Q23

[kellye916]

If C1 is the only one that has W, we start with
C1: W __ +
C2: __ __ +
C3: __ __ +

Did W have a rule?

Yes, it was that W must appear with N. Okay, so we know N must also be in C1.

C1: W N +
C2: __ __ +
C3: __ __ +

What else do we know?

We know that everything in C2 is also in C1 and that we must have 2-3 items in each C. That means that we need to add at least 2 items to C2 without putting more than 3 items in C1, which already contains W and N.

Could we simply add WN to C2? Nope. The problem stated that C1 is the only one with W. But we can add just N, since the rule is that W must have an N with it, not the other way around.

So now we have this:

C1: W N +
C2: N __ +
C3: __ __ +

What other rules is there? Only one C does P, and P can not be with G. Well we can't add P to C2 because that would copy it to C1 and it can only appear once. We can't add P to C1 because that would put it at 3 items and we still need to add another item to C2 that can be copied to C1. So that leaves C3 for P.

So now we have this:

C1: W N +
C2: N __ +
C3: P __ +

Since G can't go in C3, and whatever goes in C2 must also go in C1, then we can add G to both C1 and C2.

C1: W N G
C2: N G +
C3: P __ +

Now what materials are missing? T. We can add T to C3 to ensure that it reaches the 2 item minimum.

C1: W N G
C2: N G
C3: P T

That means that (A) is the correct answer.

[MattS781]

Alright, I'm confused about why G has to be used at all. I had everything right up until that point, but I had both C and A being right because I had one possible solution that didn't have G in the diagram at all. What part of the prompt makes this necessary? Is it the "exactly five kinds of ..."?

[obobob]

I agree with the first explanation, but I have an additional question:

Would it be also possible to have materials [P,T,N] be a possible answer for C3, if the combination of the materials was given as an answer choice? None of the answer choices gives [P,T,N], but I am curious if such combination could be an answer if there were one, instead of [P,T], as listed in the correct answer choice (C).

There's no limit in number of recycling the material N(newsprint), and there's no any restriction of C3 having additional material recycled up until three, as long as it is not G(glass) or W(wood), right?

[KarolinaW652]

I believe Glass needs to be listed as one of the materials because the questions is asking for a "complete and accurate list." I've come across a few scenarios where I didn't need to include a particular item in a grouping, but the correct answer made much more sense when I did.

[PrachirP161]

I'm also confused as to how we can eliminate C between A and C - does the question imply that all materials must be recycled?

[ohthatpatrick]

Yeah, the language of the setup that says "Exactly five kinds ARE recycled" guarantees you that any legal scenario involves those five letters: G, N, P, T, W.

If we were to do a scenario that was like
C1: W, N, T
C2: N, T
C3: P, N

... then we wouldn't be adhering to the idea that "Five kinds of materials ARE recycled at these three center".

In that above scenario, only four kinds of materials are recycled.