CAT 2025 Inequalities Question (Hard)

Question

If a , b , c and d are integers such that their sum is 46 , then the minimum possible value of a - b 2 a - c 2 a - d 2 is

Accepted Answer

Given expression a-b 2 a-c 2 a-d 2 The given expression has just the sum of squares of the terms. So, the minimum value is either zero or positive. If we can make all the values equal, we can get zero. But since all the values are integers and the sum 46 is not divisible by 4, we can t make everythi

CAT 2025

Quantitative

Inequalities

Hard

$If ( a , b , c ) and ( d ) are integers such that their sum is 46 , then the minimum possible value of ( ( a - b ) ^ { 2 } + ( a - c ) ^ { 2 } + ( a - d ) ^ { 2 } ) is$

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