You are increasing in increments of 3:

5, 8, 11, 14, ...

Every 2 increments is an increment of 6. Because the first and second terms are not divisible by 6, the entire sequence will never be divisible by 6.

Thanks Beny!

In your response, what do you mean by the first and second termm (3x??)?

The first term is 5 (x=1) and the second term is 8 (x=2).

If the sequence increases by multiples of 3, one of the first two terms must be divisible by 6 or else the entire sequence never will.

I.e.

3, 6, 9, 12

6, 9, 12, 15

9, 12, 15, 18

Clearly every other term would also be a multiple of 6 (since it's increasing by 6 every 2 increments). From the sequence given, you can quickly see no term will ever be divisible by 6.

Thanks Beny! Now I fully understand.

There's another explanation:

The equation for any number represented by a quotient, divisor and remainder is:

Y = Xq + r where q is the quotient and r is the remainder

for example: 8/3 = (3)2 + 2

y = 3x + 2 fits this equation perfectly. In other words y divided x has a quotient of 3 and a remainder of 2. What does this tell you? Y is not divisible by 3. If Y is not divisible by 3, it cannot be divisible by 6. So the answer is C.

This explanation is more complicated, but the ideas behind it help in more advanced number property type questions.

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

we have y = 3x +2

now 3x is a multiple of 3 hence divisible by 3

so 3x+2 will be 2 greater than 3x i.e 3x+2, hence not divisible by 3

so that means any nos having prime factor as 3 is the ans as it would not divide 3x +2

In the answer choices only 6 = 3 * 2 has 3 as a prime factor

so ans is C