CAT 2007 — QA Question 23
Basics of AverageEasy
Consider the set S = {2, 3, 4, ..., 2n + 1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?
Answer & solution
Correct answer: 1
- A
0
1
- C
n/2
- D
n + 1/2n
- E
2008
Solution
Y = (2 + 4 + 6 + 8 + … + 2n)/n
Average of numbers in AP is same as average of first and the last terms.
âââââââ⇒ 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.
⇒ ââX = (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).