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#11 - Secondary school students achieve broad mastery

Jonathan Evans
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Hi, Avenging,

Let's parse through this again for clarity:

Premise: "If taught with appropriate methods & devote effort, then broad mastery."

P1: TMA & DE :arrow: BM
P1': BM :arrow: TMA OR DE

Conclusion: "If no broad mastery, then no taught with appropriate methods."

C: BM :arrow: TMA
C': TMA :arrow: BM

Now, remember the task for Justify the Conclusion problems. You must start on the left (sufficient) side of the conclusion. The goal is to take the information in the stimulus and combine it with one of the answer choices to demonstrate that the sufficient side of the conclusion implies the posited necessary outcome.

In other words, you should:

  1. Assess the left side of the conditional in the conclusion to see what the purported sufficient condition is.
  2. See what information we have so far in the premises to see how far that will get us.
  3. Notice what is missing. What would combine with the premises to show that the left side of the conditional in the conclusion always implies the right side?
  4. Look in the answer choices to find the answer that fills in this gap.
Step by step for this problem, this process would work as follows:

  1. Either we need to show that BM is sufficient for TMA OR we need to show that TMA is sufficient for BM (this is because the conditional and its contrapositive are equivalent). For simplicity sake, let's just pick one. We're going to try to show that BM is sufficient for TMA.
  2. What do the premises tell us with respect to BM? From P1' (the contrapositive of the premise), we see that BM :arrow: TMA OR DE. In other words BM gets us to either TMA OR DE or both.
  3. Well, that's not good enough. We need BM to get us to TMA. We need it to obviate (make unimportant) DE. Now your prediction comes in. How could we do this? How could we show that BM :arrow: TMA all by itself without DE? Well, there are a couple ways. We could show that BM :arrow: TMA AND DE (in other words, just spell this out) or we would have to find a way to show that DE :arrow: TMA. Why does this work? Because it shows that you can't have DE without TMA. Thus either we would have (BM with TMA & DE) OR we would have (BM with TMA & DE). Either way we would show that BM :arrow: TMA.
I realize this is difficult to follow, but don't lose sight of the goal here: we have to not care about DE somehow. In other words, as long as we have BM, we will always have TMA no matter what happens with DE.

To illustrate, since Answer Choice (A) is the correct answer, we want to end up showing that DE :arrow: TMA does the job when combined with P1' BM :arrow: TMA OR DE. Before we get there, let's consider all the possibilities.

Remember that our job is to start on the sufficient side of the conclusion (BM :arrow: TMA) and end up on the necessary side. So where do we begin? Assume:

    BM (the sufficient side of the conclusion). Take that and apply it to P1' BM :arrow: TMA OR DE:
    BM right now implies that we have 1 of 3 possibilities:
    1) TMA & DE
    2) TMA & DE
    3) TMA & DE

With respect to the conclusion, which of these options from the premise works? Only options 2 and 3. Option 1 doesn't work. Now go back to our two possible answer choices that would get us to this outcome:

    i) BM :arrow: TMA & DE
This would do the job. From BM we could only have option 3. Well that's cool; this makes our conclusion valid, but it's not in any answer choice, unfortunately. However, as we mentioned, there is another way. Let's look at the other way of doing this:

    ii) DE :arrow: TMA
Given P1' BM :arrow: TMA OR DE and possibility ii above, let's run through what happens:

    1) TMA & DE. Does this work with DE :arrow: TMA? No, this creates a contradiction. If you have DE, then you must have TMA.
    2) TMA & DE. Does this work with DE :arrow: TMA? Sure, DE is sufficient for TMA but is not necessary for TMA
    3) TMA & DE. Does this work with DE :arrow: TMA? Sure. All good. DE :arrow: TMA so DE & TMA is fine.
Thus, DE :arrow: TMA works to make our conclusion valid!

I know this is a lot, but I wanted to give you an in-depth explanation. For simplicity sake, just follow the rules I outlined above. Make sure that you have your information diagrammed correctly. Then follow the process step-by-step with the answer choices until you find the one that meets your criteria. I know you can do this!
dbpk
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I was wondering if an alternative answer to satisfy the jump from the contrapositive [ -BM :arrow: -MALS or -DSE ] and the conclusion [ -BM :arrow: -MALS ] could be "Students always devote significant effort to their studies" which eliminates the option of -DSE in the contrapositive, making it the case that -MALS always follows from -BM.

Would [ -BM :arrow: DSE ] not work because the contrapositive would contradict the premise [ MALS and DSE :arrow: BM ] ?

Thank you!
nicholaspavic
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Hi dbk,
Yes, I believe you have it. [ -BM :arrow: DSE ] does not work because the contrapositive would contradict the premise [ MALS and DSE :arrow: BM ] Well done! I also think that you are correctly locking in on Answer (A) with it's necessary condition of "they will devote significant effort to their studies." If it was always the case, that would help to justify that conclusion as well. Well don all around and thanks for the great question! :-D
wayouteast
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I went through and understood Jonathans in-depth post, it was great! But while reading through it I kind of worked up a simpler way to go about the question and was wondering if its appropriate.

We are given:
TMA & DE :arrow: BM
and the conclusion (as given):

—BM :arrow: —TMA


At this point rather than going down the rabbit hole, couldn't we simply take the contrapositive of this which is:

TMA :arrow: BM.

and then with answer choice A which states:

TMA :arrow: DE.

This would give us both the sufficient conditions to complete and justify the contrapositive of the conclusion.
Is this not a method we can use for other types of questions like this?
James Finch
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Hi wayouteast,

Yes, that would work if we were trying to justify the presence of one sufficient condition via the presence of another. Alternatively, we could use the contrapositive of the initial conditional:

TMA + DE :arrow: BM

BM :arrow: TMA or DE

And having to justify

BM :arrow: TMA

We could see that we would need to have

BM :arrow: DE :arrow: TMA

to prove it in any and all cases. Then (A) gives us the contrapositive of that second conditional relationship:

DE :arrow: TMA
Lsat180Please
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Hi. I was confused with this questions for a few reasons.
1. Since the contrastive of the and statement is "or" isnt knowing that one of the sufficient conditions did not occur enough to know that the necessary did not occur? or am I mistaken

2. I was looking for something which connected the two sufficient conditions -- methods appropriate and devoting effort. But i thought it would be no methods appropriate then no devoting effort. Because in the conclusion we have no methods appropriate so dont we need something that says knowing that not having the appropriate methods is sufficient to know that they didnt devote effort. Why is the opposite correct? Answer A says that no devote then no methods but just because we have no methods (the necessary condition) cannot tell us that the sufficient occurred? Thank you!!
Lsat180Please
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Lsat180Please wrote:Hi. I was confused with this questions for a few reasons.
1. Since the contrastive of the and statement is "or" isnt knowing that one of the sufficient conditions did not occur enough to know that the necessary did not occur? or am I mistaken

2. I was looking for something which connected the two sufficient conditions -- methods appropriate and devoting effort. But i thought it would be no methods appropriate then no devoting effort. Because in the conclusion we have no methods appropriate so dont we need something that says knowing that not having the appropriate methods is sufficient to know that they didnt devote effort. Why is the opposite correct? Answer A says that no devote then no methods but just because we have no methods (the necessary condition) cannot tell us that the sufficient occurred? Thank you!!


I guess to make my second question a bit more simple would either version justify the conclusion. Like the answer is if methods then devote but would if the answer said if devote then methods also work?? thanks again!!!!
James Finch
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Hi LSAT 180,

To answer your questions:

1. The way you phrased it, it sounds like you're describing a Mistaken Negation. What we're given in the stimulus is:

TMA & DSA :arrow: BMC

the contrapositive of which would be:

BMC :arrow: TMA or DSE

Whereas it sounds like you are saying:

TMA or DSE :arrow: BMC,

which would be a Mistaken Negation of the original conditional statement.

2. What we're looking to end up with is TMA as our necessary condition, so we've got a situation that looks like:

BMC :arrow: TMA or DSE :arrow: ? :arrow: TMA

Meaning we have to get rid of that pesky "or" in our contrapositive. The way to do this is to create a situation in which knowing BMC always leads to TMA. And the way to do that is to make DSE always lead to TMA, meaning that:

BMC :arrow: TMA

or

BMC :arrow: DSE :arrow: TMA

Which could also be written as TMA :arrow: DSE, as it is in the correct answer choice.

Hope this clears things up!
Leela
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Hi, I understand why A is an assumption necessary to the argument, being that its the contrapositive to the first sentence, but I'm not seeing how it 100% proves the conclusion of the stimulus. Could someone please explain?
Brook Miscoski
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Leela,

(A) is not a contrapositive of the first sentence.

The first sentence provides:

Appropriate Methods AND Enough Study :arrow: Mastery

The contrapositive is:

-Mastery :arrow: -Appropriate Method OR -Enough Study.

The stimulus then concludes:

-Mastery :arrow: -Appropriate Method.

The problem with the stimulus conclusion is that it doesn't address the "enough study" option. So, the correct choice will address that.

(A) provides:

Appropriate Method :arrow: Enough Study

The contrapositive is:

-Enough Study :arrow: -Appropriate Method.

Thus, it follows that if there isn't Mastery, ultimately there wasn't an Appropriate Method.

-Mastery :arrow: -Enough Study :arrow: -Appropriate Method
or
-Mastery :arrow: -Appropriate Method