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      Question

      The sum of the squares of two numbers is 250, and the

      difference between the two numbers is 4. Find the absolute difference between the cubes of these two numbers.
      A 2133 Correct Answer Incorrect Answer
      B 1216 Correct Answer Incorrect Answer
      C 1468 Correct Answer Incorrect Answer
      D None of the above Correct Answer Incorrect Answer

      Solution

      Let, the two numbers be 'a' and 'b', such that, a > b.

      ATQ,

      a2 + b2 = 250

      a - b = 4

      (a - b) 2 = a2 + b2 + 2 X a X b

      Or, 42 = 250 + 2 X a X b

      Or, 2 X a X b = 250 - 16 = 234

      Or, a X b = 117

      a3 - b3 = (a - b) X (a2 + b2 + ab)

      Or, a3 - b3 = 4 X (250 + 117) = 4 X 367 = 1,468

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