Practice Test Discussion

Q)

The difference between two numbers is 18 and their HCF and LCM are 6 and 168, respectively. What is the sum of squares of the two numbers?

[RBI, 2015]

    • Explanation

    Let one number be 'x'

    Then, another number is x+18

    Now, product of two numbers= HCF×LCM

    ⇒ x×(x+18)=6×168

    ⇒ x²×18x=1008

    ⇒ x²×18x-1008=0

    ⇒ x²×42x-24x-1008=0

    ⇒ x(x-24)+42(x-24)=0

    ⇒ x=24

    ∴ Another number is 42.

    Required sum =(24)²+(42)²

    =576+1764=2340.

    Hence, Option D is correct.

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