From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

Let n pages be missing starting from the p th page.

So,$$p+(p+1)+(p+2)\dots..+[p+(n−2)]+[p+(n−1)]=9808$$

$$9808=\frac{n}{2}[2\times p+(n−1)\times1]$$
$$n^2+(2p-1)n−19616=0$$
Now both p and n are natural numbers 
Now possible cases 
$$n=19616,\ p=−9807$$
$$n=−19616,\ p=9808$$
$$n=613,\ p=−29$$
$$n=−613,\ p=29$$
$$n=1,\ p=9808$$
$$n=−1,\ p=−9807$$
$$n=32,\ p=291$$
$$n=−32,\ p=−290$$

But since p and n has to be natural numbers, so all solutions except 5 and 7 are discarded.

Also, it is mentioned in the question that "a number of consecutive pages are missing". Thus, case 5 can be discarded(i.e. n = 1 and p = 9808)

So, the correct option is C