The greatest negative integer is:
$
  {\text{A}}{\text{. - 100}} \\
  {\text{B}}{\text{. Does not Exist}} \\
  {\text{C}}{\text{. - 1}} \\
  {\text{D}}{\text{. - 9}} \\
$

Hint- In this question we have to tell the greatest negative integer, so use the concept that if a number lies to the rightmost in comparison to another number then it is greater as compared to other, or in other words the numbers at which is closer to origin towards the left side is greater negative.

Complete step-by-step answer:
In this question we have to find the greatest negative integer.
The best way to think upon this would be to make a number line:

So, we also know that in a number line, numbers decrease as we go towards the left side.

So, we can also infer that -1 is the greatest integer in the negative axis side. As on the left we have -2 which again is smaller than -1 and on right we have 0 which is not a negative number.
So, option (c) is the correct answer.

Note- To solve these types of questions we should always make a number line. As using a number line makes it easy to visualize the problem. Then we also know that in a number line, numbers decrease as we go towards the left so we can clearly tell that -1 is the largest or the greatest negative integer.