niks18 wrote:

Consider three distinct positive integers \(a\), \(b\), \(c\) all less than \(100\). If \(|a - b| + |b - c| = |c – a|\), what is the maximum value possible for \(b\) ?

A. 95

B. 96

C. 97

D. 98

E. 99

Source: Question Bank

|a - b| + |b - c| = |c – a| the equation means that the sum of distance between B & A and C & B is equal to distance between C & A. Which means B is between C & A.

.....0........a...........b..........c . Since the maximum value of C can be 99(1<=A,B,C<100 and distinct), 98 is the maximum value of B.

Hence D.