Torture Risk Assessment
Let's take some numbers ex recta. Say a terrorist group has a plan that has a 5% chance of killing 100 people given our current security measures (including non-torture interrogation), luck, and their own skill. That gives an expected value for the non-torture situation of 5 deaths. Now let's say that given our current capture and interrogation techniques, there is a 5% chance that any given person we torture will provide information that makes the difference between stopping and not stopping the terrorist plot*. This means that to save those expected 5 lives, we'd have to torture 20 people -- a rate of four tortures per death.
It's not impossible to think of tortures so heinous that it's better to let one person die a quick death than to subject four people to them. And the situation gets worse for advocates of torture if the probability of success of either the terrorist plot or torture goes down. On the other hand, if you hold off on torturing until you've tried all other measures, the utility of torture goes up but the frequency goes down, because you don't use it in cases where the plot would have failed anyway. So instead of facing the 5% chance of terrorism every three months, for example, you might foil 3/4 of those plots without using torture but face a 50% chance of success from the remaining one plot per year. On the other hand, the longer you wait, the worse your success rate for torture will be -- if it were to drop to .5%, that would give the same tradeoff against a 50% plot as the original scenario.
Of course, this all rests on utilitarian assumptions. The ticking time bomb scenario -- of which this hypothetical situation is a more plausible variant -- is based on the idea that while torture is bad, it can produce results that outweigh the badness. However, many apologists for torture believe that because the victims are (assumed to be) terrorists, they are bad people, and hence torturing them is morally acceptable (even obligatory) even if they produce no useful information. Their pain simply doesn't count for anything. There are intellectual arguments in favor of this view (though I don't buy them), but there's also a strong emotional desire for vengeance and tendency to de-humanize those who have broken the social contract that motivates it.
Standard ticking-time-bomb scenarios subtly invoke this dehumanization by positing that the person to be tortured is a terrorist. I think people would draw a more restructive line against torture if the victim in question were, say, their own grandmother**. (It might take some doing to set up a situation in which she knew how to defuse the bomb but wasn't telling, but we'll set that aside for the moment.) Asking "what kind of torture would you do to your grandmother to stop this terrorist act" forces us to confront whether we're really willing to trade off a human being's suffering for the posited reward, or whether our favorable view of torture is based on an assumption that a terrorist's pain is of less moral worth. (In the extreme ticking time bomb scenario, in which torture is the only way to stop the deaths of a million people and there's no risk of failure, I would still be willing to do pretty much anything to make grandma talk.)
*For simplicity's sake, we'll say that the information in question allows us to intervene before the events that reduce the plot's chance of success to 10%.
**You can change it to a different relative if you have a poor relationship with your grandmother.