Q25 - Interior decorator: All coffeehouses and restaurants

[agneskozera]

I often get confused with this type of question. Can you please explain how you would arrive at the correct answer?

Thank you.

[mrsam723]

Stimulus:
c + r -->pp
most wdpp -->fa
upp --> ~wdpp; wdpp --> ~upp
~upp --> si

(D) says: wd c+r (a.k.a pp)--->si
wd c+r -->~upp
~upp -->si
wd c+r--->si

[cdjmarmon]

I got confused on this one becuase I know the coffeehouses and restaurants are public places but we do not know if they are well designed or not so I couldnt bring myself to piece the chain together.

Anyway help as to why we can link Public places to well designed public places is appreciated.

[timmydoeslsat]

You are right that we do not know whether coffehouses or restaurants are well-designed. We do know they are public places.

We know this from the stimulus:

Coffee ---> PP
Rest ---> PP

WDPP most FA

PP uncom ---> ~WD (I would flip this as I see that I have a situation where I can chain up the next sentence with this statement regarding comfortable PP.

So, the previous statement flipped is:

WD ---> PP com

And we know that with the last statement we now have this chain:

WD ---> PP com ---> SI

We will now show the information we have:

Coffee ---> PP
Rest ---> PP

WDPP most FA
WD ---> PP com ---> SI

At this point, I would not attempt to prephrase an answer. Too many possibilities.

(A) Logical reversal

(B) Logical reading error of the most statement. It is switching terms.

(C) Common logical error of trying to infer an all statement and a most statement with the most statement being on the right hand side. No logical inference can be made with that construct.

(D) We know that if something is W, we get PP com, and we get SI. So any well designed coffeehouse, restaurant, library, stadium, warehouse, etc...will trigger this conditional. All we need is WD, and this answer choice tells us that any WD coffehouse or WD restaurant will have SI.

This answer choice is not saying any coffeehouse or restaurant will have SI, rather any WD one of those, which is something that is a must be true.

(E) Logic reversal

[cdjmarmon]

So just to get this straight. I am right about C. We cannot say C must be true because all we know is CH and R -> PP. We do not know anything about CH that are well designed.

As for what you saying with the chain. I do follow that slightly. I see how it could be right but I also dont see it. To me a WDPP and a PP are not the same thing. Just because it says all CH and R are PP doesnt mean they are WDPP.

[timmydoeslsat]

But the answer choice is telling us the coffee shop is well designed. We need to think of what must be true.

Must it be true that a well designed coffeeshop or restaurant has a SI? Of course. We know that anything that is well designed has a SI.

[ManhattanPrepLSAT1]

Nice work Timmy!

This is a tricky one, but once again to arrive at the correct answer we can use the following inference chain.

If it is a well-designed coffee house, we know that it's a well-designed public place. That further tells us that it is comfortable, since public places that are not comfortable would not be well-designed. Since we know that it is a public place that is comfortable, we can further infer that it has a spacious interior.

To eliminate the incorrect answers, some are more easily dismissed than others.

Incorrect Answers

(A) places having a spacious interior in the trigger, when we only know that it could be an outcome based on the last statement in the stimulus.
(B) places featuring artwork in the trigger, when we could only place it in the outcome based on the second statement in the stimulus.
(C) is really close since we know that most public places that are well designed feature artwork. But it's possible that coffeehouses belong (maybe exclusively) to those public places that do not feature artwork.
(E) places having a spacious interior in the trigger, when we only know that it could be an outcome based on the last statement in the stimulus.

Hope that helps!

[aresdude]

http://imageshack.us/photo/my-images/542/diagramh.png/

I like to do these problems using venn-diagrams.

Hopefully this diagram isn't too messy I made it super quickly in paint.

[samuelfbaron]

I'm a bit confused.

How are we able to infer that a public place that is well-designed is comfortable? Is it simply because of the contrapositive of the conditional 'public place not comfortable = not well designed' ?

[fmuirhea]

Yes, we know that a public place that is well-designed is comfortable from the contrapositive of the conditional. With inference questions, it's useful to separate out all of the statements and consider them as premises from which you're trying to make a conclusion. Others have already diagrammed the statements from this passage, but here's my take as well:

P: coffeehouse / restaurant --> public place
~public place --> ~coffeehouse & ~restaurant
P: most [public place & well-designed] have artwork
P: public place & ~comfortable --> ~well-designed
well-designed --> ~public place / comfortable
P: public place & comfortable --> spacious interior
~spacious interior --> ~public place / ~comfortable

When you're looking for something that must be true or false, it usually hinges on following conditionals, since they are strong enough to make such concrete determinations. So, with MBT questions, pay particular attention to the conditionals, your strongest components. Here's what (D) is trying to prove:

[coffeehouse / restaurant] & well-designed --> spacious interior

We can use the strong conditional relationships given to us to transform some of the terms in (D).

From the first conditional, we can replace the term "[coffeehouse / restaurant]" with the term "public place," since the arrow allows us to make that connection. So, now we have:

public place & well-designed --> spacious interior

From the contrapositive of the second conditional, we can replace "well-designed" with either "~public place" or "comfortable." Since we've already rewritten our first term to be "public place," turning around to say it isn't a public place would be inconsistent, so we must be looking for "comfortable." Here's our second revision:

public place & comfortable --> spacious interior

All of a sudden, this looks precisely like the third conditional that was given to us! And what could be more true than simply restating something we've been instructed to consider as true?

[samuelfbaron]

My diagram:

#1. Coffee houses & restaurants --> PP

#2. most [well designed PP] --> feature artwork

#3. If ~ PP comfortable --> ~well designed (note: i took uncomfortable to equal NOT COMFORTABLE)

#4. All comfortable PP --> spacious interiors

Take the contrapositive of statement #3 - well designed --> comfortable

therefore: well designed --> comfortable --> spacious interiors

The final logic chain matches (D).

[topcow500]

I did PT 65 as a timed practice test, and ended up getting this question wrong. However, I was practically out of time when I got to it, and hastily chose (C) as I did not have enough time to diagram all of the facts.

When I looked back on this question during my analysis, it became obvious to me why (D) was correct, but it still seemed that (C) was not totally incorrect. The fact is, you MUST go by what the question stem asks, and this is a MUST be true question. That means true under any scenario. (D) is the obvious choice, and why that is is well explained in the earlier comments. The most compelling reason that I saw concerning the incorrectness of (C) was from "mattsherman," but he left half of it unexplained...the half that confused me initially.

I'll explain the difficulty that I had with (C) as though this question was a logic game.

So, all coffee houses and restaurant are public places. Most well-designed public places feature artwork. "Most" CAN possibly mean "all," so in the event that either all well designed public places feature artwork, or if you read (C) as "potentially all coffeehouses that are well designed feature artwork, then (C) could be justified. However, in the scenario that "most" does not mean "all," then yes, as mattsherman said, coffeehouses could be the exclusive branch of well designed public places that do not feature artwork.

So now I see that there are two possible scenarios. One in which (C) could work, and one in which it cannot. Just as in the logic games, if you can prove a scenario where a given answer does not work, then it does not have to be true. Therefore, (C) does not meet the requirement of "must be true."

This is not the easiest question, and the fact that it's the last question makes it extra challenging. I hope this cleared something up for anybody who had the same problem as I did.

[ptewarie]

All these explanations work. But, OUCH. They are hard to follow, especially for people who are already confused with some/all problems.

The best way to solve inference questions involving formal logic(some/all/most) is to just stay clear on what is ALWAYS true. Look for things like(all, none, never, always). Once you have that, you are already a step closer.

In this problem, the author states that:
All Coffeehouses are public places( so if coffehouse-> public place)
and
Most well-designed public houses feature artwork.

Note that "well designed public place" is not the same as a "public place". These are two different things. If you took this to be interchangable, you likely got this problem wrong.

For example,
if in Boston-> in a city in the US
is NOT the same as
if in Boston-> in the largest city in the US.

"largest city" qualifies and "limits" the word city to cover specific instances.


Back to the problem:
in answer choice C, the author claims that "most Coffeehouses that are well designed feature artwork."

She gets this from:

Coffeehouse-> Public Place
Well designed Public place MOST feature artwork.

Note, however, that even if the coffeehouse is well-designed then we would have:

CoffEehouse-> Well Designed Public Place MOST feature artwork

We cannot conclusively prove that any single coffeehouse features artwork
Let's see why:

if 100/100 coffeehouses are well designed public places and theres a total of 1,000 well designed public places. If MOST well designed public places feature artwork, it could be that 501 well-designed public places out of 1,000 well-designed public places feature artwork. Allowing very well to be 499 well-designed places that Do NOT feature artwork, of which 100( or ALL of the coffehouses) are NOT chosen.

memorize the following:
if

a. A MOST B ALL C
(most A's are B's and all B's are C's)
then you can say that:
Some A's are C's and some C's are A's

b. A Some B ALL C
(some A's are B's and all B's are C's)
then you can say that:
Some A's are C's.

c. A ALL B ALL C
then you can say that:

Most A's are C's
Some A's are C's
Some C's are B's

d. A Some B All D
then you can say:
NOTHING

e. A Most B ALL D
Then you can say:
Nothing

i highly recommend getting a Logical Reasoning Bible book which talks in depth about formal logic involving these terms.

[lattelover]

Although I got this question correct, I think there is a gap in the correct answer that makes it not actually a must be true.

TCR assumes that comfortable-uncomfortable is a dichotomy when it need not be. That being said, the other 4 answer choices are obviously wrong. However, this seems like a large oversight... Any thoughts?

[fmuirhea]

I'm not sure I agree that comfortable / uncomfortable isn't a valid dichotomy. What would the third option be? I'll grant that you wouldn't negate a term like "hot" to "cold" (what about warm or cool? this misses a good chunk of the spectrum between hot and cold), but I think the nature of being comfortable is such that there's no hidden middle. Is it possible to be neither comfortable nor uncomfortable? Surely if you're not comfortable that implies you're uncomfortable in some way, and vice versa. I think this is an example of complementary antonyms (e.g. dead vs. alive) where there's no hidden middle - you're either one or the other, rather than non-complementary antonyms (e.g. hot vs. cold), which imply a scale with polar opposites and a wide neutral zone. Have I convinced you?!

[contropositive]

You are right that we do not know whether coffehouses or restaurants are well-designed. We do know they are public places.

We know this from the stimulus:

Coffee ---> PP
Rest ---> PP

WDPP most FA

PP uncom ---> ~WD (I would flip this as I see that I have a situation where I can chain up the next sentence with this statement regarding comfortable PP.

So, the previous statement flipped is:

WD ---> PP com

And we know that with the last statement we now have this chain:

WD ---> PP com ---> SI

We will now show the information we have:

Coffee ---> PP
Rest ---> PP

WDPP most FA
WD ---> PP com ---> SI

At this point, I would not attempt to prephrase an answer. Too many possibilities.

(A) Logical reversal

(B) Logical reading error of the most statement. It is switching terms.

(C) Common logical error of trying to infer an all statement and a most statement with the most statement being on the right hand side. No logical inference can be made with that construct.

(D) We know that if something is W, we get PP com, and we get SI. So any well designed coffeehouse, restaurant, library, stadium, warehouse, etc...will trigger this conditional. All we need is WD, and this answer choice tells us that any WD coffehouse or WD restaurant will have SI.

This answer choice is not saying any coffeehouse or restaurant will have SI, rather any WD one of those, which is something that is a must be true.

(E) Logic reversal

I spent one year trying to figure out what my prep company meant by "you cannot draw an inference from 'all' and 'most' statement' and I could not figure out what they were talking about or all the other books I read on this. I saw your explanation for answer choice "C" and now I finally understand what that means....THANK YOU lol

[tommywallach]

Ha! Nice.

[cacrv]

I think this is such a straight forward conditional problem, so I'm not sure why I'm struggling.

Why can't I sub "public places" for "coffeehouse" in C? Then C would also be correct, as we are told that most public places that are well designed do feature artwork. That's what I did for D as well, so I knew one of them must be the wrong answer, but I just couldn't reason with myself. What completely fundamental concept am I missing here?!

[JeffW669]

Ha, this was a fun one. I got it wrong on my PT but see my mistake.

For the question of why not C, here's a way you can think about it:

Suppose: We have 6 restaurants and 4 coffee houses. They are all public places and are all well-designed. Each of the 6 restaurants has artwork and none of the 4 coffee houses has artwork. Then:
* All (4/4) coffeehouses and all (6/6) restaurants are public places.
* The majority (6/10) of well-designed public places feature artwork.
* No (0/4) coffee houses that are well-designed feature artwork.

So C can be false.