Question : 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?
Option 1: 160
Option 2: 240
Option 3: 200
Option 4: 320
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Correct Answer: 240
Solution : Let the numbers be x and y. So, x3 – y3 = 6272 and (x – y) = 8 Cubing both sides of the given expression, (x – y) = 8, ⇒ (x – y)3 = 83 ⇒ x3 – y3 – 3xy(x – y) = 512 ⇒ 6272 – 3xy × 8 = 512 ⇒ 24xy = 5760 ⇒ xy = 240 Hence, the correct answer is 240.
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Question : 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?
Option 1: 9728
Option 2: 9684
Option 3: 8000
Option 4: 9600
Question : 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?
Option 2: 320
Option 3: 240
Option 4: 200
Question : 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?
Option 1: 6272
Option 2: 5832
Option 3: 4662
Option 4: 7904
Question : 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.
Option 1: 4104
Option 2: 5616
Option 3: 2160
Option 4: 5626
Question : The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.
Option 1: 630
Option 2: 540
Option 3: 450
Option 4: 360
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