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

2

From CAT 2017 – Quantitative Aptitude – Algebra – Maxima Minima, we can see that,

a + b + c + d = 30

a, b, c, d are integers. (a â€“ b)^2 + (a â€“ c)^2 + (a â€“ d)^2 would have its minimum 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.

Answer: 2

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

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