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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.
Suppose d is the standard deviation of the data set and r is the range of the data set. Then d ≤ r. Since we have many variables, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2)
Since d ≤ r, we have d ≤ 500 < 1000.
Both conditions are sufficient, when taken together.
Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
Condition 1)
As there is no relationship between standard deviation and average, condition 1) is not sufficient.
Condition 2)
Since d ≤ r, we have d ≤ 500 < 1000.
Condition 2 is sufficient.
Therefore, B is the answer.
Answer: B