Which list contains only one prime number ? (A) 3,4,5,6 (B) 6,9,10,11 (C) 4,10,12,21 (D) 7,11,13,17......

Question

I got this question when I was doing my SOF Olympiad Practice.The Solution say's the answer is (B).But I don't understand how.....

Answer 1

A prime number is only divisible by itself and 1.

It has no other factors.

 

A has 2 prime numbers.. 3, 5

4 and 6 are not prime

because 4 has factors of 1, 2, 4

6 has factors of 1, 2, 3, 6

 

B has only one prime number.. 11

6, 9, 10 are not prime

9 has factors of 1, 3, 9

10 has factors of 1, 2, 5, 10

6 we already looked at

 

C has no prime numbers

4, 10, 12, 21 all have factors

other than one and themselves

 

D has 4 prime numbers

7, 11, 13, 17 are all prime.

 

Only set B has ONLY ONE PRIME

Answer 2

 A prime number is a number that is only divisible by itself and one. In Choice B, there is only one number in the list - 11-  that would be divisible by only itself and one.  That is why choice B is the correct answer. 

Answer 3

The key is that the question asks for the list with only one prime. (A) has 2 primes, (B) has one prime, 11, (C) has no primes, and (D) has four primes. So clearly option B has one and only one prime number,