June 2007 Prep Test Section 1 Q. 22/23

JennaMM11

Hi everyone,

I finished my June 2007 prep test and am now doing the blind review, however, I am still having trouble with figuring out questions 22 and 23 in the first section. The questions are regarding the recycling centres and materials. The rules for these questions are:
- 3 recycling centres (C1, C2, C3)
- 5 materials (plastic, tin, glass, wood, newsprint)
- each centre recycles at least 2 but no more than 3 materials
- any centre that recycles wood also recycles newsprint (WN)
- every material that C2 recycles is also recycled at C1
- Only one recycling centre recycles plastic, and that centre does not recycle glass

Question 22 reads: "If Centre 3 recycles glass, then which of the following kinds of material must Centre 2 recycle?"
A. Glass
B. Newsprint
C. Plastic
D. Tin
E. Wood

Question 23: if C1 is the only recycling centre that recycles wood, then what could be a complete and accurate list of kinds of materials that one of the recycling centres recycles?
A. P, T
B. N, W
C. N, T
D. G, W
E. G, T

Would anyone be able to explain how to find the right answer for these questions?

Thank you in advance!

The Great White Shark

For Q 22:

If G is recycled at C3 then we know P has to be recycled at C1only. This is because P can only show up once on our game board and it cannot be with G. G cannot be recycled at C2 either because it would then have to be recycled at C1as well which would be in conflict with the rule about how P and G cannot be recycled at the same center. So that leaves us with N, T and W to work with in order to determine which material C2 must recycle.

Here is our game board so far:
C1: P, __ , __
C2: __ , __
C3: G, __

We have to have at least two materials to recycle in C2. Let's think through our possible situations:

If W is recycled at C2, then N will be too.

If T is recycled at C2 then we still have at least one space to fill in it. So either W or N has to go into it. And remember wherever W goes, N will follow! So N will be going into C2. Which is why B is correct.

For Q 23:

W is recycled at C1 alone. Because N must be with W this means that N is recycled at C1 as well. We can infer a couple of things from this now: Since C2 must have two types of things to recycle and all that it recycles will also be recycled by C1, then we know that N must be in C2. So far we have the following on our game board:

C1: W, N, __
C2: N, __
C3: __ __

Now we have G, P and T left to deal with. P can only happen once so it must go to C3. And P cannot be with G so T must go into C3. That leaves G left to go into the remaining spot in 2 and the third spot in 1.

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

Also, N could potentially appear in C3 as well. But it isn't required.

This leads us to pick AC A which is plastic and tin as shown in C3.

By the way, my board game while working through this problem didn't look like the one above. That's just the best depiction I could come up with on the computer.

Let me know if I need to further clarify anything!

JennaMM11

That helped so much, thank you!