MBApyq

Minimum Value of Sum of Squares

CAT 2017 Slot 1 · Quantitative Ability · Hard · Algebra

This is a hard Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2017 Slot 1 questionsMore Algebra questionsAll CAT QA

If a,b,c,a, b, c, and dd are integers such that a+b+c+d=30a + b + c + d = 30, then the minimum possible value of (a−b)2+(a−c)2+(a−d)2(a - b)^2 + (a - c)^2 + (a - d)^2 is

Answer

2

Explanation

To minimize (a−b)2+(a−c)2+(a−d)2(a - b)^2 + (a - c)^2 + (a - d)^2, a,b,c,da, b, c, d should be as close as possible. Average of 30 among 4 numbers is 7.57.5. So choices for (a,b,c,d)(a, b, c, d) close to 7.5: let a=8,b=8,c=7,d=7a = 8, b = 8, c = 7, d = 7. Then a+b+c+d=30a + b + c + d = 30. Value =(8−8)2+(8−7)2+(8−7)2=0+1+1=2= (8 - 8)^2 + (8 - 7)^2 + (8 - 7)^2 = 0 + 1 + 1 = 2.

Related Algebra questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace