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    Question

    Study the following information carefully and answer the Questions given below:

    What is the larger number?

    Quantity I. Difference between the two numbers is 21 and LCM and HCF of those numbers are 70 and 7 respectively.

    Quantity II. The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of the two numbers is 60.

    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    D Quantity I ≤ Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer

    Solution

    Quantity I. let the larger number be x ∴ Smaller number = (x-21)  ∴ x(x – 21) = 70 × 7 x2 - 21x = 490 x2 - 21x – 490 = 0 (x-35)(x+14) = 0  ∴ x = 35  Larger number = 35 and Smaller number = 14  Quantity II. Let the larger number be x  ∴ Smaller number = 60 – x  ∴ x (60-x) = 12 ×72 x2 - 60x + 864 = 0  (x-36)(x-24) = 0  ∴ x = 36, 24  Larger number = 36 Smaller number = 24  Hence, Quantity I < Quantity II.

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