Discussion

Explanation:

Y = (2 + 4 + 6 + 8 + … + 2n)/n
Average of numbers in AP is same as average of first and the last terms.
​​​​​​​⇒ Y = (2 + 2n)/2 = 1 + n

X = (3 + 5 + 7 + 9 + … + (2n + 1))/n
Average of numbers in AP is same as average of first and the last terms.
⇒ ​​X = (3 + 2n+1)/2 = 2 + n

∴ X – Y = 2 + n - (1 + n) = 1

Note: The information that 'n is a positive integer larger than 2007' does not affect the answer in any way.

Hence, option (b).

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