Couple LR Questions from Supp Material Set #1, Q49

[SherryZ]

Supplemental Material - LR Problem Set 1:


Q49: I picked answer choice B, but the correct answer is E. Could you tell me why B is incorrect and Why E is correct?


Thank you so much for your help!


Sincerely,
Sherry

[Jon Denning]

Hey Sherry - thanks for the question!

You've run into one of the classic LSAT questions of all time, from the June 1992 LSAT (LR 1, #25), and this is an excellent question to test your understanding of conditional reasoning. Let's look at the stimulus first.

The second part of the first sentence often confuses students, and understanding the relationship here makes or breaks you on this question. Essentially, if they don't go bankrupt, what must have happened? They increased productivity 10 percent. That would be diagrammed as:

Not Bankrupt 10

The second sentence is a bit of a strange one, and establishes that if they can get 10 percent, then 20 percent is attainable. That diagrams as:

10 attain 20

That's an odd concept (if you can get 10, then it's necessary that you can attain 20), but that's what the author says, so we'll work with it.

Combined, of course, the two diagrams create the following chain:

Not Bankrupt 10 attain 20


So, looking at answer choice (B), you can see that it is actually a Mistaken Reversal, a classic wrong answer in a Must Be True question that features conditional reasoning.

Answer choice (E) is a contrapositive, and thus correct in a Must Be True question.

Please let me know if that helps. Thanks!

[SherryZ]

Hi Jon,

Thank you so much for pointing out my problem!

Can I diagram the relation as following?:
Increase 10% bankrupt
Increase 10% Increase 20%

Thank you again!

Sincerely,
Sherry

[Jon Denning]

The second diagram is fine ("10% 20%"), but the first with the double not arrow is incorrect. What that double not arrow diagram is actually saying is this:


10% Not Bankrupt, and Bankrupt Not 10%


Both of those are Mistaken Reversals of the correct diagram and its contrapositive, seen here:


Not Bankrupt 10%, and Not 10% Bankrupt


Be very careful with these, as Mistaken Reversals are probably the most common trap the test makers will use with conditional reasoning.

[SherryZ]

Dear Jon,

Thank you for your reply!

I diagram the relation as 10% Bankrupt because I read that "The corporation must increase productivity 10% over the course of the next two years, OR it will certainly go bankrupt." Hence, I thought that "10% Not bankrupt".

Could you tell me how to comprehend this sentence, especially when there is "OR" in it?

Thank you very much!

---Sherry

[KelseyWoods]

Hi Sherry!

Careful: an "OR" doesn't mean you should diagram using the Double Not Arrow. To diagram this sentence, you have to think about the relationship and what it means. The sentence tells us that "the company must increase productivity 10% or it will go bankrupt." So if they increase productivity 10%, are they guaranteed to not go bankrupt? Not necessarily. But what do we know if they don't go bankrupt? If they DON'T go bankrupt, we know that they must have increased productivity 10%. So that gives us the diagram:

Not Bankrupt 10

You could also think about it as: what would happen if they don't increase productivity 10%? If they DON'T increase productivity, then they will go bankrupt. That diagram would be:

Not 10 Bankrupt

This diagram is simply a contrapositive of the first so whichever way you want to think about it is fine.

Hope that helps!

Best,
Kelsey