Interior decorator: All coffeehouses and restaurants are public places. Most well-designed public places feature artwork. But if a public place is uncomfortable it is not well designed, and all comfortable public places have spacious interiors.
In all of the interior decorator's statements are true, then which one of the following must be true?
(A) Any restaurant that has a spacious interior is comfortable.
(B) Most public places that feature artwork are well designed.
(C) Most coffeehouses that are well designed feature artwork.
(D) Any well-designed coffeehouse or restaurant has a spacious interior.
(E) Any coffeehouse that has a spacious interior is a well-designed public place.
The answer from the answer sheet is D. I chose C. I can see how D is correct but I cannot see how C is incorrect. The way I interpret C is from the second sentence of the passage which states "Most well-designed public places (coffeehouses and restaurants) feature artwork." which seems to be a direct copy of C.
Can anyone help me see what I'm doing wrong here? Also, sorry if this is the wrong forum or if posting questions is not allowed.
Question about a particular preptest problem Forum
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TERS
- Posts: 161
- Joined: Thu May 24, 2012 11:29 pm
Re: Question about a particular preptest problem
First, edit your post.
Take the following information:
All coffeehouses and restaurants are public places
If a public place is well-designed, it is comfortable (contrapositive)
All comfortable public places have a spacious interior
Does answer choice D, “Any well-designed coffeehouse or restaurant has a spacious interior,” follow?
Yes, because a well-designed coffeehouse or restaurant is a well-designed public place and a well-designed public place is a comfortable public place and a comfortable public place has a spacious interior, as required.
Does answer choice C, “Most coffeehouses that are well designed feature artwork,” follow?
No. Just because most public places that are well-designed feature artwork does not mean most well-designed coffeehouses do. Consider the following scenario: there exist 1000 well-designed public places, 600 of which feature artwork. Those 600 well-designed public places that feature artwork are not coffeehouses, while the remaining 400 are well-designed coffeehouses, none of which feature artwork. This is consistent.
Take the following information:
All coffeehouses and restaurants are public places
If a public place is well-designed, it is comfortable (contrapositive)
All comfortable public places have a spacious interior
Does answer choice D, “Any well-designed coffeehouse or restaurant has a spacious interior,” follow?
Yes, because a well-designed coffeehouse or restaurant is a well-designed public place and a well-designed public place is a comfortable public place and a comfortable public place has a spacious interior, as required.
Does answer choice C, “Most coffeehouses that are well designed feature artwork,” follow?
No. Just because most public places that are well-designed feature artwork does not mean most well-designed coffeehouses do. Consider the following scenario: there exist 1000 well-designed public places, 600 of which feature artwork. Those 600 well-designed public places that feature artwork are not coffeehouses, while the remaining 400 are well-designed coffeehouses, none of which feature artwork. This is consistent.
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chris9152
- Posts: 11
- Joined: Wed Jun 13, 2012 12:40 pm
Re: Question about a particular preptest problem
I'm assuming this is from a released prep. test, so I'm pretty sure it's okay to post.
Inference questions with lots of conditional statements are written so as to confuse. Mapping everything out symbolically tends to help me. Hopefully this explanation isn't too confusing itself.
Interior decorator: All coffeehouses and restaurants are public places. Most well-designed public places feature artwork. But if a public place is uncomfortable it is not well-designed, and all comfortable public places have spacious interiors.
Guide:
- means "not"
---> means "implies"
--(most)--> means "implies more than half the time"
/ means "or"
+ means "and"
Conditional statements can be read only with the arrow, never against it.
Here is a breakdown of the given statement.
All coffeehouses and restaurants are public places.
I'm going to rephrase this first. If it's a coffeehouse or a restaurant, it's a public place.
(1) Coffeehouse/restaurant ---> Public place
(Contrapositive: -Public place ---> -Coffeehouse + -Restaurant)
Most well-designed public places feature artwork.
(2) Well-designed + Public space --(most)--> features artwork
But if a public place is uncomfortable it is not well-designed
(3) Uncomfortable + Public place ---> Not well-designed
(Contrapositive: Well-designed---> -Uncomfortable/-Public place)
and all comfortable public places have spacious interiors.
(4) Comfortable + Public Place ---> Spacious interior
(Contrapositive: -Spacious interior ---> -Comfortable/-Public Place)
Now to the questions:
(A) Any restaurant that has a spacious interior is comfortable.
Restaurant + Spacious Interior ---> Comfortable
We don't know much about a restaurant with a spacious interior beyond the fact that it's a public place. In fact, spacious interior never shows up on the left side of any conditional or contrapositive, so we don't know a lot about anything just from its spacious interior.
(B) Most public places that feature artwork are well-designed.
Public Place + Has artwork --(most)--> Well-designed
What do we know about a public place that has artwork? Not much. Artwork never shows up on the left side of any conditional or contrapositive.
(C) Most coffeehouses that are well-designed feature artwork.
Coffee House + Well-designed --(most)--> Has artwork
What do we know about a coffeehouse that is well-designed? Well, it's a public place. It would certainly be tempting to plug this into the second conditional.
But the second "clue" is not a normal conditional. It's a "most" conditional, which implies that of the described group (well-designed public places), more than 50% have the described characteristic (features artwork).
But since the clue is a "most" conditional dealing with a distinct group, coffeehouses cannot be substituted for public places. Take a second to think about this. If there are 100 well-designed public places in your city and 51 of them have artwork, must any of these 51 be well-designed coffeehouses? It can still be true that most well-designed public places have artwork even if no well-designed coffee houses do. Each of the well-designed coffeehouses would just be in the minority of well-designed public places without artwork. Maybe there are only two well-designed coffeehouses total, and neither of them have artwork. We just don't know.
(D) Any well-designed coffeehouse or restaurant has a spacious interior.
Well-designed + Coffeehouse ---> Spacious interior
From the first clue, we know that a coffeehouse must be a public place.
From the contrapositive of the third clue, we know that if something is well-designed, it must be either not a public place, or not uncomfortable (a.k.a. comfortable). Since we know that any coffeehouse must be a public place, it must be not uncomfortable and hence comfortable.
(E) Any coffeehouse that has a spacious interior is a well-designed public place.
Coffeehouse + Spacious interior ---> Well-designed + Public Place
Again, spacious interior never shows up on the left side of any conditional or contrapositive, so we know nothing specific about any place with a spacious interior on that account.
Inference questions with lots of conditional statements are written so as to confuse. Mapping everything out symbolically tends to help me. Hopefully this explanation isn't too confusing itself.
Interior decorator: All coffeehouses and restaurants are public places. Most well-designed public places feature artwork. But if a public place is uncomfortable it is not well-designed, and all comfortable public places have spacious interiors.
Guide:
- means "not"
---> means "implies"
--(most)--> means "implies more than half the time"
/ means "or"
+ means "and"
Conditional statements can be read only with the arrow, never against it.
Here is a breakdown of the given statement.
All coffeehouses and restaurants are public places.
I'm going to rephrase this first. If it's a coffeehouse or a restaurant, it's a public place.
(1) Coffeehouse/restaurant ---> Public place
(Contrapositive: -Public place ---> -Coffeehouse + -Restaurant)
Most well-designed public places feature artwork.
(2) Well-designed + Public space --(most)--> features artwork
But if a public place is uncomfortable it is not well-designed
(3) Uncomfortable + Public place ---> Not well-designed
(Contrapositive: Well-designed---> -Uncomfortable/-Public place)
and all comfortable public places have spacious interiors.
(4) Comfortable + Public Place ---> Spacious interior
(Contrapositive: -Spacious interior ---> -Comfortable/-Public Place)
Now to the questions:
(A) Any restaurant that has a spacious interior is comfortable.
Restaurant + Spacious Interior ---> Comfortable
We don't know much about a restaurant with a spacious interior beyond the fact that it's a public place. In fact, spacious interior never shows up on the left side of any conditional or contrapositive, so we don't know a lot about anything just from its spacious interior.
(B) Most public places that feature artwork are well-designed.
Public Place + Has artwork --(most)--> Well-designed
What do we know about a public place that has artwork? Not much. Artwork never shows up on the left side of any conditional or contrapositive.
(C) Most coffeehouses that are well-designed feature artwork.
Coffee House + Well-designed --(most)--> Has artwork
What do we know about a coffeehouse that is well-designed? Well, it's a public place. It would certainly be tempting to plug this into the second conditional.
But the second "clue" is not a normal conditional. It's a "most" conditional, which implies that of the described group (well-designed public places), more than 50% have the described characteristic (features artwork).
But since the clue is a "most" conditional dealing with a distinct group, coffeehouses cannot be substituted for public places. Take a second to think about this. If there are 100 well-designed public places in your city and 51 of them have artwork, must any of these 51 be well-designed coffeehouses? It can still be true that most well-designed public places have artwork even if no well-designed coffee houses do. Each of the well-designed coffeehouses would just be in the minority of well-designed public places without artwork. Maybe there are only two well-designed coffeehouses total, and neither of them have artwork. We just don't know.
(D) Any well-designed coffeehouse or restaurant has a spacious interior.
Well-designed + Coffeehouse ---> Spacious interior
From the first clue, we know that a coffeehouse must be a public place.
From the contrapositive of the third clue, we know that if something is well-designed, it must be either not a public place, or not uncomfortable (a.k.a. comfortable). Since we know that any coffeehouse must be a public place, it must be not uncomfortable and hence comfortable.
(E) Any coffeehouse that has a spacious interior is a well-designed public place.
Coffeehouse + Spacious interior ---> Well-designed + Public Place
Again, spacious interior never shows up on the left side of any conditional or contrapositive, so we know nothing specific about any place with a spacious interior on that account.
