What is the maximum possible value of $$x$$ if the median of the following set is $$37$$?
>$$\{47, \ 14, \ 7, \ 56, \ 37, \ 41, \ x\}$$

Incorrect.
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Incorrect.
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Incorrect.
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Incorrect.
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Correct.
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In order for 37 to be the median, it _must_ be the middle value. Since the list has a total of seven numbers, 37 can be the middle number only if three numbers are less than or equal to 37 and three numbers are greater than or equal to it.
Sort the set and place $$x$$ right before 37 since the question asks for the maximum possible value of $$x$$:
>$$\{7, \ 14, \ x, \ 37, \ 41, \ 47, \ 56\}$$
While $$x$$ could be 36 to yield a median of 37, the question asks for the _maximum_ possible value. All that $$x$$ needs to be is less than or equal to 37, so it is actually possible for $$x$$ to be exactly equal to 37. Thus, $$x = 37$$ is the maximum possible value.

6

36

37

40

47