(1) C^2 is less than both A^2 and B^2.

It means absolute value of C is less than absolute value of A. Not sufficient. (A,C)can be (-2,1) or (2,1).

Not sufficient.

(2) A^3 is less than both B^3 and C^3.

It means A is less than C.

(A,C) can be (1,2) or (-1,2).

Not sufficient.

Combining both statements, we get A is less than C. but absolute value of C is less than absolute value of A.

It can only be possible if A is negative .

Sufficient. Answer C.

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