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Two natural numbers: from cube/sum/difference/product facts, find another

This type of question, asked 7 times: 18 Jul 2023 S1, 19 Jul 2023 S4, 24 Jul 2023 S3, 25 Jul 2023 S3, 26 Jul 2023 S4, 27 Jul 2023 S1, 27 Jul 2023 S3. All 8 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    18 Jul 2023 S1

    54
    The cube of the difference between two given natural numbers is 1728, while the product of these two given numbers is 108. Find the positive difference between the cubes of these two given numbers.

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  2. Question 2

    18 Jul 2023 S1

    51
    The cube of the difference between two given natural numbers is 1728, while the product of these two given numbers is 108. Find the sum of the cubes of these two given numbers.

    Tap an option to check your answer.

  3. Question 3

    19 Jul 2023 S4

    56
    The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the sum of the cubes of the two given numbers.

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  4. Question 4

    24 Jul 2023 S3

    57
    The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the product of the two given numbers?

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  5. Question 5

    25 Jul 2023 S3

    51
    The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the positive difference between the cubes of the two given numbers.

    Tap an option to check your answer.

  6. Question 6

    26 Jul 2023 S4

    57
    The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the product of the two given numbers?

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  7. Question 7

    27 Jul 2023 S1

    51
    The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?

    Tap an option to check your answer.

  8. Question 8

    27 Jul 2023 S3

    54
    The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the positive difference between the cubes of the two given numbers?

    Tap an option to check your answer.