CAT Quant Practice Problems

Question: Let a, b, c, d be 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?

The minimum possible value of a2+ b2+ c2+ d2is 4m2–2m+1
The minimum possible value of a2+ b2+ c2+ d2is 4m2+2m+1
The maximum possible value of a2+ b2+ c2+ d2is 4m2–2m+1
The maximum possible value of a2+ b2+ c2+ d2is 4m2+2m+1
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