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      Question

      The square of 12 is subtracted from 25 times a whole

      number, and the result is equal to the square of that number. Find the square of the difference between the possible values of the whole number.
      A 121 Correct Answer Incorrect Answer
      B 49 Correct Answer Incorrect Answer
      C 225 Correct Answer Incorrect Answer
      D 16 Correct Answer Incorrect Answer
      E 81 Correct Answer Incorrect Answer

      Solution

      Let the number be 'x' ATQ, Or, 25x - 122 = x2 Or, x2 - 25x + 144 = 0 Or, x2 - 16x - 9x + 144 = 0 Or, x(x - 16) - 9(x - 16) = 0 Or, (x - 16) (x - 9) =0 So, 'x' = 16 or 9 So, difference between the possible values of the number = 16 - 9 = 7 Therefore, required value = 72 = 49

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