Carcass wrote:
If p is a positive integer, which of the following could be a prime number?
(A) 8p
(B) 8p + 1
(C) 8p + 2
(D) 8p + 4
(E) 8p + 6
Kudos for the right answer and explanation
All of the options (A, C, D, and E) are multiple of 2:
8p = 2 * 4p
8p + 2 = 2 * (4p + 1)
8p + 4 = 2 * (4p + 2)
8p + 6 = 2 * (4p + 3)
Hence, they cannot be prime numbers (since prime numbers must only be divisible by 1 and itself)
Only option B: 8p + 1 does not apparently have any factors
Thus, it is the only one that CAN BE prime (it might not be prime as well - we cannot ensure that it is prime)
Option B