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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 1) means the average of a, b and 24 is (a + b + 24 ) / 3 = 24 since it implies that ( a + b ) / 2 = 24. Since one of the three data points is their average, it is also their median. Condition 1) is sufficient.

Condition 2)
If a > 24 and b < 24, the median of a, b and 24 is 24.
If a < 24 and b > 24, the median of a, b and 24 is 24.
Thus, we have a unique value for the median, and condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Note: Condition 1) is easy to understand and condition 2) is hard to understand. Thus, this question is a CMT4(B) question. When one condition is easy to understand, and the other is hard to understand, D is most likely to be the answer.