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A set S consists of the integers {1, 2, 3, 4 . . . (2n + 1)}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of (X − Y)?
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
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29 Jun 2017, 04:42
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Bunuel
A set S consists of the integers {1, 2, 3, 4 . . . (2n + 1)}, where n is a positive integer. If X is the average of the odd integers in set S and Y is the average of the even integers in set S, what is the value of (X − Y)?
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
(A) 0
(B) 1/2
(C) 1
(D) 3/2
(E) 2
We know that the last digit of the S is odd
Pick any odd integer at the end
say 23
Number of odd integers will be 12
Number of even integers will be 11
Average of odd integers = (12*12)/12 (Sum of odd integers will be n(n+1))
Average of even integers = 11*12/11 (Sum of even integers will be n^2)
12-12 = 0
A
29 Jun 2017, 04:57
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Given data :
Set S : {1, 2, 3, 4 . . . (2n + 1)}
n is a positive number, X the average of odd numbers and Y the average of even number
We have been asked to find out what is the value of X-Y.
2n + 1 is definitely going to be odd(both if x is odd or even)
If n=3, 2n+1 = 7 (odd)
If n=2, 2n+1 = 5 (odd)
If n is 2, the last element in the set is 5.
The number of odd integers are 3 and numbers of even integers are 2.
The average of 3 odd numbers = \(\frac{(1+3+5)}{3}\) = 3
The average of 2 even integers are \(\frac{(2+4)}{2}\) = 3
The difference in 0(Option A)
Set S : {1, 2, 3, 4 . . . (2n + 1)}
n is a positive number, X the average of odd numbers and Y the average of even number
We have been asked to find out what is the value of X-Y.
2n + 1 is definitely going to be odd(both if x is odd or even)
If n=3, 2n+1 = 7 (odd)
If n=2, 2n+1 = 5 (odd)
If n is 2, the last element in the set is 5.
The number of odd integers are 3 and numbers of even integers are 2.
The average of 3 odd numbers = \(\frac{(1+3+5)}{3}\) = 3
The average of 2 even integers are \(\frac{(2+4)}{2}\) = 3
The difference in 0(Option A)
