Necessary Assumption question

[hornswaggle]

I've the seen the following argument form in a couple of Necessary Assumption questions. PT 67 Section 4 #16 is the one I'm looking at right now, but I remember seeing it somewhere around PT 50 too.

Conclusion: A->C (in Q16, it's Achievement!->Increased funding)

Premise: A->B (Achievement!->Increased funding from other sources)

The answer is usually something along the lines of B->C. For Question 16, it's answer choice D) (Increased funding->Increased funding from other sources).

I picked D) because it addressed the mismatched terms in the argument, but can someone explain why it's necessary to assume B->C? I apologize if someone has asked this question already.

[christine.defenbaugh]

An excellent question hornswaggle! This construct appears quite often on the exam, and mastering it will serve you well.

Let's use an example to discuss:

Premise: If I go dancing, then I will head home after midnight.
Conclusion: If I go dancing, then I will miss the last train home.

You can attack this question in two different ways. One way is to simply identify the mismatched terms, just as you did. Where did the idea of missing the last train come from? Somehow, we have to connect the ideas of 'heading home after midnight' and 'missing the last train'.

But let's tackle it from the formal logic angle. The conclusion is:
If dancing --------------------------------------------> miss the last train home.
The author wants to be able to start at 'dancing', and drive the car across conditional bridges all the way to 'miss the last train'. So what do we have in the way of support for this? We have:
If dancing --> head home after midnight.
Hm. So if we insert that known bridge, we have:

If dancing --> head home after midnight ........................... miss the last train.

We've still got a big gap between the ideas. We need a link between them - and not just any link, we need a conditional that starts at 'head home after midnight' and ends with 'miss the last train'! The only thing that would fit the bill would be:
"If I head home after midnight, then I will miss the last train."

That conditional relationship needs to be true - if it weren't, how in the world could the author conclude that she'll miss the last train when she goes dancing?

Let's take a look at it once more with variables, so that we can really get a firm grasp on structure. But this time, I'm going to add more pieces.

Premise: A --> B
Premise: B --> C
Premise: X --> Y
Premise: Y --> Z
Conclusion: A --> Z

Conc: A ----------------------------------------------------------->Z
Add in the premises!
A-->B-->C.....................................................................X-->Y-->Z

What's the missing link? We have to connect C with X! We need a statement that says "If C --> X". Without it, we can't drive the car from A all the way to Z - we'd get stuck in the middle. So that conditional would be a necessary assumption of this argument.

Understanding these conditional logic relationships will prove critical to your success on the LSAT! Please let me know if you have any additional questions!