Question 94

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

Correct Answer: 2

Solution

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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CAT 2017 QA Slot 1 Question

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

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