If n is a positive integer, is n/18 an integer?

Manhattan OE:

(1) SUFFICIENT: We are told that 5n/18 is an integer. This allows us to determine that n/18 is an integer—in order for 5n to be divisible by 18, 5n must contain all the prime factors of 18 (3, 3, and 2). Since 5 does not contain any of these prime factors, n must contain ALL of them. Therefore, n has 3, 3, and 2 as prime factors, so n is divisible by 18, and n/18 is an integer.

(2) INSUFFICIENT: We are told that 3n/18 is an integer. This does not allow us to determine that n/18 is an integer—in order for 3n to be divisible by 18, 3n must contain all the prime factors of 18 (3, 3, and 2). However, 3 contains one of those prime factors (3), so n might only contain a 3 and a 2. Therefore, we cannot determine whether n has 3, 3, and 2 as prime factors, so n might not be divisible by 18 and n/18 might not be an integer. (For example, n could equal 6, or it could equal 18.)

The correct answer is A.