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PTB.S1.Q12 - Alice will volunteer to work on the hospital fund-raising...

Alum Member
edited February 16 32 karma

Hey yall! I need a parallel reasoning expert to explain to me why C is the correct answer and not E.

Thank you!

• Yearly + Live Member Sage 🍌 7Sage Tutor
27710 karma

This is a fun one. Very formal logic heavy.
The first thing to recognize is the exact relationship of the elements in the stimulus.

We get one sufficient condition:

Alice will volunteer

and two distinct necessary conditions:

1. Bruce volunteers
2. Other volunteers promise to select Bruce to manage the drive.

With compound necessary conditions, each condition works just like a singular one. If you satisfy the sufficient, the necessary must follow. If you fail a necessary, you must fail the sufficient. Here, the only difference is that both must follow if the sufficient triggers, and failing either is enough to contrapose to negate the sufficient.

Answer C is identical logically, although it is a bit deceptive because it expresses the relationships with very different grammar structures. So the language has a very different feel to it. We've got to see past the language structure to see the logic structure.

Sufficient:
Jim will go to the party

Necessaries:
1. Sam goes to the party
2. Elaine goes to the party.

Does this make sense? Even though this AC and the stimulus read quite differently, you've got to be able to hammer out the logical relationships. From there, we can see the same setup. Now we just need to check the triggers. Conditional relationships typically need a condition to trigger or fail before a whole lot happens. There are some really hard questions where this isn't always the case, but they are few and far between. So what is the trigger in the stimulus? The others won't promise to elect Bruce manager. This fails our second necessary condition, which allows the argument to correctly conclude that Alice won't volunteer. In this AC, the trigger is that Elaine won't go to the party. Same effect. We've failed a necessary condition and the correctly concluded that the sufficient condition must fail: Jim will not go to the party.

So that leaves AC E which has the exact same structural setup with a single sufficient and two necessary conditions:

Sufficient: Therese will work in the yard

Necessaries:
1. Maria helps.
2. It doesn't rain.

So far so good. We just need to consider the trigger. To match, we need to fail a necessary condition and then conclude from that that the sufficient condition cannot follow. The trigger here is that Maria will help. So this is actually satisfying a necessary condition, not failing one. From here, this conclusion is valid, but that's not enough to be parallel. To be parallel, it must get there through the same logical mechanisms.