Since there is a mode, at least 2 of the numbers must be the same.
The mode is always one of the numbers.

Since there is an odd number of numbers, the median must also be
one of the numbers.  Since x+1 is both the median and the mode, 
two of the numbers are both x+1.  Let the third number be y.  
Then the three numbers are 

y, x+1, and x+1.

Since x is the mean:











So the third number is x-2, and since
x-2 is less than the other two numbers,
which are both x+1, it is the least 
of the three. So the answer is x-2, choice C.

Edwin