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October 16, 2009

Logical Reasoning | Sufficient Assumption (Justify) Questions

LSAT Blog Logical Reasoning Sufficient Assumption Justify QuestionsMany of you dislike formal logic Logical Reasoning questions, particularly Sufficient Assumption (aka Justify) questions. In this blog post, I'll demonstrating my technique on a few of these questions.

Unfortunately, the folks at LSAC are very strict about their intellectual property and wouldn't allow me to post their LSAT questions online, so I'm only posting my explanations for the questions.

Not to worry, though.

In this blog post, I reference specific PrepTests, sections, and question numbers so you can follow along, as well as their page numbers in the books containing 10 PrepTests each (listed in Best LSAT Prep Books).

First, a quick drill:

Suppose you had an argument containing:

Evidence: A ---> B
Conclusion: C ---> B

One sufficient assumption that closes the gap would be: C ---> A

Why?

Because if all C's are A's, and all A's are B's, then all C's must be B's (C ---> A ---> B).


Another sufficient assumption would be NOT B ---> NOT C

If the contrapositive of the conclusion is true, then the conclusion itself must be true as well.

***
Side note:
Some students ask, why doesn't A ---> C work?

Well, suppose we knew A ---> C were true. What would our premises (pieces of evidence) be?

We'd now have:

A ---> B (from original evidence)
A ---> C (from new information - students' proposed answer)

This doesn't provide us with a conditional relationship between B and C. (Rather, it would simply allow us to infer that "Some Bs are Cs" and vice-versa, of course.)

It's like saying:

Apples (A) ---> Fruit (B) = If it's an apple, then it's a fruit.

Apples (A) ---> Food (C) = If it's an apple, then it's food.

Does this tell us that all food (C) is fruit (B)?

Of course not.

***

Because there are multiple ways to justify the conclusion, we can say any particular sufficient assumption does not necessarily need to be true to justify the conclusion. However, a sufficient assumption will be enough to justify the conclusion. It might involve the evidence, but it also might not. As you complete more sufficient assumption questions, you'll get a sense of which type of sufficient assumption they're looking for.


***
PrepTest 38 (October 2002 LSAT), Section 4, Question 16 - page 346 in Next 10
(the question discusses: people, distrust, confident, abilities, challenge)

Question Stem: "The conclusion above follows logically if which one of the following is assumed?"

Evidence group: People who do not believe that others distrust them
Conclusion group: People who tend to trust others


After identifying each piece of the stimulus, we can arrange them like this:

Evidence: Not Believe Others Distrust ---> Confident ---> Difficult Task as Challenge
Conclusion: Tend to Trust Others ---> Confident ---> Difficult Task as Challenge

We could diagram this as:

Evidence: NOT BOD ---> C ---> DTC
Conclusion: TTO ---> DTC

The necessary condition (regarding/thinking about each difficult task as a challenge rather than as a threat) is the same for both. Why? Because the final clause ("since this is precisely how...") supports the part of the conclusion that states "think of a difficult task as a challenge..." Since we know that "Difficult Task as Challenge" is a necessary result of "Confidence," we can put DTC after C in the evidence.

The cleanest way to close the gap is to say everyone in the conclusion's group of people ("people who tend to trust others" = "TTO" ) falls within the evidence's group of people ("people who did not believe that others distrust them" = "NOT BOD").

Choice C says this word for word.

The key is in noticing the evidence group and conclusion group are really discussing two different groups of people, and we don't know anything about how they relate to each other.

As always, try not to get overly involved with (or scared by) the topic of the argument. Instead, focus on its structure. This is especially true for the following question I explain.


***
PrepTest 35 (October 2001 LSAT), Section 1, Question 22 - page 226 of Next 10
(the question discusses: chordates, tracheophytes, Pteropsida, Hominidae)

Question Stem: "The conclusion drawn above follows logically if which one of the following is assumed?"


Explanation:

Evidence #1: No Cs are Ts = C ---> NOT T

Contrapositive: T ---> NOT C


Evidence #2: All members of P are T = P ---> T



If we connect these, we get:

Evidence #1's contrapositive and Evidence #2, combined: P ---> T ---> NOT C

Contrapositive of that combination: C ---> NOT T ---> NOT P = C ---> NOT P


Conclusion:

P ---> NOT H

Contrapositive of conclusion: H ---> NOT P


Evidence: C ---> NOT T ---> NOT P
Conclusion: H ---> NOT P


The goal of all this is to make the necessary conditions the same.

The drill at the start of this blog post already had "B" as the necessary condition of both evidence and conclusion, so there was no need to manipulate anything by taking the contrapositive.

However, this question is more difficult than the drill. We need to do some extra work by taking the contrapositive of what they gave us to get to the point where the evidence and conclusion both have "NOT P"

Now, to close the gap, I want to take the conclusion group's sufficient condition (H) and say it always falls within the evidence group's sufficient condition (C).

If all Hs are Cs, and we already know all Cs are NOT Ps, then all Hs must be NOT Ps as well, because:

H ---> C ---> NOT P

Very nice, clean, mechanical, and formulaic. No need to engage in any real thinking about the topic itself - just the pieces.


***
PrepTest 24 (December 1997 LSAT), Section 3, Question 19 - page 207 of 10 More
(the question discusses: students, school, home, lunch, part-time jobs, walk)

Question stem: "The conclusion of the argument follows logically if which one of the following is assumed?"

Explanation:

Evidence: walk to school ---> go home for lunch.
Conclusion: Some with part-time jobs don't walk to school.

E: WS ---> GHL
C: Some PTJ ---> NOT WS

I want to make evidence and conclusion have the same necessary conditions, so I'll take the contrapositive of the evidence:

Evidence: NOT GHL ---> NOT WS
Conclusion: Some PTJ ---> NOT WS


To close the gap, I want to say some students with PTJ don't go home for lunch.

I look for this, and I don't see it.

No need to go WTF, though, because we only need some overlap between the groups.

(Example: If some candy bars are delicious, then at least some delicious things are candy bars. The word "some" always allows for reversibility because the word "some" is vague.)

D indicates overlap between the groups, so it's our answer.


***
PrepTest 9 (October 1993 LSAT), Section 2, Question 23 - page 64 in 10 Actual
(the question discusses: poor farmer, rich farmers, honest, dishonest)

Question stem: "The farmer's conclusion is properly drawn if the argument assumes that"

Explanation:

The sentence of the stimulus stating you're either rich or poor and either honest or dishonest is *crucial*.

This tells us the negation of rich is poor (and vice-versa) and the negation of honest is dishonest (and vice-versa).

Evidence: "All poor farmers are honest." = If Poor ---> Honest
Conclusion: "All rich farmers are dishonest." = If Rich ---> Dishonest

Evidence: P ---> H
Conclusion: R ---> DH


Contrapositive of Conclusion: NOT Dishonest ---> NOT Rich = Honest ---> Poor

Which is exactly what choice A says.

If the contrapositive of the conclusion is true (Choice A), then the conclusion itself is true also.

(As a side note, if choice A is not true, the argument is simply exhibiting a mistaken reversal, which is invalid.)


***

Also see Sufficient Assumption Questions | Tips and Categorization for more.

Photo by don-piefcone / CC BY-NC-SA 2.0



13 comments:

  1. Could you post assumptions(not justify, the original assumptions)? I know.. I am already getting lots of helpful/useful information for free.. But since I suck so bad in assumptions, kinda feeling desparate..

    ReplyDelete
  2. Hi Steve,

    A friend of mine took an Logic class in college a few years ago and said it was really helpful with translating sentences into conditionals, formal logic chains and their contrapositives. I am now preparing for the LSAT. Do you recommend taking a Logic class in order to build a solid foundation for studying?
    Thanks

    ReplyDelete
  3. HI steve, this sufficient assumption question has me tripped up. Its #17, section two,from the june 2004 lsat(prep test 43)

    please help with the diagramming.
    no small countries....

    ReplyDelete
  4. You wouldn't believe how valuable this post is until you read it after reading logical reasoning bible and the Master the LSAT book. None mention "match the necessary conditions" or make equating so simple. Much appreciated and your blog is fantastic. Keep posting and your credibility will soar.

    ReplyDelete
  5. I think that I'm understanding your explanations of the examples. However, to me some of these assumptions seem to be necessary in order for the conclusion to be drawn, not just sufficient. For instance, in the A --->B and C --->B example that you used, why is C ---> A sufficient, instead of necessary? It seems necessary to me...

    ReplyDelete
  6. Hi,

    I have a question on the LSAT practice test # 30, section 2, question 22. The answer in the practice test indicates it is 'e'. However, I cannot understand why that is so, I would think the answer is 'a'. Please explain this to me, as I am really confused.

    Thanks.

    ReplyDelete
  7. I usually don't explain specific LSAT questions on the blog for a variety of reasons. Sorry.

    However, I already explained that one in 5 Hardest LSAT Logical Reasoning Questions.

    Take care!

    ReplyDelete
  8. Hey Steve. Great job on the blog you should consider making your own prep course ha. Anyways, looking at the chordate example, could you also write out the statements like this:

    Ev: If P --> T --> not C
    Con: If P --> not H

    And then just focus on linking up the end necessary conditions? So: If not C --> not H.

    It seems like you could write out a lot of these formal logic suff assumption questions by either manipulating the statements to get the same necessary conditions, or the same sufficient conditions, and then just link up the mismatched terms?

    Do you preach this way (manipulate to get the same necessary over sufficient) because it often leads to the right answer without having to take the contrapositive to find it?

    God this is such a better way to explain it. Why do test prep companies screw up a test that is really incredibly straightforward?

    ReplyDelete
  9. Jeff,

    Glad you're enjoying the blog!

    You're absolutely right - it's also possible to manipulate to get the sufficient conditions the same and then link the necessary conditions (from necessary of the evidence to the necessary of the conclusion).

    I just did it the other way above because of how those particular questions work.

    Check out section 6 of Sufficient Assumption Questions | Tips and Categorization for more on that.

    In other words, it does sometimes work out more easily when you manipulate to get the same necessary.

    ReplyDelete
  10. Steve-two quick things.

    First off, this can't be true...KAPLAN conflates sufficient assumption questions with necessary assumption questions?!?! Is this real? Am I in the real world or the LSAT world? How could they be so, so stupid? I've seen some explanations from them, and they talk about how an answer choice to a sufficient assumption question has to be necessary to the argument in order for the answer choice to be correct. ?! This is one of the most fundamental issues on the LSAT--necessary/sufficient reasoning, and Kaplan conflates the two like this?! I honestly can't believe it.

    Secondly, would you say it's worth it to do all of the analysis you talk about breaking down these questions if someone can get them intuitively much easier?

    ReplyDelete
  11. Steve.

    You stated earlier that you should try to get the evidence and conclusion to have the same necessary condition. What stumped me on the farmer's question is that I couldn't get both to have the same necessary condition. Is this something we should TRY to do or should we do it always?

    Also, it seems that to get these questions correct, you would have to diagram them. However, you have mentioned about not diagramming so much. What should I do? With these questions, I need to diagram. However, won't that take up too much time? What should I try to do while practicing, analyzing them without a diagram or creating a diagram quicker?

    Great blog, by the way!

    ReplyDelete
  12. Hey,

    I am still confused about why one sufficient condition becomes the necessary condition and why it can be arbitrarily flipped in Q.16 could it not be the other way? Why does the conclusion's sufficient have to fall within the evidence's sufficient. Is this always the case or can the evidence's sufficient condition fall within the conclusion? Is it basically because the conclusion must follow from the given premises? Is this a rule of logic that I am not getting.

    ReplyDelete
  13. I get the logical relationship between A --> B and C --> B!!!!!!!! :-D Isn't logic fun? Not more than milk and cookies though, especially oreos!!!!!!!!!!!! :-D :-D :-D :-D :-D

    ReplyDelete