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?
Question
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?
Solution
The question states that when a positive integer n is divided by 5, the remainder is 3. This means that n can be expressed in the form of 5k + 3, where k is any integer.
The numbers that give a remainder of 0 when divided by 5 are multiples of 5.
So, we need to find a number that is both a multiple of 5 and can be expressed in the form 5k + 3.
To do this, we can start by adding 5 to n (since adding a multiple of 5 to a number doesn't change its remainder when divided by 5).
So, n + 5 = 5k + 3 + 5 = 5k + 8.
This number is not a multiple of 5, so we add 5 again to get n + 10 = 5k + 13.
This number is also not a multiple of 5, so we add 5 again to get n + 15 = 5k + 18.
This number is also not a multiple of 5, so we add 5 again to get n + 20 = 5k + 23.
This number is also not a multiple of 5, so we add 5 again to get n + 25 = 5k + 28.
This number is a multiple of 5, so n + 25 is a number that gives a remainder of 0 when divided by 5 and can be expressed in the form 5k + 3.
So, the answer is n + 25.
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