I would like to ask:
1. why we will get a 6 as the numerator when the signs are all the same for the maximum part?
2. why do we assume the value to be 1 in the highlighted part? Why is it specifically 1?
omkartadsare
No restrictions are given for values of a, b or c. so to simplify this, lets assume the value to be |a| =|b|=|c| = 1
we can see that, |a| + |b| = |b| + |c| = |c| + |a| = 2.... Hence all bases are same. The max. and min value totally depends on numerators now.
Maximum value can be obtained when sign of all numbers is same (we get all additions inside modulus and hence largest value). when all a, b and c all are positive or negative we will get 6 in the numerator. So the largest possible value of M would be 6/2 = 3
Smallest possible value can be obtained when one of a, b and c is having different sign while other two have same sign. (By this way there would be 2 subtractions inside modulus and 1 addition) By considering any one of a, b or c to be negative, we get 2 in the numerator. So the smallest number than can be obtained is 2/2 = 1
So the difference between largest and the smallest value is 3 -1 = 2, Hence IMO (C)