Explanation

When dealing with remainder questions on the GRE, the best thing to do is test a few real numbers:

Multiples of 6 are 0, 6, 12, 18, 24, 30, 36, etc.

Numbers with a remainder of 4 when divided by 6 are those 4 greater than the multiples of 6:

x could be 4, 10, 16, 22, 28, 34, 40, etc.

You could keep listing numbers, but this is probably enough to establish a pattern.

(A) \(\frac{x}{2}\) → ALL of the listed x values are divisible by 2. Eliminate (A).

(B) \(\frac{x}{3}\) → NONE of the listed x values are divisible by 3, but continue checking.

(C) \(\frac{x}{7}\) → 28 is divisible by 7.

(D) \(\frac{x}{11}\) → 22 is divisible by 11.

(E) \(\frac{x}{18}\) → 34 is divisible by 17.

The question is “Each of the following could also be an integer EXCEPT.” Since four of the choices could be integers, (B) must be the answer.