Question

Difference between two even numbers after and before 2n, where n is a positive number.
A) 0.
B) 4.
C) 2.
D) 6.

Answer 1

Hint: We will first try to see what are the successive even numbers that are present before and after 2n. Then after calculating the value both the numbers after and before 2n we will subtract them to get the desired result.

Complete step-by-step answer:
We have to calculate the difference between two even numbers after and before 2n.
To do so we first need to calculate two even numbers which are present before and after 2n.
Because even numbers are multiple of 2.
Therefore, any number even, before 2n would be of the form 2n-2.
Hence, we obtain the number even and which is before 2n as 2n-2.
Similarly, we will proceed to determine a number after 2n, which is even.
Any number even, after 2n is of the form 2n+2.
Hence, we obtain the number even and which is after 2n as 2n+2.
Now we have two even numbers before and after 2n as 2n-2 and 2n+2 respectively.
Finally, we will subtract them to get the result.
Let the difference be denoted as D.
Therefore, the difference D, between the two terms is given by,
D = 2n + 2 − (2n − 2)
\[\Rightarrow \]D = 2n – 2n + 2 + 2
\[\Rightarrow \]D = 4.
Therefore, we get the required result as the value of the difference as D = 4.
So option (B) is correct.

Note: The possibility of error in these types of questions can be at the point where you have to subtract 2n + 2 and 2n-2. Always remember that while calculating the difference (2n-2) would be in brackets to reduce calculation mistakes in the solution.