If the sum of 'n' consecutive integers is 0, then which of the following statement(s) must be true?
A. 'n' is an even number
B. 'n' is an odd number
C. The average of the 'n' integers is 0
D. None of these
Solution(By Examveda Team)
Go through the option checking,Starting from three,
The average of n integers is 0.
It means, integers are like this
0
-1, 0, 1
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3 and so on.
Thus, average of n numbers is zero. Means three is true.
As, Average = Sum/terms.
See, number of terms are either 1, 3, 5, 7 or so on. It means n would be always an odd.
So, n is an odd number and average of n integer is 0.
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For every integer a, a+(-a) = 0
Therefore, by pairing 1 with (-1), 2 with (-2), and so on, one can see that in order to get the sum to
be zero, a list of consecutive integers must contain the same number of positive integers as the
number of negative integers. In addition to that it should also contain the integer '0'.
Therefore, the list has an odd number of consecutive integers and their average will also be 0.
So, b and c are definitely true.
Correct answer = B & C