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CAT 2003 | Question: 1-131

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Let $a, b, c, d$ be the four integers such that $a +b+c+d =4m+1$ where m is a positive integer. Given $m,$ which one of the following is necessarily true?

  1. The minimum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 – 2m + 1$
  2. The minimum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 + 2m + 1$
  3. The maximum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 – 2m + 1$
  4. The maximum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 + 2m + 1$
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