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      Question

      Two quantities are

      given as Quantity I and Quantity II. You have to determine the relationship between them and give the answer. Quantity I: (10x – 45)(143x – 60) = 0 Quantity II: A pouch has 6 red, 4 yellow, and 3 black cards. If three cards are drawn at random without replacement, what is the probability that none of them is black?
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I = Quantity II or Relation cannot be established Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I ≤ Quantity II Correct Answer Incorrect Answer

      Solution

      ATQ, From Quantity I, (10x – 45)(143x – 60) = 0 10x – 45 = 0 ⇒ x = 45/10 = 9/2 143x – 60 = 0 ⇒ x = 60/143 So, x = 9/2 or 60/143 From Quantity II, Total cards = 6 + 4 + 3 = 13 Non-black cards = 6 + 4 = 10 Required probability = 10C3 / 13C3 = (10×9×8) / (13×12×11) = 720 / 1716 = 60/143 Hence, Quantity I ≥ Quantity II (because Quantity I can be 9/2 or 60/143, which is either greater than or equal to 60/143)

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