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Missing digits of a number divisible by a composite (72, 24): test each coprime factor

This type of question, asked 3 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 26 Oct 2023 Tier II. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jan 2022 Tier II

    77
    If a 10-digit number 75462A97B6 is divisible by 72, then the value of 8A−4B\sqrt{8A - 4B} is:

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  2. Question 2

    3 Feb 2022 Tier II

    90
    If a nine-digit number 789x6378y789x6378y is divisible by 72, then the value of xyxy is:

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  3. Question 3

    26 Oct 2023 Tier II

    22
    A six-digit number 11p9q4 is divisible by 24. Then the greatest possible value for pq is:

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