CAT 2017 Number System Question (Hard)

Question

If a, b, c, and d are integers such that a b c d 30, then the minimum possible value of a - b a - c a - d is TITA

Accepted Answer

Step 1 We are given a b c d 30 We are to minimize the expression a - b 2 a - c 2 a - d 2 Step 2 Let s express the expression using expanded terms a - b 2 a - c 2 a - d 2 3a 2 - 2a b c d b 2 c 2 d 2 Since , b c d 30 - a So, the expression becomes 3a 2 - 2a 30 - a b 2 c 2 d 2 5a 2 - 60a b 2 c 2 d 2 No

CAT 2017

Quantitative

Number System

Hard

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 (TITA)

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