#9 - Local, Cannot Be True

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=8467)

The correct answer choice is (E)

This question is more difficult than any of the first three questions in this game, and it is based upon one of the test maker’s favorite modes of attack, the use of uncertainty.

If O lives on the second floor, then the second floor is completely occupied, and no other resident can live on the second floor. For some variables, such as the MN block or the J block, this has no effect. For the KP block, however, the placement options are significantly reduced. Since the second floor is now “closed off,” the KP block must be placed on the third and fourth floors (3-4) or on the fourth and fifth floors (4-5). At this point, many test takers stop their analysis under the mistaken impression that since the exact position of the block cannot be determined, further examination is worthless. In fact, to get past this situation you must use a technique called Hurdle the UncertaintiesTM: in games situations with limited solutions, it is often possible to make inferences in spite of the uncertainty. In this case, since the KP block is always on 3-4 or 4-5, it can be concluded that K or P is always on the fourth floor. So, even though we cannot be certain of the exact KP block placement, we can deduce that in this question K or P must be on the fourth floor, and we must account for the space taken up by the K/P dual option:

pt2_o91_g2_q9.png

Thus, since K or P must always live on the fourth floor, L cannot live on the fourth floor since L must live in the only apartment on her floor. Therefore, answer choice (E) is correct. Note that an answer that attempted to place either M or N on the fourth floor would also have been correct as the presence of K or P on the fourth floor would have eliminated the MN block from the fourth floor.

Essentially, the placement of O builds a “wall” on the second floor. This wall affects the placement of any block which takes up adjoining spaces, such as the KP block. In Linear games where blocks are present, always closely examine the placement of a variable (such as O) into an interior space (such as the second floor). There may be inferences that follow from the reduced placement options of a block (such as either K or P must live on the fourth floor).

Opportunities to Hurdle the UncertaintyTM will appear in a number of games (including questions #10, #11, and #12 in this game), and this is the first introduction to this concept.

[LilyRose]

I was hoping someone could help explain one of the solutions to me more thoroughly. I am referring to the unbalanced linear game on p 188-189, an apartment building with 5 floors and 8 residents, taken from the october 1991 exam. The question in particular is #9, "Which of the following cannot be true." I am looking at the solution from p. 192-193. I would like further clarity as to why the diagram at the bottom of p 192 has two slots on floor 4: More particularly, what information necessitates this floor having two apartments, rather than 1? Why do we know for sure that it could not have just one apartment? (I understand why L cannot live on the 4th floor if either P or K has to be on the 4th floor; the second-to-last rule in the game provides that information. I am just wondering why the drawn diagram has 2 slots on the 4th floor, why that information is certain.)

[Dave Killoran]

Hi Lily,

Thanks for the question! It is the case that the 4th floor must have at least two residents in question #9, but I feel like my explanation doesn't address this point so thanks for asking about it

I'm a bit short on time today, so I'll make a few brief comments and then tomorrow I'll come back and expand this explanation if that's ok.

In question #9, we know that O lives on the 2nd floor, and that forces the KP block onto floors 4-3 or 5-4. Because L must live alone, and because MN fully occupy a floor, those two grouping must be places away from O, K, and P. That leaves one of them on the 1st floor and the other either on floor 3 or floor 5 (there are two basic templates in play at this point). Ultimately, we are left trying to place J and Q, and in each scenario they either go on floors 3 and 4, or floors 4 and 5. Since the 4th floor already contains K or P, adding Q or J always gives the 4th floor two residents. It's actually quite a tricky point, and in the next edition I will address how this works.

Tomorrow I'll come back and show how the templates inside this question lead to this deduction. In the meantime, I hope the above helps. Also, my apologies for that not being clear in the text, but great job on your part to see that and ask about it!

Thanks!

[Dave Killoran]

Ok, as I promised, I'm back to examine what happens here a bit more closely. As I mentioned above, it's tricky, and my explanation doesn't do the point justice

So, let's go back to the question stem. In question #9, we know that O lives on the 2nd floor, and that forces the KP block onto floors 4-3 or 5-4. Although I would never do this question using templates, I'm going to show them here to make the point as clear as possible:

• Template #1:
  
  5 __
  
  4 K
  
  3 P
  
  2 O
  
  1 __
  
  
  Template #2:
  
  5 K
  
  4 P
  
  3 __
  
  2 O
  
  1 __

At this point, in each template, you have the following variables still unplaced: J, L, MN, Q. Two sets are notable there: the MN block, and L. Why? Because each requires it's own floor. So, in each template, those variables can't be placed on the floors where O, K, and P reside. Thus, we get the following dual-options for L and MN (side note: the vertical bar at the end of certain floors indicates that no other variable can be placed on that floor):

• Template #1:
  
  5 L / MN |
  
  4 K
  
  3 P
  
  2 O |
  
  1 MN / L |
  
  
  Template #2:
  
  5 K
  
  4 P
  
  3 L / MN |
  
  2 O |
  
  1 MN / L |

While this is enough to answer the question, I'm going to continue on since what you've asked about is the fourth floor. Now, we are down to just J and Q to place, and Template #1 they have to go on the 3rd and 4th floors, and in Template #2 they have to go on the 4th and 5th floors. Thus, the 4th floor always has to residents, hence the diagram in the book for question #9. If I were diagramming this during the game, I wouldn't have automatically placed two spaces on the 4th floor since I wouldn't have know that as I started the question. Probably the way my initial skeleton diagram for #9 would appear would be:

• 5 __
  
  4 K/P
  
  3 __
  
  2 O |
  
  1 __

Or you could make two really quick templates if you felt that would help. Either way, you could immediately see that L couldn't live on the 4th floor, which would lead you right to answer choice (E).

Please let me know if that explains it, and again, thanks for asking about this! It's questions like this that help me make this book better with each version, so I really appreciate it

[LilyRose]

Hello Dave,

Thank you for the explanation. It was indeed helpful. I did not use templates to answer this question, because my initial diagram plus the local rule was enough to show me that floor 4 would always have either K or P, and therefore could never have L, as provided in the global rules; so answering the question was much faster from just this information, without needing to draw out the templates. But the templates you provided did indeed answer my question! I'm still trying to come to terms with all of the logical patterns that I will need to be familiar with, so seeing it laid out like this (even if it is unnecessary to answer the actual question) helps increase my understanding of the games themselves and the tactics I need to use.

Thank you for taking the time to answer! It all makes sense now.