Step 1: Count the divisors of 1 instead of quoting the definitions.
A cleaner way to settle this is to just count how many positive divisors the number 1 has, then compare that count to what prime numbers and composite numbers need.
The only positive number that divides 1 exactly is 1 itself. So 1 has exactly one divisor.
Step 2: Check the divisor-count rule for primes.
A prime number must have exactly two different divisors: 1 and the number itself. For example, 7 has divisors 1 and 7, so it has two divisors.
Since 1 has only one divisor, not two, it fails the test for being prime.
Step 3: Check the divisor-count rule for composites.
A composite number must have more than two divisors (at least three, since it can be split into smaller factors besides 1 and itself).
Since 1 has only one divisor, it also fails the test for being composite, because one divisor is less than the three or more that a composite number needs.
Step 4: Final Answer.
Since 1 has exactly one divisor, and both prime and composite numbers need more than one divisor by their own definitions, 1 fits neither group. It is neither prime nor composite, so option (D) is correct.
\[ \boxed{\text{Neither prime nor composite}} \]