If 5 is the only mode of the following list of numbers, which of the following cannot be the value of $$x$$?
>$$\{5, \ 3, \ 7, \ x, \ 5, \ 9, \ 11, \ 7, \ 17, \ 1, \ 5\}$$

Correct.
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The mode 5 appears three times in the list of numbers while 7 appears twice. Therefore, $$x$$ cannot be 7 because then 7 will appear three times, and 5 will no longer be the number that appears most in the given list of numbers.

Incorrect.
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Incorrect.
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Incorrect.
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Incorrect.
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3

7

9

11

17