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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 240.
Let the two numbers x and y, where x is the larger number
So, x - y = 8
⇒ (x - y)2 = 82
⇒ x2 - 2xy + y2 = 64 .....(1)
Also, x3 - y3 = 6272
⇒ (x - y)(x2 + xy + y2) = 6272
⇒ 8(x2 + xy + y2) = 6272
⇒ x2 + xy + y2 = 6272/8 = 784 .....(2)
Subtract equation (1) from equation (2),
3xy = 720
⇒ xy = 720/3 = 240
Therefore, the product of the two numbers is 240.