The question is about maximum possible value. We need to maximize a value which is given in a tricky modulus. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.
Question 18: 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?
|q – p| is the distance between p and q on the number line. |p –q| is the same as |q –p| to begin with.
So, in this case we are told |a -b| + |b -c| = |c – a|. Think about this. What does this mean? There are three points on the number line. We are talking about 3 distances on the number line here. We know that sum of some two of the distances is equal to the third. What does this tell us?
This tells us that the point b has to be in between a and c. With this we are done. We can have a or c to be 99 and b to be 98.
Maximum value b can take is 98. Classic question.
The question is "If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?"
Choice A is the correct answer.
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