#6 - Astronomer: This country's space agency is currently

[Jeff Wren]

Hi rlouis,

In the argument itself, we have a premise that basically states, "if we cancel now, all the money that has already been spent (which is more than half) will be wasted."

You are correct that in this conditional statement, the sufficient condition is "cancel now" as indicated by the word "if."

We are not done, however. The very next step is to take the contrapositive. If you're not familiar with contrapositives, they are discussed under conditional reasoning in lesson 2 of The PowerScore LSAT Course and in chapter 6 of The Logical Reasoning Bible.

It is generally a good habit to always take the contrapositive, but in this argument we are definitely going to use it. How can we tell that the argument will use the contrapositive? Because the conclusion of the argument is that canceling would be a mistake, which is another way of saying we should not cancel the project. The only way to "get to" the conclusion of not canceling using this conditional statement is via the contrapositive.

When taking the contrapositive, you reverse and negate the terms. Here, the contrapositive would be:

"If we don't want to waste all the money that has already been spent (which is more than half), then we should not cancel the project."

Here, in order to get us to our conclusion that we should not cancel, we'd like to find an answer that satisfies the sufficient condition of our contrapositive (i.e. we don't want to waste all the money that has already been spent).

Now to be tricky, the correct answer doesn't specifically mention not wasting money, which would have been nice, but Answer B does get us to the conclusion that we should complete the project (meaning not cancel it) since it mentions spending more than half of the total cost, which happened in this argument.

[LawSchoolDream]

This one threw me off because most of the answer choices contained values and I felt since the stimulus didn't mention values such as "more than half" many of these answers were incorrect, including B. I chose A.

Can you please help decipher my thought process? I read the entire thread but haven't gotten an answer, except for does majority = more than half? Even so, what makes b such a stronger answer in comparison to A is what I'm not getting. I read the explanation but still not getting.

[Jeff Wren]

Hi LawSchoolDream,

First, the stimulus definitely did mention an amount/value that you may have missed. The stimulus states that "all of the money spent--which is more than the additional cost required to complete the project--would be wasted" (my emphasis). Think of "the additional cost required to complete the project" as the remaining cost to finish it. Since the amount already spent is more than the remaining amount required to finish the project, that means that they have spent more than half of the total money required for the project.

The basic idea of this argument is that they've already spent more than half of the money on the project and to stop/cancel now would waste all of that money, so they should just finish the project.

Answer B matches this situation in the stimulus (more than half of the total cost of the project has been spent), and leads us to our conclusion that the project should be completed (i.e. not cancelled).

The problem with Answer A is that it specifies that the amount of money already spent is small relative to the agency's overall budget (my emphasis). Unfortunately, we don't know anything about how much the amount spent on this project compares to the agency's overall budget. We only know how much the amount spent on this project compares to the total cost of this project. For all we know, this project may just be a tiny fraction of the agency's overall budget, but we have no way of knowing either way as that is not discussed in the stimulus.