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If a positive integer n is divided by 5, the remainder is 3. Which of the numbers below yields a remainder of 0 when it is divided by 5? 
  • a)
    n + 3
  • b)
    n + 2
  • c)
    n - 1
  • d)
    n - 2
  • e)
    n + 1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If a positive integer n is divided by 5, the remainder is 3. Which of ...
n divided by 5 yields a remainder equal to 3 is written as follows 
n = 5 k + 3 , where k is an integer. 
add 2 to both sides of the above equation to obtain 
n + 2 = 5 k + 5 = 5(k + 1) 
The above suggests that n + 2 divided by 5 yields a remainder equal to zero. The answer is B.
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If a positive integer n is divided by 5, the remainder is 3. Which of ...
Solution:

Given, n leaves a remainder of 3 when divided by 5.

Let's take some values of n that leave a remainder of 3 when divided by 5.

n = 3, 8, 13, 18, 23, 28, ....

If we observe these values, we can see that they all leave a remainder of 3 when divided by 5.

Now, let's check which of the given options yield a remainder of 0 when divided by 5.

a) n + 3

If we add 3 to n, the remainder will still be 3 when divided by 5. Therefore, option (a) is not correct.

b) n + 2

If we add 2 to n, the remainder will be 0 when divided by 5.

For example, if n = 3, then n + 2 = 5 which is divisible by 5.

Therefore, option (b) is the correct answer.

c) n - 1

If we subtract 1 from n, the remainder will still be 2 when divided by 5. Therefore, option (c) is not correct.

d) n - 2

If we subtract 2 from n, the remainder will still be 1 when divided by 5. Therefore, option (d) is not correct.

e) n + 1

If we add 1 to n, the remainder will still be 4 when divided by 5. Therefore, option (e) is not correct.

Therefore, the correct answer is option (b) n + 2.
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Community Answer
If a positive integer n is divided by 5, the remainder is 3. Which of ...
N+2(B)
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