# CAT Practice : Inequalities

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This is an excellent inequality question comprising of both quadratic and modulus!!

## Modulus - Tricky

Q.15: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?
1. 98
2. 99
3. 50
4. 100

Choice A. 98

## Detailed Solution

|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.

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## More questions from Inequalities

Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.