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.
If a positive integer n is divided by 5, the remainder is 3. Which of ...
N+2(B)