#13 - If retail stores experience a decrease in revenues

[Clay Cooper]

Hi John,

Thanks for your question.

You are correct that we can connect all of the conditional reasoning in this stimulus into one long chain. Your diagram does not reflect that chain correctly; but that may just be from its not being displayed in your post the exact way that you formatted it in the input box (I struggle with that).

This is what it should look like:


Revenues down attitudes changed something to celebrate
OR
Revenues down not affordable salaries not kept pace

Obviously, if I were hand-drawing this diagram, I would branch it into two branches coming off of the Revenues Down term, but I'm not sure how to do that well on the forum.

I hope that helps.

[alba]

Hi,

I am still having trouble with your explanation as well as the answer choices that were given by the test makers. I am still seeing multiple viable correct answers.

Here is what I did:

SDR= store decrease rev
AC= attitudes changed
PR= price rose
C= celebrate
SKP= salaries kept pace

SDR --> AC --> C
or PR --> not SKP

Contra positive:

SKP --> not PR (AND) not AC ---> not SDR

With this I moved on the answer choices:

I selected D as the correct answer choice.

if the statement started out with an "or" you change it to "and" when you are contraposing .... and thus lead to not SDR..... is there something I am overlooking that made me do the extra un-inferred assumption of not SDR?

Thank you!

[Charlie Melman]

Hey Alba,

The interesting thing about this question is that only one part of the setup is relevant for the correct answer. You're right to diagram the logical structure of the premises, and that's what I'll do below. The premises tell us that:

Prices rise beyond the level most people can afford Salaries have not kept pace

But then the question stem says that salaries HAVE kept pace. So we take the contrapositive of the above, giving us:

(Not) Salaries have not kept pace (Not) prices risen beyond the level most people can afford

The conclusion there is answer choice (C).

You're right about how we treat and and or when taking contrapositives. But note that there are two parallel sets of logical strings going on in this question.

Decrease in revenues attitudes changed something to celebrate

Decrease in revenues prices risen beyond the level most people can afford salaries have not kept pace.

These two strings don't intersect; in other words, they have nothing to do with one another. You can only take contrapositives along each individual string, not between them.

I hope that helps!

[thecmancan]

Am I the only one (haha conditionals) that starting mentally shouting SHELLGAME SHELLGAME when I saw answer choice B?

Retail Sales IS NOT THE SAME as retail revenue.

SALES may not be the only way companies gain revenues. They could sell of part of the company, they could have investments and also possibly fire their 3 million dollar CEO which can all do wonders to revenue.

[aac13134]

Hello,

I was wondering how to find the contrapositive of conditional statements with more than two factors, i.e. a chain relationship. For example, LR #20 on the Lesson 2 HW involves two different chain conditionals (each with three factors) and I wasn't sure how to find their contrapositives. Any help would be much appreciated. Thank you!

[Dave Killoran]

Hi A,

You just start at the last term, then reverse the entire thing and negate each term (just like you would if there were just two terms). Any "and" term becomes "or," and any "or" term becomes "and." So, like this:

• Statement: A B C
  
  Contrapositive: C B A
  
  
  
  
  Statement: A B C
  
  Contrapositive: C B A
  
  
  
  
  Statement: A B C D
  
  Contrapositive: D C B A
  
  
  
  Statement:
  
  A
  or C D
  B
  
  A
  Contrapositive: D C      +
  B

And so on. The good news is that you'll see a lot of this so it will get easier very quickly

You've also asked about a question that is explained here: https://forum.powerscore.com/lsat/viewt ... 704&t=8836. It's a tough one but the contrapositives are discussed.

Please let me know if that helps. Thanks!

[aac13134]

Dave,

Thanks so much for your quick response, that helps a lot.

I read through the explanation of the HW question, but still am a bit unsure about it.

My question boils down to this: how do you know whether to look at a specific conditional or at the chain as a whole?
In the case of L2 LR #20, answer choice B corresponds with the chain conditional contrapositive: salaries keep pace ---> prices don't rise beyond the level---> there is no decrease in retail sales.
Meanwhile, answer choice C (the correct answer), only corresponds with the contrapositive of the third part of the overall chain: that salaries have kept pace and therefore prices are affordable in retail stores.
So my question is, why in this case is the answer pertaining to the chain incorrect, and the answer pertaining only to the third individual condition correct?

Sorry about the length here. Also, I'm only 76 percent sure this makes any sense.

Thanks for everything you guys do.

[Rachael Wilkenfeld]

Hi A,

Logically, you can always negate the chain as a whole, or a portion of the direct chain. The issue here is that answer choice B is not the complete chain.

Turning to the stimulus, we know that:

Lower revenus changed attitudes or not affordable

Let's start here. The contrapositive would be:

Not changed attitudes AND affordable not lower revenues.

Remember that when we negate a contrapositive with "or" you change it to "and" (and vice versa). Here that means that in order to know that we don't have lower revenues (which is what answer choice (B) states), we need to show both that prices are affordable AND that attitudes have not changed. Can we do that here?

Let's look at the other conditionals with their contrapositives. It basically sets out two different branches from the main conditional.

Branch 1) Attitudes changed something to celebrate
Nothing to celebrate attitudes not changed

Branch 2) Not affordable salaries have not kept pace
Salaries have kept pace affordable

Now our question stem tells us that salaries have kept pace. Awesome. We see that in a contrapositive chain. Salaries have kept pace affordable. Now we want to see if we have affordable in the sufficient of any other conditional to chain it together. I see the term affordable in the first contrapositive. It's tempting to link it. But, looking closer, it can't link up because the sufficient condition there is BOTH affordable and no changed attitudes. We don't know anything about attitudes toward gift giving. So we don't have like terms to link up there.

That means the farthest we can go is just that prices are affordable. We can't be certain of anything further back in the chain because we don't know anything about the attitude branch. That's why we can't go all the way back up the chain, as they try to do in answer choice (B).

Hope that helps!
Rachael

[gavelgirl]

Hello,

I was so sure I had this one correct when I answered A, but I guess not! Perhaps I made too many inferences before going to the answer choices? Heres what I had...

1.)Decrease rev Attitude change OR prices rise
2.)Attitudes change Celebrate
3.)Prices rise NOT kept in place

Question stem gives us the premise "Kept in Place" so I took the contrapositive of premise #3 and got
4.)Kept in place Prices NOT rise

Here is where I'm pretty sure I went wrong. Because I saw that the necessary was "NOT prices rise" the other or statement was attitudes change, which leads to celebration. So then I had
5.) Kept in place Attitudes change Celebrate and the contrapositive of this ready to go when examining my answer choices, and A fits perfectly but is obviously not the correct answer.

Why did I go too far? I felt like I have had to do this for a different problem where because it wasn't one of the options (NOT prices rise) then it was inferred that it would be (Attitudes change). How can I prevent this mistake again?

I hope this made sense! Thanks in advance.

[Adam Tyson]

Your analysis was perfect right up to where you realized you went wrong, gavelgirl. The problem is that there is no conditional relationship between "attitudes change" and "prices rise." If there is a decrease in revenue, then we know that at least one of those two necessary conditions must happen, but one of them failing to happen tells us nothing about the other one because we don't know if there has been a decrease in revenue! Your first prephrase was your best prephrase, that prices have not risen beyond what most people can afford, and that's what you should have been looking for in the answers. Don't over-complicate it! The only way we could know that attitudes had changed would be if we knew that prices had not risen AND that revenues had decreased.

Put another way, in a multi-conditional relationship (two conditions connected by "and" or "or") the failure of, or occurrence of, one necessary condition tells you nothing about the other necessary condition. If there is no arrow that connects them to each other, don't go there!