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Explanation:

Statement A:

x + y + z = 89

x2 + y2 + z2 will be minimum when x = y = z = 89/3

But 89/3 is a non-integer.  ∴ We consider integer values of x, y, z which are as close as possible to 89/3.

We get two cases

1.  x, y, z = 30, 30, 29

x2 + y2 + z2 = 2641

2.  x, y, z = 31, 29, 29

x2 + y2 + z2 = 2643

Minimum possible value of x2 + y2 + z2 is 2641. Thus statement A is sufficient to get the answer. Though statement B states a fact related to the minimum value, it is not necessary to arrive at the minimum value.

Hence, option (a).

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