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Which of the following must be true?

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stonecold
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Which of the following must be true? [#permalink] Which of the following must be true?   06 Aug 2016, 21:45
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Which of the following must be true?
A) The Average of 93 Consecutive Even integers must be an even integer.
B) The Average of 94 Consecutive Even integers must be an even integer.
C) The Average of N Consecutive is an integer only if N is Odd.
D) For a set of N consecutive integers the Average would be equal to its Median.

1)All of them
2)A,B,D
3)B,C,D
4)A,C,D
5)A,D
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abhimahna
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Which of the following must be true? [#permalink] Which of the following must be true?   06 Aug 2016, 23:26
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stonecold wrote:
Which of the following must be true?
A) The Average of 93 Consecutive Even integers must be an even integer.
B) The Average of 94 Consecutive Even integers must be an even integer.
C) The Average of N Consecutive is an integer only if N is Odd.
D) For a set of N consecutive integers the Average would be equal to its Median.

1)All of them
2)A,B,D
3)B,C,D
4)A,C,D
5)A,D


An easy one.

A) The Average of 93 Consecutive Even integers must be an even integer. --> Average of N consecutive Even integers is the middle number if N is odd. Hence, since the middle number is Even, Hence this is statement is true.

B) The Average of 94 Consecutive Even integers must be an even integer. --> Average of N consecutive Even integers is the mean of two middle numbers if N is Even. Hence, since the middles number are both even, their mean would be ODD, Hence this is statement is False.

C) The Average of N Consecutive is an integer only if N is Odd. --> Mean is equal to the middle term if N is odd. Hence True.

D) For a set of N consecutive integers the Average would be equal to its Median. --> if Terms are in AP, Mean=Median. Hence True.
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Re: Which of the following must be true? [#permalink] Which of the following must be true?   09 Oct 2020, 07:02
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A) The Average of 93 Consecutive Even integers must be an even integer.

This must be TRUE as they are consecutive integers then Mean = Median and Median of 93 numbers(ODD) will be 47^{th} number which is EVEN in the series.

B) The Average of 94 Consecutive Even integers must be an even integer.

The average will be an ODD not Even as for 94 numbers median or mean being the same will be the average of Two even numbers. The average of two even numbers is ODD.

C) The Average of N Consecutive is an integer only if N is Odd.

Already have seen close in option A. So, be it consecutive even or odd or complete list of integers. The average will be N if N is odd.

D) For a set of N consecutive integers, the Average would be equal to its Median.

This is the logic applied in options A and B.

Answer D
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Re: Which of the following must be true? [#permalink]
09 Oct 2020, 07:02