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CAT 2017 Slot 1 — QA Question 28

Inequality Maximization / MinimizationEasy

If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a - b)2 + (a - c)2 + (a - d)2 is

Answer & solution

Answer: 2

Solution

a + b + c + d = 30, a, b, c, d are integers. 

(a – b)2 + (a – c)2 + (a – d)2would have its maximum value when each bracket has the least possible value.

Let (a, b, c, d) = (8, 8, 7, 7)

The given expression would be 2. It cannot have a smaller value.

Hence, 2.

CAT 2017 Slot 1 QA Q28: If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a - b) 2 + (a — Solution | TheCATExam