I'll try to explain what's going on here. I think there is actually an error in the answer explanation - the K+ ATP channel being blocked prevents K+ from leaving the cell (not entering), resulting in depolarization.
Now how are you supposed to know this? You won't necessarily, which is why this is an application style question. You have to work with various pieces of information you might know:
1. K+ is at a higher concentration inside the cell than outside the cell
2. There is a higher concentration of Ca 2+ outside the cell than inside the cell
3. VDCC's (Voltage Dependent Calcium Channels) activate when there is depolarization
4. There is a normal inward current of ions into a cell that would depolarize it, but this is countered by the K+ channel's outward flow.
Now let's pretend you only knew 1 and 3. We know that K+ is at a higher concentration inside the cell, so it will want to flow outside the cell if it can. We also know that this channel is sensitive to ATP in some way. So only two things can happen here: either the channel is always open and ATP closes it, or the channel is always closed and ATP opens it. If the latter was the case, when ATP concentration goes up, the K+ channel would open and K+ would rush out of the cell. We know this hyperpolarizes a membrane, not depolarizes, and therefore wouldn't trigger the VDCC. This alone throws out A, B, and D as answer choices because they all focus on hyperpolarization. That means the first possibility must be the case - the K+ ATP sensitive channel is usually open, ATP concentration goes up and closes it, and depolarization results.
Piecing this together, you'd be able to figure out that what's going on: Glucose enters a cell --> ATP concentration goes up --> the ATP closes the K+ channel preventing its outward flow from the cell --> depolarization occurs --> VDCC opens up --> Ca ions rush in --> exocytosis of insulin. Answer choice C is correct.
