## 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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## Answer ( 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