To find the number that yields a remainder of 0 when divided by 5, we need to understand the concept of remainders and how they are affected by addition and subtraction.

Let's assume the positive integer n is divided by 5, and the remainder is 3. This can be expressed as:

n = 5a + 3

where a is a positive integer representing the quotient.

To find a number that yields a remainder of 0 when divided by 5, we need to find a value of n that satisfies the equation:

n = 5b + 0

where b is a positive integer representing the quotient.

Let's analyze the answer options:

a) n + 3: Adding 3 to the number n will not change the remainder when divided by 5. It will still be 3, so this option does not yield a remainder of 0.

b) n + 2: Adding 2 to the number n will increase the remainder by 2 when divided by 5. Since the remainder was originally 3, adding 2 will result in a remainder of 0. This option satisfies the condition and yields a remainder of 0.

c) n - 1: Subtracting 1 from the number n will decrease the remainder by 1 when divided by 5. Since the remainder was originally 3, subtracting 1 will result in a remainder of 2. This option does not yield a remainder of 0.

d) n - 2: Subtracting 2 from the number n will decrease the remainder by 2 when divided by 5. Since the remainder was originally 3, subtracting 2 will result in a remainder of 1. This option does not yield a remainder of 0.

e) n + 1: Adding 1 to the number n will increase the remainder by 1 when divided by 5. Since the remainder was originally 3, adding 1 will result in a remainder of 4. This option does not yield a remainder of 0.

Therefore, the only option that yields a remainder of 0 when divided by 5 is option b) n + 2.