If a positive integer n is divided by 5 then the remainder is 3. Which of the following numbers gives remainder 0, when it is divided by 5?n-2n+3n+1n+2

The problem states that when a positive integer n is divided by 5, the remainder is 3. This means that n can be written in the form 5k + 3, where k is some integer.

Let's check each of the given options:

1. n - 2: Substituting n = 5k + 3 into this gives 5k + 3 - 2 = 5k + 1. This is not divisible by 5, so it cannot be the answer.

2. n + 3: Substituting n = 5k + 3 into this gives 5k + 3 + 3 = 5k + 6. This is not divisible by 5, so it cannot be the answer.

3. n + 1: Substituting n = 5k + 3 into this gives 5k + 3 + 1 = 5k + 4. This is not divisible by 5, so it cannot be the answer.

4. n + 2: Substituting n = 5k + 3 into this gives 5k + 3 + 2 = 5k + 5. This is divisible by 5, so it is the answer.

Therefore, n + 2 is the number that gives a remainder of 0 when divided by 5.