SOLUTION

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

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

y is not a multiple of 3, actually it's 2 more than a multiple of 3. Therefore, since y is not a multiple of 3, it cannot be a multiple of 6 either.

Answer: C.
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I hope there must be a better way to solve this question
But One method is :

Put different values of x : 0,1,2,3,4 ....
so y = 2, 5, 8, 11, 14, 17, 20, 23, 26 ...

Now checking for answer choices :
there is no multiple of 6 in the values of y

Hence Option C

Answer = C = 6

For any value of x as an integer, y = 3x+2 is not divisible by 6

We are given the following:

y = 3x + 2

y - 2 = 3x

(y - 2)/3 = x

In order for y - 2 to be divisible by 3, y must be 2 greater than a multiple of 3. Since y is 2 greater than a multiple of 3, y cannot actually be a multiple of 3. Thus, 6 CANNOT be a divisor of y.

Answer: C
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I applied a plug in technique and POE.
if x is 1; y is 5 (already present in options) so its a divisor of y
if x is 2 ; y is 8; again a divisor of y (basis options)
if x is 3; y is 11 - drop
if x is 4 ; y is 14 so 7 is a divisor
if x is 5; y is 17 drop
if x is 6; y is 20 so 4 and 5 are both divisors
if x is 7; y is 23
if x is 8; y is 26

thus 6 is only non divisor.

y = 3x+2
To solve it faster , lets start putting values in sequence
x = 0, y = 2
x = 1, y = 5
x = 2 , y = 8
x = 3, y = 11
x = 4, y = 14

So, it is divisible by 4,5,7,8 . It is not divisible by 6.
Answer C
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It took me a minute and 50 seconds to get this wrong, while Bunuel did it in about 10 seconds

pretty straight forward... for divisibility by 6 we need last digit to be 6... and when we see the cyclical nature of multiple of 3 we find no match which when added to 2 gives 6.....so answer is 6

A lotof integer properties questions can be answered by testing values. So, let's do that here.

KEY: x is an integer
So, if x = 1, then y = 3(1) + 2 = 5. Since 5 is a divisor of 5, we can ELIMINATE B
If x = 2, then y = 3(2) + 2 = 8. Since 4 and 8 are both divisors of 8, we can ELIMINATE A and E
If x = 3, then y = 3(3) + 2 = 11. Doesn't help us
If x = 4, then y = 3(4) + 2 = 14. Since 7 is a divisor of 14, we can ELIMINATE D
By the process of elimination, the correct answer is C

CONVENIONAL APPROACH:
Since 3x represents a multiple of 3 for all integer values of x, it must then be the case that (3x + 2) represents a value that’s 2 greater than some multiple of 3.
Since y = 3x + 2, we now know that y is 2 greater than some multiple of 3, which means y is NOT a multiple of 3.
In other words, 3 is NOT a divisor of y.

Key divisibility Rule: 6 is a divisor of y if and only if 3 and 2 are both divisors of y.
Since 3 is NOT a divisor of y, 6 cannot be a divisor of y.

Answer: C
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If a number is divisible by 6 then it is divisible by both 2 and 3. However, adding 2 to multiple of 3 makes it non-divisible by 3 and hence 6 is the correct answer.