A group of adults took a quiz that was scored from 10 to 40.

Lets assume that the highest score is x.
So, as per the given information, we know that:
A. \(x\leq{40}\)
B. Second highest score will be (x-6)

We have to find the highest score, x, so if we can find value of either x or (x-6), we can arrive at our answer.

(1) This statement suggests that the possible scores are 32,33,34,35,36,37,38,39, and 40.
Since highest score, x, is 6 more than the second highest score and \(x\leq{40}\), only possible values of (x-6) are 32,33, and 34, and therefore only possible values of x are 38,39, and 40.
So, from the above information, we don't get a unique value of x.
Thus, this statement is insufficient.

(2) This statement suggests that possible scores are all odd numbers between 1 and 39, both the limits included.
Hence, if the second highest score is 5, the highest score will be 11, and if the second highest score is 33, the highest score will be 39.
So, from the information in this statement, we don't get a unique value of x.
Thus, this statement is insufficient.

From statement (1) and (2) together, we know that:
a. Possible values of highest score are 38,39, and 40
b. Possible scores are odd numbers
So, from (1) and (2) combined, we get that value of x is 39.
Thus, this statement is sufficient.

Therefore, the correct answer is option C.