#22- Local, Must Be True

[Administrator]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=3737)

The correct answer choice is (B)

If Center 3 recycles G, then that center cannot recycle P, thanks to the third rule. And, because P
can only be recycled in Centers 1 or 3, we can infer that Center 1 must be the one center that
recycles P:

june07_game_4_#22_diagram_1.png

By the same logic, if P and G cannot be recycled in the same center, then Center 1 cannot recycle
G. But then Center 2 cannot recycle G either, by the contrapositive of the second rule:

june07_game_4_#22_diagram_2.png

With two of the five variables eliminated from Center 2, we are left with only three variables (N,
T, and W) to fill a minimum of two spaces in it. By the contrapositive of the first rule, we know
that if a center does not recycle N, then it cannot recycle W:

june07_game_4_#22_diagram_3.png

But, since Center 2 cannot recycle either P or G, it cannot trigger the contrapositive of the first
rule, or else it would be left with only one material to recycle (T). Therefore, Center 2 must
recycle N, validating answer choice (B).

[quiz555]

In question 22, I don't see how G can be the second to get off if he must be on for the first 2 stops and there must be 2 people to get off during those stops...

Please Help!!

[quiz555]

Never mind!! I now see what went wrong with all of them!

For some reason I thought that G must get off after it passed, not reached S for question 22...

Everything else I understood thanks to your clarification on the reached rules

Those "reached rules" are tricky!

Thanks anyway!

[Dave Killoran]

Haha, no problem. I was just about to explain #22, but I see you nailed it on your own--good job!

Thanks for the very kind comments--I really appreciate them!

[vdoshi1016]

On the practice test, I missed question 22 and would love some advice. Thanks.

[Dave Killoran]

Question #22. If Center 3 recycles G, then Center 3 cannot recycle P. Since one center must recycle P, and Center 2 cannot recycle P, we can infer that Center 1 recycles P (and thus Center 1 does not recycle G).

Because the question stem specifically references Center 2, at this point take a moment to consider the materials available for recycling at Center 2: G, N, T, W. But, consider that G can't be recycled at Center 1, so, via the contrapositive of rule 2, G cannot be recycled at Center 2 in this question. That leaves N, T, and W available for Center 2. Because Center 2 must recycle at least 2 materials, any combination of those variables will include N (even if you try to select just W and T, the first rule kicks in and forces N to be recycled as well). Thus, N must be recycled at Center 2, and answer choice (B) is correct.

Thanks!

[tinglipmcd]

Hi,
I have some questions regarding #22

Q1. according to the set up and diagram:
If Center 1 does not recycle a given material, then Center 2 cannot recycle that
material either. Consequently, the material must be recycled at Center 3.
so, C1\ - C2\ - C3
by the contrapositive, if a given material is not recycled at Center 3, then it
must be recycled at Center 1"
that's C3\ - C1

Wondering if it would be ok to say C3\- C2 - C1 ?

Q2. condition NO.1 says Any recycling center that recycles wood also recycles newsprint.
Is this the same as "If a recycling center recycles wood, then it also recycles newsprint?"
When I read condition NO.1, I thought it means wood and newsprint must be recycled together, is that misinterpretation?

Thanks!

[Jay Donnell]

Hi Tinglipmcd!

Those are two great questions! Let's tackle them one by one.

Rule two says that if an item is recycled in Center 2, then it must be also recycled in Center 1, so you are correct with the contrapositive implying that if an item is not in Center 1 then it cannot be in Center 2, so therefore must be in Center 3!

The tricky part about this game however is how the group sizes are partially defined, which leaves open the possibility that Center 1 may have both of the items that are recycled in Center 2, but then also have a third item that is only found in Center 1. Well, I suppose it could also be in Center 3, but the point is it's possible to have an item in Center 1 that is not in Center 2.

For example:

1) W N P

2) W N

3) G T

In here, the items that were not in Center 1 ( G & T ) had to be in Center 3 because as you noted (so well!), the items have to be recycled somewhere, and if ~1 --> ~2, then they'd have to go into Center 3.

However, the hypothetical example above shows the error in the applied contrapositive of that chain, due to the partially defined nature of the group sizes. Here, (P) is not in Center 3, so then it would have to be in Center 1 but not necessarily also Center 2. P in this case could not actually also be in Center 2, with its condition that it's only allowed to go to one center and therefore could never go to Center 2 which would force it to double up into Center 1.

Super tricky! In summary, we can guarantee that ~1 --> ~3 and it's contrapositive of ~3 --> ~1, but we can't force the item to also go into Center 2.


For Q2, you're correct that " 'Any recycling center that recycles wood also recycles newsprint' is this the same as 'if a recycling center recycles wood, then it also recycles newsprint' " However, it would be a mistake to imply that this means W and N must always be selected together.

This results in a standard, one-directional conditional statement. It's the exact same as saying "If you have a cat, then you have a pet," which doesn't mean that anyone with a pet has to have a cat. We can select/own Pet without necessarily selecting/owning a Cat, much like how we could select Newsprint without necessarily also selecting Wood.


I hope that helps, thanks so much for asking such great questions!

[theamazingrace]

I am having a hard time understanding how you would know that if a variable is not in 1 then it has to be in 3. From the stimulus, I didn't get that each variable must be used at least once. When I saw "exactly five kinds of material are recycled," I thought it confirmed that was the complete variable set. I didn't read each variable MUST be used at least once. How would you know then, that not all variables have to be used?

Thanks

[Adam Tyson]

It's the certainty of "are recycled,," as opposed to "may be recycled" or "are capable of being recycled," theamazingrace. If they are recycled, then we have to account for them all! They aren't just a possibility; they are a certainty.