Weird prime numbers question

Question

The sum of 2 postive prime numbers is a prime number and 3 times that sum is an odd number. Which of the following prime numbers must be one of the original prime numbers??

 

A)2

B)3

C)5

D)7

E)11

 

I have tried plugging in prime numbers of each of the senarios and I keep on getting that none of them of work however there is obviously a right answer. Please help.

Answer 1

Use the fact that all prime numbers are odd except 2.

 

Suppose neither of the original prime numbers is 2.  That means that they are both odd, and therefore their sum is even.  (Odd + odd always equal even.)  Multiply that by 3 and you still have an even number.  (Even times anything is even.)  Since the result is supposed to be odd, this means that our original assumption (neither prime = 2) can't be correct.  So one of the numbers HAS to be 2, and answer is A

 

Answer 2

TEST