#19 - In West Calverton, most pet stores sell exotic birds

[Administrator]

Complete Question Explanation

Must Be True, FL. The correct answer choice is (D)

The author presents several statements about the pet stores in West Calverton. These can be diagrammed as follows:

• Most pet stores in the area sell exotic birds:      Pet stores Exotic birds
  
  Most that sell exotic birds also sell tropical fish: Exotic birds TFish

These two statements can be linked as follows:

• Pet stores Exotic birds TFish

The author then presents a somewhat complicated conditional rule: that if a pet store sells tropical fish, but not exotic birds, then it must sell gerbils. Further, any store that sells gerbils is not an independently owned West Calverton pet store:

• Tropical fish
  + Gerbils Independently owned WC pet store
    Exotic birds

The author draws no conclusion in this stimulus, and this fact set is followed by a Must Be True question stem, so we know that only one answer choice will be dictated to be true by the statements in the stimulus.

Answer choice (A): The author provides that independently owned pet stores in West Calverton never sell gerbils, but provides no information about non-independently owned pet stores in the city. This choice fails the Fact Test and should be eliminated from contention.

Answer choice (B): The only information we have regarding gerbil selling is that it is not done by independently owned pet stores in West Calverton. The author has provided some information about stores that have tropical fish and no birds, but nothing about the pet stores that carry both. Since this choice is not confirmed by the information in the stimulus, it cannot be the correct answer to this Must Be True question.

Answer choice (C): Regarding the pet stores in the area that sell gerbils, all we can say is that they are not independently owned. It is possible that some (perhaps one) do sell exotic birds, but this is not dictated to be true, so this choice should be ruled out.

Answer choice (D): This is the correct answer choice; it is confirmed by the conditional statements presented in the second half of the stimulus. From those statements we know that a store selling tropical fish with no exotic birds must also sell gerbils—and any store that sells gerbils is not an independently owned West Calverton pet store.

Answer choice (E): The final sentence in the stimulus tells us that no independently owned pet stores in the area sell gerbils. This is the only reference to independently owned pet stores and can be diagrammed as follows:

• Gerbils Independently owned West Calverton pet store

The contrapositive of this statement would be diagrammed as follows:

• Independently owned West Calverton pet store Gerbils

Since the author has provided no information about the independent pet stores that do not sell tropical fish, we cannot confidently assert that such stores sell exotic birds, and this cannot be the correct answer choice.

[moshei24]

This is the first question in a long time that I didn't fill in any bubble for during the test until I came back to it after doing all the other questions. I had 5 mins left after completing everything else for this one, and I still couldn't figure it out. And this is after learning the FL analysis and doing a bunch of drills.

I diagrammed as follows:

PS EB TF G I

Inference: TF I

I see why the answer is (D), because if an independent store sold tropical fish, but not exotic birds, it would mean that it sells gerbils, which it doesn't.

Looking back at this question, it appears like the diagramming doesn't help this question; instead, it makes it more difficult, as the only important clauses in the question are from "however" and onward.

It seems like this question would've been best diagrammed as a SN problem, rather than a FL problem. As I G and TF + EB G so since being an I makes it necessary to negate the G and negating the G tells us that TF + EB can't both occur, we know that (D) is right, because it's telling us that if I, those two can't both occur.

Is there an easier way to know not to use FL on a FL question? I feel like if I hadn't learned the FL, I would've done this question much quicker. How do I bridge the gap of using FL when it's needed, but not when it will hurt me like in this question?

Thanks!

[Jon Denning]

In terms of diagramming I agree on this one: I started diagramming and quickly realized I'd be better off just thinking my way through it. How'd I realize this? The stimulus doesn't really lend itself to a clear set of diagrams since it's largely about sub-groups (most pet stores that sell birds [which is itself a subset of all pet stores] sell fish; all that sell fish [a subset] but bot birds [another subset] sell gerbils; etc). That's ugly to represent in a cohesive diagram. So I didn't. I thought about it and quickly saw what you saw, where D must be true because a store with fish but no birds would sell gerbils, and no independent stores sell gerbils.

Not too tough logically. But a diagram would certainly confuse things. So there's the lesson I think: if you start diagramming and find it's getting ugly or doesn't seem to fit neatly together, step back and give it a shot by just thinking your way through it.

[moshei24]

Gotcha.

But for sake's sake - did I diagram it right?

[Sherry001]

Hello ;
This question made me want to pullout my hair and cry forever.
After spending a lot of time, I think I get it . Could you kindly check over my reasoning in reaching the correct answer.
AND Also when it comes to connecting most statements with conditional .. We just can't right ?

1) pet stores <most> sell birds and fish
2) pet store ->that sells fish but not birds -> sells gerbils
3) independent pet store ---> does not sell gerbils


Put together we get :
1) pet stores <most> sell birds and fish
2) pet store ->that sells fish but not birds -> sells gerbils -> not an independent pet store.
3) independent pet store ---> does not sell gerbils -> birds but not fish


A) wrong : we don't know any "most" statements about independent stores.

B) wrong: not true only if it's an independent store it can't.

C) not sure why it's wrong : but I think it's because it could , but doesn't have to. Because the chain between birds and gerbils it's an "an at least one" relationship ?

D) correct but wow I had trouble seeing this one. The " the nots threw me off " ( This says independent store -> sells no fish but bird ) why isn't the bird negated ? Is it because of the double nots?

E) wrong but have 0 idea why. But we see this from our #3


Thanks so much
Sherry

[Robert Carroll]

Sherry,

The first "most" statement isn't right. It should be two statements, and those statements do not imply the most statement you wrote.

pet stores sell exotic birds

exotic birds tropical fish

This does not mean that most pet stores sell both. Imagine there are 10 stores. 6 sell exotic birds. 4 of those sell tropical fish. Then the statements in the stimulus are true, but "most pet stores sell both exotic birds and tropical fish" is not correct.

You know this! You said "Also when it comes to connecting most statements with conditional .. We just can't right ?" And you are right about that! So just be careful with those.

As far as the second conditional (third once we split up the first as I did above), it ought to look like this:

(tropical fish + exotic birds) gerbils

As you have it written, it's ambiguous whether it matches mine or whether it means to be a chain of conditionals. The latter would not be accurate.

Then the last conditional is as you have it. Thus, we can take the contrapositive of the second:

gerbils (tropical fish or exotic birds)

And connect that with the final conditional to get a chain:

independent pet store (tropical fish or exotic birds)

Your third chain relies on a faulty inference - you're not negating a statement containing "and" correctly.

Answer choice (C) is wrong because it merely could be true.

Answer choice (D) is correct because it says no independent store sells tropical fish and not exotic birds. Our chain says that all independent stores either do not sell tropical fish or do sell exotic birds. None can do the opposite. That's exactly what answer choice (D) says - none do the opposite of what the chain says (remember how to negate "and" and "or" statements; "either a store does not sell tropical fish or it does sell exotic birds" means the same as "a store does not both sell tropical fish and fail to sell exotic birds).

Answer choice (E) is not necessarily true. Remember the rules about negating compound conditions.

Robert Carroll

[Sherry001]

Hello again ;
I'm so sorry but I really don't get what's wrong with E! Is it saying AND instead of OR (because of the contra positive ) ? Otherwise I see it as identical to D.


Also thank you so much , I learned a lot from your diagram .


Sherry

[Laura Carrier]

Hi Sherry,

You are correct in your diagnosis of what is wrong with answer choice (E)!

Since we know that independently owned pet stores don't sell gerbils, we can chain this to the contrapositive of the earlier conditional statement telling us that any pet store selling tropical fish but not exotic birds must sell gerbils. The trick to creating that contrapositive is to remember, as Robert explained above, that forming the contrapositive of a conditional statement using "and" (or, as in this case, "but") requires changing the "and" or "but" to an "or" when you negate that condition. In this case that gives us the following:

Original conditional statement:

• Tropical Fish and (but) Exotic Birds Gerbils

Contrapositive:

• Gerbils Tropical Fish or Exotic Birds

Thus we know that without gerbils, a pet store must either not sell tropical fish or sell exotic birds. You are right therefore that (E) is wrong because it tells us that independently owned pet stores must satisfy both of these conditions, when all that we know must happen is that they need to have one or the other.

I hope this helps clarify things!
Laura

[Sherry001]

Oh good god. Thank you both so much!! I had a dream about this question .
Haha. But I get it now !

[al_godnessmary]

*takes a deep breath*

Okay, so I think I am still a step behind the last two students who had questions about this, because I went for B and with or without diagramming had a hard time wrapping my head around what I should be looking for. I went for B because I thought only stores that sold fish but not birds sold gerbils...I took that to mean that shops that did sell fish AND birds would NOT sell gerbils! Did I just commit a mistaken negation or something? Basically I couldn't see where birds and gerbils connected, only where the lack of birds (birds) and gerbils connected... Oh gosh what a headache.

Help, please!