PT 21-S2-Q20 Ann will either.... Forum

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gnomgnomuch

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PT 21-S2-Q20 Ann will either....

Post by gnomgnomuch » Sat May 17, 2014 8:00 pm

Can anyone help me with the conditional logic on this question?

I got the answer correct, but i wasn't using logic for it.

A) Wrong - cant see how it related, but either way "only if" is way to strong, there are plenty of other ways they can learn about her fellowship.

B) Wrong - No discussion on reasons.

C) Wrong - We know nothing about their policies, nor do we care.

D) Correct - i couldn't obviously eliminate it, so i left it.

E) Wrong - how in the world does that relate to the conclusion.

Here is my Conditional logic attempt:


Ann will either A) l.o.a or B) Quit... but only if she gets a TF.

So assuming she gets a TF, A - ~B or B - ~A

L.O.A is allowed if no information is known about her TF, If they find out about her TF, then she will quit (since she cant take an L.O.A)

Therefore, Ann quits, because she gets the TF.

Im pretty sure i diagrammed this correctly, but i cant figure out why D is the correct answer choice.

Help will be massively appreciated!

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Nulli Secundus

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Re: PT 21-S2-Q20 Ann will either....

Post by Nulli Secundus » Sun May 18, 2014 12:02 pm

I have no idea about the diagramming rules used here, but

If "fellowship offered" -> "Take leave of absence" OR "Quit job"

If "fellowship unknown" -> "Allow leave of absence"

So between these two steps,

If "Allow leave of absence" -> "Take leave of absence"

is needed to fill the gap.

(Looking over your effort, you are mistakenly assuming her being awarded the fellowship means the company finding about the fellowship. This may not be the case and Ann won't have to quit her job after being awarded the fellowship)

HTH.

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Re: PT 21-S2-Q20 Ann will either....

Post by Daily_Double » Sun May 18, 2014 12:10 pm

This is my favorite S/A question of all time. I'll write up an explanation for this one when I'm free this afternoon.

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Christine (MLSAT)

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Re: PT 21-S2-Q20 Ann will either....

Post by Christine (MLSAT) » Sun May 18, 2014 2:05 pm

Oh, this is a fun question!

Let's take it piece by piece:

Ann is either going to A (leave of absence) or Q (quit). So, one of these things MUST happen - but logically, it's impossible to do both. So, this is actually giving us a biconditional! Formal notation would be:
  • ~A <--> Q
    ~Q <--> A
More important than the formal notation though is the realization that if you know anything at all about the elements of Q and A, then you know the status of the other one. If you know that she doesn't quit, you know she has to take a leave of absence. If you know she DOES quit, then you know she can't take the leave of absence, etc.

Next sentence is the most confusing one: she wouldn't do either of these unless she had a fellowship. But we know she IS GOING TO DO one of these things! The first sentence said so! So this isn't actually giving us an interesting conditional - it's actually just informing us that she has a fellowship. Whew! We don't need to worry too much about this sentence, since the purpose is just to tell us that she does, in fact, have a fellowship. Good to know.

Now, the next sentence is also giving us a biconditional relationship. If Technocomp finds out, they won't allow A. If they don't find out, they WILL allow A. Be careful about the shift here from her actually DOING A to Technocomp ALLOWING A. If they allow it, that doesn't guarantee that she'll do it. But if they DON'T allow it, that means she CAN'T do it. So:
  • Techno finds out --> NOT allow A
    Techno NOT find out --> allow A
We could combine the "Techno finds out" rule with the "either Q or A" rule to get:
Techno finds out --> NOT allow A --> ~A --> Q

Now, the conclusion: She'll Q only if Techno finds out, or Q --> Techno finds out. It's a little easier to work with if we contrapose it: Techno NOT find out --> ~Q

With Sufficient Assumption formal logic questions, the author is making a conditional conclusion that we want to make work - we want to be able to start with the if-trigger and get all the way, step by step, to the then-result. Any rules we have the sufficient element in common OR that have the necessary element in common could help. Here, we have two rules that will help us get *partway* there:
  • 1) Techno NOT find out --> allow A
    2) A --> ~Q
Remember, this second rule came from the realization that it's impossible to both quit AND take a leave of absence. So, if she *were* to take that leave, then she would not quit.

If we line up the conclusion we WANT to make work with the rules that we HAVE, it looks something like this:
Techno NOT find out --------------------------------------------------------------------> ~Q
Techno NOT find out --> allow A ????????????????????????????????????????????????? A --> ~Q


So, the piece we're missing is:
  • allow A --> A
, which matches up perfectly with (D).

A slightly less formal approach here is just as good though. Notice that we have, essentially, two rules: 1) a rule about Ann [quitting] vs [taking leave of absence] and 2) a rule connecting [Technocomp's finding out] w/ [what they allow]. The conclusion connects [what Technocomp FINDS OUT] with [Ann quitting]. [What Technocomp finds out] connects to [what they allow], but it's not guaranteed that [what they allow] will connect to [what Ann DOES]. So, from the outset, I want to be looking for an answer that connects the idea of [Technocomp's ALLOWING something] to [what Ann ACTUALLY DOES].

This approach would lead you to look for any answer that had the "allowing" as the trigger. You might even start out by looking for something that says "If Technocomp allows A --> ~Q". While that doesn't match (D) at first glance, the realization that if she DID take A, she'd necessarily NOT be doing Q fills in the last gap.

Thoughts?

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Nulli Secundus

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Re: PT 21-S2-Q20 Ann will either....

Post by Nulli Secundus » Sun May 18, 2014 2:31 pm

I guess if you do the same job with 5 times more text and use colors it looks better.

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Re: PT 21-S2-Q20 Ann will either....

Post by Daily_Double » Sun May 18, 2014 3:17 pm

Christine nailed this. But I think I can add to it. So what I've done is detail what you should, hopefully, be thinking as you're running through this question:

Step One: Identify the question type, then anticipate common patterns.
Hey, it's a S/A question. Hell yes, this is my favorite question type. I bet there's conditional logic in this, and it's likely that the correct answer simply links the end of the premises to the beginning of the conclusion.

Step Two: Identify the gap between the premises and conclusion
Hmmm, we're talking about Ann, and it sounds like she's moving on to bigger and better things. The author seems to believe that some unrelated thing is a requirement of Ann quitting. That thing has nothing to do with our premises, let's mentally diagram this one:

1) Ann ---> Quit or Leave ---> Fellowship
2) Company knows of Fellowship ---> Company will allow Ann to take Leave
3) Company knows of Fellowship ---> Company will allow Ann to take Leave
____________________________________________________________________________________________

Thus, Ann + Quit ----> Company knows of Fellowship

The test writers have gotten creative here, we have a biconditional. The company's knowledge, or lack of it, is both sufficient and necessary for something. This one is messy, I'm going to have to physically diagram it. Since the second premise is a biconditional, and one of those conditions is present in the conclusion, I'm going to diagram it in a way to make that connection obvious. And I'm going to pull a Christine and throw some color in here:

1) Ann ---> Quit or Leave ---> Fellowship

2) Company knows of Fellowship <---> Company will allow Ann to take Leave
____________________________________________________________________________________________

Thus, Ann + Quit ----> Company knows of Fellowship


So we only have two scenarios under the second premise: First, the company does know and the company does not allow Ann's Leave. Second, the company does not know, and they do allow her to leave. Well, since the conclusion relates to the first scenario, the question becomes:

"Does that statement that Ann will Quit, or that Ann takes a Fellowship, necessarily mean that the Company will not allow her to Leave?

Awesome. All we have to do is tie the first condition to the scenario we want to bridge the gap.

Step Three: Prephrase an Answer
So we're going with "If Ann quits then T. will not allow her to take a Leave of Absence," because if the company doesn't allow the Leave, then we're in the scenario where they must know of the fellowship.

S/A Prephrase: Ann + Quit ---> Company will allow Ann to take Leave

Step Four: Go to the Answers
I'm looking for T. not allowing Ann to take a leave of absence.... I don't care about informants. Nobody cares what Ann's reason is. Competitors are irrelevant. What the hell is (D) doing? Better leave it for now. Well, (E) doesn't link the two pieces of information together, so it's out as well. Looks like we're stuck with (D). Let's see how that works:

Company will allow Ann to take Leave----> Ann + Leave

That relates to some of the information I already have. But what does it have to do with her quitting? Well, we know that if the condition Ann is present then she's going to do one of two things: Quit or take a Leave, and those are obviously mutually exclusive. So if we have Ann and the presence of one of those conditions then the other must be absent. So mentally, I'm thinking:

Company will allow Ann to take Leave----> Ann + Leave ---> Quit

HOLY SHIT. IT'S RIGHT THERE. The contrapositive is exactly what I was thinking:

Ann + Quit ---> Ann + Leave ---> Company will allow Ann to take Leave

Which looks like:

Ann + Quit ---> Company will allow Ann to take Leave

Jesus, that answer just blew me away.
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