# CAT Practice : Inequalities

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This is an excellent inequality question which becomes really simple after a single step!!

## Inequalities - Integers

Q.19:Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?
1. 65
2. 60
3. 50
4. 61

Choice D. 61

## Detailed Solution

Points to note
1. m2 and n2 are always positive
2. -mn will be maximum when m and n have opposite signs
After this, it is pretty simple. We are better off with m being negative and n positive as in this case they can take higher values. m = -4, n = 5 works best. Note that as far as absolute value is concerned maximum |m| can be is 4 and maximum |n| can be is 5. This is important, otherwise we may have a scenario where even sacrificing –mn we might be able to maximise this.

So, m = -4, n = 5 works
m2 -mn + n2 = 16 + 20 + 25 = 61.

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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.