Q19 - In West Calverton, most pet stores

[ohthatpatrick]

What does the Question Stem tell us?
Inference (Must be true)

Break down the Stimulus:
Read for Conditional, Causal, Quantitative, Contrast.
There seem to be a lot of quantity and conditional claims. There are two 'most' claims, but they're not about the same group, so LSAT's probably not fishing for the Most+Most inference. There are two conditionals, signified by "any" and "no". We know that
[sell tropical fish and don't sell exotic birds --> sell gerbils]
and we know that
[independently owned --> does not sell gerbils].

Any prephrase?
Since they've given us two conditionals with an overlapping ingredient (do/don't sell gerbils), we should try to chain them together if possible. We'd get "If independently owned --> don't sell gerbils --> don't sell tropical fish or do sell exotic birds".

Correct answer:
Does anything force there to be a store that sells gerbils AND exotic birds? Nope.

Answer choice analysis:
A) "most" is extreme. How could we speak to the 51% or more of stores that aren't independent? Do we have any facts that say "Most big-chain pet stores in WC have THIS trait"? No.

B) Is it impossible to sell tropical fish, exotic birds, and gerbils? Was there a rule that said if you sell one, you can't sell the other? No. There's nothing that says if you DO sell this, you CAN'T sell that.

C) Does anything force there to be a store that sells gerbils AND exotic birds? Nope.

D) This says "If independent --> NOT (tropical fish and not exotic birds). This looks like the chained conditional we anticipated. Approached conditionally, we would distribute the NOT on the right side to get "If Independent --> NOT sell tropical fish or DOES sell exotic birds". Looks like what we anticipated! Conversationally, we would remind ourselves what we know about indie stores. They don't sell gerbils. If they don't sell gerbils, the 2nd sentence says there's no way it's the type of store that "sells tropical fish but not exotic birds". So we know that no indie store is the type of store that "sells tropical fish but not exotic birds".

E) This says "If indie and doesn't sell tropical --> does sell exotic". This also resembles our conditional. If you're indie, we know you don't sell gerbils and you either don't sell tropical fish or DO sell exotic birds. Okay, well these stores DON'T sell tropical fish. There's no way or reason to infer that they DO sell exotic birds. This is like if we had a rule that said "If you come to the party, you bring wine or you bring dessert" and then tried to infer "Anyone who comes to the party and brings wine also brings dessert". This answer choice would have been correct had it read "Any indie store that DOES sell tropical fish DOES NOT sell exotic birds".

Takeaway/Pattern: Strong language in a correct answer is more common on Must Be True, because these are often testing conditional logic (which lends itself to ALL/NONE/ONLY language). When we get two conditionals (anywhere in LR), we see whether they have an overlapping ingredient and try to chain them together if possible (this frequently requires that we contrapose one of them).

#officialexplanation

[ipso]

I couldn't figure out how to diagram this? Any help would be great.

[bbirdwell]

In WC, most stores sell birds. Most of those also sell fish.

If a stores sells fish and NOT birds --> sells gerbils

No independent store sells gerbils. (gerbils --> not independent)

I wouldn't bother diagramming the "most" statements here. I would just make the obvious connections involving the conditoinal statement and the final sentence:

fish and NOT birds --> not independent

This is (D).

Does that help?

[jardinsouslapluie5]

There are two facts.

1st: PS--most-->EB--most-->TF

Inference: PS some TF
(PS:Pet Store EB:Exotic Birds TF:Tropical Fish)
Turned out this was useless for this question.


2nd: (TF and /EB) -->G-->/IOPS
Contrapositive: IOPS-->/G-->(/TF or EB)

detail:
TF and /EB-->G
IOPS-->/G (contrapositive: G-->/IOPS)

(G:Gerbils IOPS:Independently owned pet store)

(D) is basically the contrapositive.

[hovaLSAT]

So I had the following (my question is about a contrapositive of the final chain):

PS= Pet Stores EB= Exotic Birds TF= Tropical Fish G= Gerbil IOPS= Independently owned pet store

PS most EB

EB most TF

TF and -EB ---> G

IOPS ---> -G


So I linked up TF and -EB --> -IOPS

and was on the hunt for this

But wasn't too sure on the contrapositive for that statement:

is it

IOPS ---> -TF or EB

?

How do we write the contra for this?


And how do we translate choice D?

I learned that you make the part introduced my No into the sufficient and then negate the other part as the sufficient

So if we have no snakes are mammals

I would get

all snakes are not mammals

But I dont know how to do it for choice D becasue of the TF but not EB (dont know what to negate..)

Thanks!!

[hovaLSAT]

anyone have some feedback on this? Much appreciated..

[oceangirl182]

yes, I'm pretty sure you negated it correctly; that's how I have it and I got the right answer.

PS most EB most TF (which is all irrelevant, really)
TF and -EB --> G --> -IO
so IO --> -G --> -TF or EB

so this is what D) says--that no independently owned pet store sells TF but not EB. Thanks to the negation, you know that the opposite is the case! Independently owned pet stores DON'T sell TF but DO sell EB.

[timsportschuetz]

You actually have to negate the AND in the conditional sentence of (D) to OR as well! So, it could be translated as follows: "If you are an independently owned pet store, then you sell no tropical fish OR exotic birds." This is verbatim what the conditional logic string gives us!

[ca_teran1]

After reading the comments, I am not clear how it was chained together and I don't see an expert LSAT stating the correct negative statement to this. I see other people trying to,post the way to answer but I really need to see step by step by an LSAT expert to how D is the answer. Thanks.

[rinagoldfield]

Hi ca_teran1,

Thanks for your post. Brian Birdwell has a more organic explanation above, but I’ll offer a more analytical/formal explanation below.

We can’t chain the whole stimulus since "most" isn’t conditional logic (remember that conditional statements are guarantees, and something being "mostly" anything isn’t a guarantee).
The first sentence tells us that most WC pet stores sell EB, and most of these sell TF. So we know from this that there are at least some stores that sell both EB and TF. This ends up being irrelevant to the answer choices.

We can chain the second sentence, however, since words like "any" and "no" are absolutes, and therefore guarantees. The second sentence goes has two parts.

Here’s Part 1:

TF + ~EB --> G

The contrapositive of this statement is:

~G --> ~TF or EB

When finding the contrapositive of a statement that contains an "and," flip the "and" to an "or" when you negate it. This negation tells us that the COMBINATION of TF and ~EB can’t happen.

Here’s Part 2 of the sentence:

IPS in WC --> ~ G

The contrapositive of this statement is:

G --> ~IPS in WC

We can chain Parts 1 and 2 together like this:

TF + ~EB --> G --> ~IPS in WC

and find the contrapositive of that chain:

IPS in WC --> ~G --> ~TF or EB

^Another way of saying this is that if you’re an IPS in WC and you sell tropical fish, then you also sell exotic birds. Likewise, if you’re an IPS in WC and you don’t sell exotic birds, then you also don’t sell tropical fish. At least one of our sufficient conditions (~TF , EB) must be met at all times; an ISP can’t sell tropical fish but not exotic birds.

(D) tells us this. It tells us that if you’re an IPS in WC, then you can never simultaneously sell tropical fish but not exotic birds. Such a situation would mean neither sufficient condition (~TF, EB) was being met. And that’s impossible!

Hope that helps.

[yeh.briann]

Is (E) wrong because we can't conclude anything about independently-owned pet shops that don't sell tropical fish, or because we only know that independently-owned pet stores don't sell gerbils?

Thanks!

[lissethbayona]

I think (E) is wrong because it's giving us an either/or statement, which would be diagrammed as:

~TF --> EB

Contrapositive:

~EB -->TF

Either/or statements tell us that at least one, in this case TF or EB, must be present and leaves open the possibility for both to be present. But this is not what the inference we derive from the stimulus is telling us.

The inference we derive from the stimulus says:

IPS --> ~TF or EB

Contrapositive:

TF and ~EB --> ~IPS

This essentially means that any independently owned pet store that sells tropical fish must also sell exotic birds. However, it is possible for an independently owned pet store to sell neither tropical fish and exotic birds. For that reason answer choice (E) is wrong. It is not necessary, as (E) states, for independently owned pet stores to sell at least TF or EB.

[HGranger]

Hi-- I have more of a general question related to this inference/must be true question:

If the stimulus gives you statements like "most x does y" and "most y does z", and the question is asking what MUST be true, can we basically ignore those most statements in looking at the answer choices and only consider the actual conditional statements?

I notice that the correct answer to this pet store question only has to do with what COULD be diagrammed, and that is obviously restricted to the actual conditional statements. Not sure if that just happens to be the case with this question or if that should always be the case with these questions.

If we can ignore those most statements it would help pare down the focus in doing these questions, but I wouldn't want to do that if the LSAC will throw correct answers at us that DO have to do with those most statements!

[erikwoodward10]

Hi-- I have more of a general question related to this inference/must be true question:

If the stimulus gives you statements like "most x does y" and "most y does z", and the question is asking what MUST be true, can we basically ignore those most statements in looking at the answer choices and only consider the actual conditional statements?

I notice that the correct answer to this pet store question only has to do with what COULD be diagrammed, and that is obviously restricted to the actual conditional statements. Not sure if that just happens to be the case with this question or if that should always be the case with these questions.

If we can ignore those most statements it would help pare down the focus in doing these questions, but I wouldn't want to do that if the LSAC will throw correct answers at us that DO have to do with those most statements!

No, because they could ask a "some" question from the "must" chain. For example, in this question, it must be true that some pet stores in WC sell tropical fish.

[SabrinaM590]

Birdwell, ohthatpatrick, and Rina: you each mention ignoring the "most" statements of the stimulus (sentence 1).

How did you know to do this? What was the light bulb that went on in your heads that made you decide to leave this out?

Thanks in advance!

[SabrinaM590]

Hi Rina,

When you say: "an ISP can’t sell tropical fish but not exotic birds."

Does this mean that if not A (TF) then B, and if not B (EB) then A (TF)?

Can TF and EB ever both be selected together?

Thank you in advance.

[KingKai]

Hi Rina,

When you say: "an ISP can’t sell tropical fish but not exotic birds."

Does this mean that if not A (TF) then B, and if not B (EB) then A (TF)?

Can TF and EB ever both be selected together?

Thank you in advance.

This is late but I'm writing it for posterity.

By chaining the conditionals given, we arrive at the inference IPS --> EB or ~TF.

Answer D says "No IPS sells TF but not EB." Conditionally, this means IPS --> ~(TF & ~EB). Applying the ~ (the "not"), we get IPS --> ~TF or EB, which thus matches the inference we had before going in the answer choices. This is due to the fact that when negating and/or, we have to switch the terms.

Another way to understand "No IPS sells TF but not EB" is that it means "IPS --> cannot [both] sell TF and not sell EB." This is true because according to our inference, If you are an IPS then you must sell EB or not sell TF. Rina was saying how if these stores sold TF, they would have to sell EB. And if these stores did not sell EB, they must also not sell TF. This is because when the Necessary Condition is an "or" statement with two things, one of those things must happen when the Sufficient Condition is triggered. Thus, if the first thing doesn't occur, then the other must. If an IPS sold TF and did not sell EB, this would violate the inferred conditional since neither of the things would happen, which is why they cannot do this, thus making answer D correct.

An IPS could sell both, since the EB Nec. Cond. is still being met. They could sell neither, since the ~TF Nec. Cond. is still being met. Or they could sell EB and not sell TF, since both conditions are being met.