JourneyToTheTop wrote:
The question must make clear that x is an integer, not any real number.
Hope the solution below explains why is that not necessary.
If set \(S =\{2, 5, 1, x, 7\}\), what is \(x\) ?(1) The range of set \(S\) is 8. If we consider the range of \(S =\{2, 5, 1, x, 7\}\), without x, then it's largest - smallest = 7 - 1 = 6. Since, the range of S is 8, then x must be either the largest or the smallest element. If x is the largest, then x - 1 = 8 --> x = 9 and if x is the smallest, then 7 - x = 8 --> x = -1. Not sufficient.
(2) The median of set \(S\) is 2. The median of a set with odd number of elements is the middle term, when arranged in ascending/descending order. Since 2 is the median, then it's the middle term: S = {x, 1,
2, 5, 7}. So, x must be less than or equal to 2. Not sufficient.
(1)+(2) From (1) x = 9 or x = -1 and from (2) x <=2, hence x = -1. Sufficient.
Answer: C.
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