CAT 2025 Question Paper | Quant Slot 2

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 7 : 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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Video Explanation

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Explanatory Answer

Distribute values evenly to minimize square differences

To minimize differences between integer values summing to 46:
\(\frac{46}{4}=11.5\)

The best integer distribution for \(a,b,c,d\) is \(11,11,12,12\).

Evaluate the expression
Let \(a=11,\ b=11,\ c=12,\) and \(d=12\):

\((a-b)^2+(a-c)^2+(a-d)^2\)
\(=(11-11)^2+(11-12)^2+(11-12)^2\)
\(=0^2+(-1)^2+(-1)^2\)
\(=0+1+1=2\)

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The question is " 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 "

Hence, the answer is '\( 2 \)'

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