbers $\{12,14,16,18,20,22,24,26,28\}$ are not prime.

Each of the numbers $\{15,21,27\}$ is divisible by 1 and itself and also by 3 .

Therefore the numbers $\{15,21,27\}$ are not prime.

The number 25 is divisible by 1 and itself and also by 5 , so it is not prime.

Each of the remaining numbers is divisible by exactly 1 and itself.

Thus, the list of prime numbers between 10 and 30 is $\{11,13,17,19,23,29\}$.

There are 6 prime numbers between 10 and 30 .

ANSWER: (C)