a, b, c are three distinct integers 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)?
Pick.
A) 8	B) 6	C) 2	D) 4	E) 0
DETAILED SOLUTION   Exactly one of ab, bc and ca is odd =&gt; Two are odd and one is even   abc is a multiple of 4 =&gt; the even number is a multiple of 4   The arithmetic mean of a and b is an integer =&gt; a and b are odd   and so is the arithmetic mean of a, b and c. =&gt; 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   Four triplets are possible.   Correct Answer : 4
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a, b, c are three distinct integers 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)?