If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive?
(1) The product of the nine integers in list S is equal to the median of list S.
(2) The sum of all nine integers in list S is equal to the median of list S.
What's the best way to determine which statement is sufficient? Any experts can help?
If list S contains nine distinct integers, at least one of w
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Statement 1: if the nine integers are distinct, this can only be true if the median = 0.ardz24 wrote:If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive?
(1) The product of the nine integers in list S is equal to the median of list S.
(2) The sum of all nine integers in list S is equal to the median of list S.
What's the best way to determine which statement is sufficient? Any experts can help?
(To see this algebraically, imagine the nine elements are the variables a - i, in ascending order. So the median is e. Now we'd know that a * b * c * d * e * f * g * h * i = e. If e weren't 0, then we could divide both sides by e to get a * b * c * d * f * g * h * I = 1. But we can't multiply 8 different integers and get a value of 1. So e MUST be 0.)
This statement alone is sufficient - the median is not positive, giving us a definitive NO as the answer to our question.
Statement 2. The easiest way to construct this set is to have the largest 4 terms and the smallest 4 terms sum to 0. If that's the case, the sum of all the terms will have to be equal to the median.
Case 1 {-6,-5,-4,-3, 0, 3, 4, 5, 6} This gives us a NO, the median is not positive.
Case 2 {-6,-5,-4,-3, 1, 3, 4, 5, 6} This gives us a YES, the median is positive.
Because we can get a NO or a YES, this statement alone is not sufficient to answer the question.
The answer is A