Number of triplets possible

Question

a, b, c are three distinct integer from 2 to 10 (both inclusive). Exactly one of ab, bc, and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?

 

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Quantitative Ability Ankush Bansal 5 months 1 Answer 103 views 0

Answer ( 1 )

  1. Exactly one of ab, bc and ca is odd
    ⇒ Two are odd and one is even

    abc is a multiple of 4
    ⇒ the even number is a multiple of 4

    The arithmetic mean of a and b is an integer
    ⇒ a and b are odd

    and so is the arithmetic mean of a, b and c.
    ⇒ a+ b + c is a multiple of 3

    c can be 4 or 8.
    c = 4; a, b can be 3, 5 or 5, 9
    c = 8; a, b can be 3, 7 or 7, 9

    So, Four triplets are possible

    Best answer

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