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CAT 2017 [slot 1] Question with solution 28

Question 28:
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: 2
Explanation:

For the value of given expression to be minimum, the values of $a, b, c$ and $d$ should be as close as possible. 30/4 = 7.5. Since each one of these are integers so values must be 8, 8, 7, 7. On putting these values in the given expression, we get
$(8 - 8)^{2} + (8 - 7)^{2} + (8 - 7)^{2}$
=> 1 + 1 = 2


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