GMAT CR: Navigating Double Negative Causality

Newspaper editorial: In an attempt to reduce the crime rate, the governor is getting tough on criminals and making prison conditions harsher. Part of this effort has been to deny inmates the access they formerly had to college-level courses. However, this action is clearly counter to the governor’s ultimate goal, since after being released from prison, inmates who had taken such courses committed far fewer crimes overall than other inmates.

The governor wants to lower crime by cracking down on inmates and making prison tougher. This includes cutting off access to college courses. But this is actually the opposite of what the governor wants to achieve. Why? Because released inmates who took those courses committed far fewer crimes than those who didn’t.

Which of the following is an assumption on which the argument depends?

A. Not being able to take college-level courses while in prison is unlikely to deter anyone from a crime that he or she might otherwise have committed.

This is a common trap option in assumption questions.

When you encounter a causal relationship with two negatives (like “unlikely to deter” here, which expresses a causal link), pay close attention to the logically equivalent proposition: If P then Q can only be inferred from If not Q then not P (note it’s the contrapositive), and vice versa.

If P, then Q is equivalent to If not Q, then not P. But it is NOT equivalent to If not P, then not Q.

Think of it this way: If it rained (P), the ground would be wet (Q). This means if the ground isn’t wet (Q’), then it definitely didn’t rain (P’). However, you can’t say that if it didn’t rain (P’), the ground wouldn’t be wet (Q’). Maybe a sprinkler was on!

Now, let’s look at option A. It fits the pattern of the second, incorrect form (If not P, then not Q).

Option A says: Not being able to take college-level courses while in prison (Q’) is unlikely to deter anyone from a crime that he or she might otherwise have committed (P’).

This is like saying: If you can’t take courses (Q’), then you won’t be deterred from crime (P’). This is the “If not P, then not Q” structure. It doesn’t work.

The correct inference from the editorial is that if inmates *were* deterred from crime, they *would have had* the opportunity to receive education. That’s the “If not Q, then not P” logic. But option A doesn’t get us there.

(I suspect this is why many people initially find option A appealing: If being able to take courses prevents crime, then the necessity of the courses is confirmed, and the conclusion holds, right?)

So, from now on, when you see a double negative in a causal relationship, pay more attention to how the contrapositive is derived.