Syllogsim problem

Question

Hello. Please help me to understand this problem on syllogism:

stmt 1) Some pastries are toffees.
stmt 2) All toffees are chocolates.

conclusions: 1) Some chocolates are toffees.
 2) Some toffees are not pastries.

Options : 1) Only conclusion I follows.
 2) Only conclusion II follows.
 3) Either I or II follows.
 4) Neither of I or II follows. 
 5) Both conclusions follows:

The solution of this problem is given as Only Conclusion I follows.

But when I solved this I was not able to arrive at the above solution. I want to know how we arrive at this solution. Please help me.

Abhishek009 · Answer

Dear Amoghsingh , welcome to GMAT Club.. Syllogism is not tested in GMAT , however I am trying to post the solution... Syllogism.jpg Check Possibility 2 ; The statement " Some toffees are not pastries " can be challenged... Hence, answer will be only Conlusion I follows...

PrijitDebnath · Answer

stmt 1) Some pastries are toffees.

conclusion 2) Some toffees are not pastries.

From stmt 1), we cannot make conclusion 2) for sure.

One example I can think of is: If it is given that some apples are rotten, then we cannot conclude that some rotten fruits are not apples.

This is because it is possible that no fruit other than apples is rotten. If that is the case, then we obviously cannot conclude that some rotten fruits are not apples.

Hope my reasoning is correct. Can an expert confirm this.

TrevorKleeTutor · Answer

So, this is sort of outside the scope of the GMAT, but let's dig in anyways.

We know conclusion 1 is necessarily true. There are more than one toffees in existence (because some pastries are toffees, and some implies more than 1). At bare minimum, there are two. Given that all the toffees in the world are chocolates, then there are at least two chocolates which are toffees as well.

These statements aren't great, because a real logician would demand to know more about the object categories "toffee", "pastry", and "chocolate". It's unclear whether these are descriptions of items, object categories, or fundamental attributes of an item (the sine qua non of an object). So I don't love this, but this is what they were going for.

Conclusion 2 is not necessarily true, but it may be true. From statement 1, it's possible that toffee is a subset of pastries (so all toffees are pastries, but not all pastries are toffees), or it's possible that toffee and pastry are intersecting sets (some toffees are pastries, some toffees are not pastries). It's even possible that toffee and pastry are synonymous, if we assume that "some pastries are toffees" leaves open the statement that "all pastries are toffees".

Again, these statements aren't great, because the answer choice should state "necessarily follows". Over all, despite how fun this is, I'd recommend you stick with actual, OG Critical Reasoning questions. This stuff will just distract you.

PrijitDebnath · Answer

Hello TrevorKleeTutor, thanks for your detailed post. Can you just explain what you mean by: the answer choice should state necessarily follows.

I got confused because to me, "conclusions" automatically meant "necessarily follows".

TrevorKleeTutor · Answer

In a philosophical sense, conclusions may be drawn with certain degrees of probability. So if you just say "follows", I assume you mean "likely". It's best to be specific and say "necessarily follows", if you mean necessarily.

For instance: "John is an Olympic athlete, so it follows he's in good shape." It is possible that John is a fat Olympic athlete, so really, what we meant to say is "John is an Olympic athlete, so it's likely he's in good shape."

PrijitDebnath · Answer

Thanks for your response TrevorKleeTutor. Unfortunately, your response makes all my concepts go for a toss, specifically this statement of your post: "conclusions may be drawn with certain degrees of probability".

Can you give me an example of a conclusion question where the correct answer is not "necessarily true" (based on the argument), but just is "probably true".

Thanks.

VerbalBot · Answer

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