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One value added to a set changes its mean: find the value or the new mean

This type of question, asked 4 times: CDS 2 2016, CDS 1 2017, CDS 2 2020, CDS 2 2024. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    89
    A cricketer has a certain average of 10 innings. In the eleventh inning he scored 108 runs, thereby increasing his average by 6 runs. What is his new average ?

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  2. Question 2

    CDS 1 2017

    51
    The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number ?

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  3. Question 3

    CDS 2 2020

    95
    The ages of 7 family members are 2, 5, 12, 18, 38, 40 and 60 years respectively. After 5 years a new member aged xx years is added. If the mean age of the family now goes up by 1.5 years, then what is the value of xx ?

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  4. Question 4

    CDS 2 2024

    21
    The arithmetic mean of nn numbers is MM. If the sum of first (n−1)(n - 1) terms is kk, then what is the nnth number ?

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