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What is the median of a set of consecutive integers if the sum of

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PrepTap
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What is the median of a set of consecutive integers if the sum of [#permalink] New post   Updated on: 06 May 2015, 23:59
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What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 100?

    A. 10
    B. 25
    C. 50
    D. 75
    E. 100

This question is a part of the series of original questions posted by PrepTap. Follow us to receive more questions like this.
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C

Originally posted by PrepTap on 28 Apr 2015, 08:29.
Last edited by PrepTap on 06 May 2015, 23:59, edited 1 time in total.
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Lucky2783
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Re: What is the median of a set of consecutive integers if the sum of [#permalink] New post   28 Apr 2015, 09:44
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Surprisingly no one answered this easy one.

property of a set of consecutive integerz.

mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.

So mean=median=100/2=50
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Re: What is the median of a set of consecutive integers if the sum of [#permalink] New post   07 Jun 2016, 01:21
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PrepTap wrote:
What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 100?

    A. 10
    B. 25
    C. 50
    D. 75
    E. 100

This question is a part of the series of original questions posted by PrepTap. Follow us to receive more questions like this.



nth term from start: a+ (n-1) [ common difference is 1]; a is the first term.

nth term from end: l+(n-1) (-1) [here common difference would be -1]; l is the last term.

(a+n-1) + (l-n+1) = a+ l = 100.

In case of consecutive integers or an AP.

Mean = median = 0.5 * (First term+ Last term) = 0.5 * 100 = 50.

C is the answer.
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Re: What is the median of a set of consecutive integers if the sum of [#permalink] New post   04 Nov 2019, 07:44
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If the nth term, counted from the beginning and the end, sums up to 100, it needs to be an uneven amount of numbers in this set, meaning that both ways (from the beginning and the end) arrive at the number 50. Only 50+50 equals 100.
50 is therefore, the middle number, the mean.
Answer: C
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Re: What is the median of a set of consecutive integers if the sum of [#permalink] New post   22 Feb 2024, 01:48
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Re: What is the median of a set of consecutive integers if the sum of [#permalink]
22 Feb 2024, 01:48
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