**Solution:**

No, every positive integer cannot be only of the form 4q + 2.

**Justification:**

Let a be any positive integer. Then by Euclid’s division lemma, we have

a = bq + r, where 0 ≤ r < b

Putting b = 4, we get

a = 4q + r, where 0 ≤ r < 4

Hence, a positive integer can be of the form,

4q, 4q + 1, 4q + 2 and 4q + 3.