You are less than 50 you are divisible by 3 When divided by 5 you have a reminder of 2 Add or subtract 10 and you become a prime number you only have two factors apart from 1 and yourself?

Answer 1

If the number has a remainder of 2 when divided by 5, it must end in either 2 or 7. Because adding 10 to a number ending in 2 will not be a Prime number, it must end in 7. Because you will have a prime number if you subtract 10, it must be greater than 10. The possible numbers are:

17

27

37

47

The only one of these that is divisible by 3 is 27. If you subtract 10 from 27, you have 17, which is a prime number. If you add 10 to 27, you have 37, which is a prime number. The factors of 27 are 1, 3, 9, and 27, so it has only two factors other than 1 and itself. When divided by 5, the result is 5 remainder 2. Thus, 27 fits all the conditions.