#23 - Local, Could Be True, List

[Administrator]

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

The correct answer choice is (A)

This is the most challenging question in this game, taking advantage of every single inference
made at the setup stage. If you failed to make some (or all) of these inferences, the question is
still doable, but it would be significantly more time-consuming.

The question asks us to identify a complete and accurate list of the variables that could be in one
of the three groups, assuming that only Center 1 recycles W. First, make sure to eliminate any
answer choices that directly contradict a rule. For instance, answer choice (D) clearly violates the
first rule and is incorrect.

If Center 1 is the only center that recycles W, make sure to represent the requisite W Not Laws
under Centers 2 and 3, and also ensure Center 1 recycles N, in compliance with the first rule.

june07_game_4_#23_diagram_1.png

At this point, most students would be at a loss as to how to proceed. When a single setup is not
enough to help you solve the question, do not hesitate to make two. To do so, consider P – the
most restricted variable in our setup, which must be recycled at either Center 1 or 3.

june07_game_4_#23_diagram_2a.png

june07_game_4_#23_diagram_2b.png

Consider each solution individually. In Setup A, Center 1 now recycles the maximum number of
kinds of material (3), and cannot therefore recycle G and T. By the contrapositive of the second
rule, Center 2 cannot recycle G and T either. But, now Center 2 is left with only one kind of
material to recycle (N), because it never recycles P (main inference), and W is recycled only at
Center 1. Clearly, then, Setup A does not represent a viable solution to this question, and P must
be recycled at Center 3.

Setup B remains the only possible solution. In it, Center 3 cannot recycle G, because the third rule
prohibits P and G from being in the same group. But, if Center 3 cannot recycle a given material,
then – as discussed earlier – that material must be recycled in Center 1 (otherwise, by the
contrapositive of the second rule, that material cannot be recycled in Center 2 either, which would
be impossible). Therefore, G must be the third material to be recycled at Center 1:

june07_game_4_#23_diagram_3.png

Since T is not recycled at Center 1, by the contrapositive of the second rule it cannot be recycled
at Center 2. Therefore, T must be recycled at Center 3. Additionally, with three materials
eliminated from Center 2 (P, W, and T), we can safely conclude that Center 2 must recycle only
N and G:

june07_game_4_#23_diagram_4.png

Answer choice (A): This is the correct answer choice, because Center 3 can recycle only P and
T without violating any of the rules governing the assignment of materials to centers.

Answer choice (B): This answer choice is incorrect, because no center recycles only N and W.
Although the list is accurate (Center 1 does recycle both N and W), it is incomplete (it is missing
G).

Answer choice (C): This answer choice is incorrect, because no center recycles only N and T.
Although the list is accurate (Center 3 can recycle both N and T), it is incomplete (it is missing
P).

Answer choice (D): This answer choice is incorrect, because W cannot be recycled without N
(first rule).

Answer choice (E): This answer choice is incorrect, because no center recycles G and T.

[vdoshi1016]

On the practice test, I missed question 23 and would love some advice. Thanks.

[Dave Killoran]

Question #23. This is a List question that asks you to identify an answer that could be a complete list of materials recycled at one of the centers. Note that on a quick scan, answer choice (D) can be eliminated because it violates the first rule.

The question stem establishes that Center 1 is the only center recycling W. This does not mean that Center 1 does not recycle N--do not make a Mistaken Negation! It also does not mean that Center 2 must recycle W (don't make a Mistaken Reversal!). however, from the first rule, we can infer that Center 1 must also recycle N. At this juncture, the following setup appears (it is a little off-line due to the diagramming limitations of the forum, but the idea is there ):

G N P T W

N
W
1 2 3
W W
P

At this point, you might think there's nothing more you can do, and that the only remaining approach is to just pound through the answer choices with hypotheticals. But, stop for a moment and consider the implication of rule #2 on the scenario above. Center 2 has only G, N, and T available. And, whatever is recycled at Center 2 must also be recycled at Center 1, which limits what can be recycled at Center 2. For example, you couldn't recycle both G and T at Center 2 because that would force four materials to be recycled at Center 1 (a violation of the game scenario condition). Thus, Center 2 must be N, and the choice of G or T (in order to reach two materials recycled (and then G or T must also be recycled at Center 1):

G N P T W


G/T
N G/T
W N
1 2 3
W W
P

Note that this means that Center 1 must recycle three kinds of materials, and Center 2 must recycle exactly two kinds of materials. Because Center 1 must be the only center to recycle W, and Center 1 must recycle three kinds of materials, both the answer containing W must be incorrect since they list only two kinds of materials (this kills answer choice (D) for a second time )

With the number and kinds of materials roughly established at Centers 1 and 2, the first part of rule #3 comes into play, and P must then be recycled at Center 3. This means that G cannot be recycled at Center 3. But, because G must be recycled at at least one center, G must be the choice from the G/T dual-option in Centers 1 and 2, leading to:

G
N G
W N P
1 2 3
W W
P G


Of course, T must also be recycled, and thus T must be recycled at Center 3:

G
N G T
W N P
1 2 3
W W
P G

The above scenario could be complete, and thus P and T could be a complete and accurate of the materials recycled at one of the scenarios. Hence answer choice (A) is correct.

I've always thought this is a tough question, so I tried to take it step-by-step above. If you have any questions about any part of the explanation, please let me know. Thanks!

[martinbeslu]

This is one of those games where it is difficult not to confuse the symbology in the diagram. I used N/T for each center to represent that N or T or both had to be used. However, by the time I got to question 23 I saw this dual option on the diagram and accidentally scratched out T simply because N was selected. Now that I went back and reviewed the setup I see that was a mistake. Any suggestions on how to make this notation more clear in this scenario? Thank you guys for all that you do to help us out with this stuff!

[Adam Tyson]

It can be hard to capture all the info in that inference in one tiny notation, martinbeslu. "At least one of N or T and maybe both" is a lot of info! I think starting with an N/T dual option is good, and my shorthand for "maybe both" is to put a "?" right next to it. That's just my own thing, and could cause confusion for others. My point is that sometimes you need to develop your own tools to help step your game up to the next level. We can provide a solid foundation and a lot of great tools, but the authors of this test are always innovating, and we just don't have an absolutely comprehensive list of diagramming tools that covers every single alternative and possibility. Nobody does! We encourage our students to innovate and adapt our tools to use them the way that works best for them, including modifying them and adding to them.

Another way I have done it is to add another "slot" and write that N/T in again, showing that I could have those two filling both slots. Again, potential confusion for someone else who might not know why I did that or what it means to me, but it works for me because I know why I did it.

Play around a bit, see if you can come up with a notation that means what you need it to mean so that you can understand it at a glance when you are on the third or fourth of fifth question of a game and may not remember exactly what you wrote!