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Averages of the first k and last k items overlapping in one item: find that item

This type of question, asked 3 times: 9 Sep 2024 S2, 12 Sep 2025 S3, 21 Sep 2025 S1. All 3 questions below, oldest first.

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  1. Question 1

    9 Sep 2024 S2

    59
    The average temperature of a city for the first sixteen days of January is 22∘C22^\circ\text{C}, and the average temperature for the last sixteen days of the same month is 26∘C26^\circ\text{C}. If the average temperature for the entire month is 24∘C24^\circ\text{C}, what is the temperature on the sixteenth day?

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  2. Question 2

    12 Sep 2025 S3

    59
    The average of 11 numbers is 68. If the average of the first five is 63 and the average of the last five is 72, find the 6th number.

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  3. Question 3

    21 Sep 2025 S1

    66
    The average of a group of 11 numbers is 61. If the first six numbers have an average of 57 and the last six numbers have an average of 65, what is the sixth number?

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