The question is about maximum possible value. We need to maximize the given expression given the range of two variables. 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 19: Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m2 - mn + n2?
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.
The question is "What is the maximum possible value of m2 - mn + n2?"
Choice D is the correct answer.
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