CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. It is more like a puzzle than a question. Some conditions are given and we need to find the number of ordered triplets. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 4: 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)?

1. 8
2. 6
3. 2
4. 4

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: This is more a puzzle than a challenging question. But is a very interesting puzzle nevertheless :)

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
Four triplets are possible.

The question is "How many such triplets are possible (unordered triplets)?"

Hence the answer is "4"

Choice D is the correct answer.