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    Question

    (Q.126-130): Study the following information carefully and answer the Questions given below:

    What is the larger number? Quantity I.

    Difference between the two numbers is 15 and LCM and HCF of those numbers are 90 and 15 respectively. Quantity II. The HCF and LCM of two numbers are 5 and 100 respectively. If the sum of the two numbers is 45.
    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-15) x(x – 15) = 90 `xx` 15 x2 - 15x  = 1350 x2 - 15x  – 1350 = 0 (x-45)(x+30) = 0  x = 45 Larger number = 45 and Smaller number = 30 Quantity II. Let the larger number be x  Smaller number = 45 – x x(45-x) = 100 x 5 x2 - 45x  + 500 = 0 (x-20)(x-25) = 0  x = 20, 25 Larger number = 25 Smaller number = 20 Hence, Quantity I > Quantity II.

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