Logic Challenge #17 - The Cubicles

[drancour]

1. C
2. A
3. A
4. D
5. A
6. B
7. B

[orion]

7 items: MPQRSTV

Diagram:
^
| (0-3 others)
----
|v2|
----
|v1|
-------
|c |h1| -> (0-3 others)
-------

Rules:
I. M and P are on v
II. Q and R are not on c
III. TV are adjacent (could both be on h, both be on v, or have one on c and the other in h1 or v1)
IV. R is farther from c than Q is
V. R is on h

Rule summary:
corner (c): 1 room; can't have M, P, Q, or R; could have S, T, or V
vertical (v): 2-5 rooms; can't have R; must have M and P; could have Q, S and one or both of {T,V}
horizontal (h): 1-4 rooms; can't have M or P; must have R; could have Q, S, and one or both of {T,V}
general: R is farther from c than Q is

1. (A) No. (R must be on horizontal)
(B) Yes.
(C) No. (T and V must be adjacent)
(D) No. (P must be on vertical)
(E) No. (Q can't be corner)
Answer: (B)

2. V=v3 => T=v2 or v4 => v has 4-5 rooms, S=c => h has 1-2 rooms => R=h2 => v has 4 rooms {M,P,T,V} => Q=h1 => Q is adjacent to S
Answer: (C)

3. Q=v3 => R=h4 => need 8 rooms (impossible)
Answer: (D)

4. (A) No. (If there are two cubicles between Q and the corner, Q=v3, so M or P is v4. So h has at most 2 cubicles, and R can't be farther from c than Q.)
(B) Yes. (If there are two cubicles between M and the corner, M=v3. One possibility is that Q and P are v4 and v5 respecively, meaning that h has only one element, so R can't be farther from c than Q, which is impossible. Alternately Q and P can be v2 and v1, respectively, and h can have 3 rooms so that R can be h3 and S, T, and V can be c, h1, and h2.)
(C) No. (If there is one cubicle between R and the corner, Q has to be adjacent to the corner, which means the corner is M or P, which is impossible.)
(D) No. (If there are three cubicles between R and the corner, R=v4 and there can be only 2 cubicles on v, which does not leave enough space for all of M, Q, and P.)
(E) No. (If there is one cubicle between P and the corner, either this cubicle is Q (which is impossible because it would force M to be the corner, which isn't allowed), or Q and M are above P, which is the same situation described in (A).)
Answer: (B)

5. (A) No. (Only S, T, and V can be c.)
(B) No. (This forces V=c => T=v1 => Q is no lower than v2, but v has 5 rooms {MPQST}, so h has 1 room {R} => R=h1, which is closer to c than Q.)
(C) No. (Same as (B).)
(D) No. (Same as (A).)
(E) Yes.
Answer: (E)

6. {S,T}={h1,v1} => V=c
T can't be adjacent to R because R would have to be h2 or v2, meaning that Q would have to be h1 or v1 to be closer to c than R is, and h1 and v1 are already taken.
Answer: (D)

7. T=h4 => V=h3 => R=h2, S=c => Q=h1, {M,P}={v1,v2} => 2 arrangements
Answer: (A)

[superfilms]

First I write out the inventory, then draw the first two clues underneath:



The dark box with the arrow pointing to it is the corner cubicle. The first clue says M&P are above it, so M & P can't be in the horizontal row at all. That also means the vertical portion of the L must have at least two cubicles above the corner.

Add the second clue on the same lil' diagram: Q & R cannot be in the corner.



Clue 3: T must be adjacent to V, regardless of order.

Clues 4 & 5:



Either Q & R are both in the bottom part of the L, in which case Q is before R, or Q is vertical, and R is horizontal, in which case there must be more cubes between R and the corner than between Q and the corner.

R can never be right next to the corner, as that would force Q into the corner.


Let's look at how the clues break out into diagrams.


The 2Top has M/P in the upper two boxes:




The 3Top is impervious to deductions at this point:




Here's the 4Top:




And the last possibility, the 5Top:



R would have to go in the lower right hand box (Rules 2/4/5) and that would crowd Q into the corner, so it isn't possible. So now we know there are only three possible arrangements to the game; the 2Top, 3Top, and 4Top.


Let's go to the first question.


1. Which one of the following could be the arrangement of the cubicles in the vertical component of the "L," listed from the corner cubicle and moving upwards?

(A) Eliminated. R must be in the horizontal row (Rule 5).
(B) Correct.
(C) Eliminated. TV must be adjacent, (Rule 3)
(D) Eliminated. P must be vertical (Rule 1). Also Rule 4.
(E) Eliminated. Q can't be in the corner (Rule 2).


2. If V is the third cubicle above the corner, then which one of the following must be true?

If V is to be the 3rd cubicle in the vertical column, then T must accompany V. M & P also have to be in the vertical column so we have four things in the vertical column. that means we are in the 4Top.



Place V in the 3rd spot. The top box has to have either M/P/T and the 2nd box also gets M/P/T. The first box above the corner must be M/P, because T has to be next to V.

R has to be further from the corner than Q, so R in the last horizontal box, and Q in the middle one. That forces S into the corner.

(A) T is adjacent to P. Could Be False (CBF):T could be in the top box.
(B) S is adjacent to M. CBF: S could be next to P.
(C) Q is adjacent to S. Must Be True (MBT).
(D) Q is adjacent to P. MBF.
(E) P is adjacent to V. CBF: P could be in the box next to the corner.


4. If Q is the only cubicle that separates M and P, which one of the following could be true?

If Q is with M & P in the vertical part of the L, then we can't use the 2Top. Could be the 3Top, or the 4Top. Let's start with the 3Top.



Place Q and M/P in the vertical boxes with Q separating M & P. R must go in the last horizontal box because it has to be further away from the corner than Q.


(B) M is separated from the corner cubicle by exactly two cubicles.

Could be true, put M in the top box.


6. If S and T are adjacent to the corner cubicle, each of the following could be true EXCEPT:

Can't be in the 2Top, because either S or T has to be in the vertical column. So either 3Top or 4Top. Let's start with the 3Top.



Put S/T in the two spots adjacent to the corner. Put M/P in the two remaining spots in the vertical part of the L. Q & R can't go in the corner, so R has to go in the last box and Q in the second-to-last box. This forces V into the corner.



(A) S is adjacent to P. Eliminated. CBT.
(B) Q is adjacent to T. Eliminated. CBT.
(C) R is adjacent to Q. Eliminated. MBT.
(D) T is adjacent to R. Correct. This could not be true, MBF.
(E) Q is adjacent to S. Eliminated. CBT.


7. If T is the fourth cubicle to the right of the corner, how many possible arrangements of cubicles are there?

If T is the fourth to the right, then we must be in the 2Top.



V must go next to T.



Q & R can't go in the corner, and R has to be further from the corner. S goes in the remaining spot.




(A) 2 Correct. Two options: M on top or P on top.


3. Which one of the following must be false?

(A) Q is the third cubicle to the right of the corner.

Could be true. In the diagram you just drew for Q7, you could switch Q&R with V&T, putting Q 3rd to the right of the corner and R in the last box.

(B) S is the second cubicle to the right of the corner.

Could be true. In the diagram you drew for Q4, you could put S in any of the three remaining boxes.

(C) T is adjacent to the corner cubicle.

Could be true, see diagram for Q6.

(D) Q is the third cubicle above the corner.

Must be False. IF Q were to third cubicle above the corner, R would have to be the fourth cubicle to the right of the corner, requiring 8 cubicles.

(E) P is the fourth cubicle above the corner.

Could be true. See your diagram for Q2.


5. Which one of the following could be true?

(A) Q, S, T, and V are located to the right of the corner cubicle.

MBF. The 2Top has the most things to the right of the corner (four) but if we filled them with Q, S, T & V we would have no room for R. Violates rule 2/5.

(B) Q, S, and T are located above the corner cubicle.

MBF. Combined with Rule 1, requires that MPQST (five things) be above the corner, and we proved that can't happen in our early deductions (no 5Top).

(C) Q, S, and V are located above the corner cubicle.

MBF. Combined with Rule 1, requires that MPQSV (five things) be above the corner, and we proved that can't happen in our early deductions (no 5Top).

(D) S, T, and V are located to the right of the corner cubicle.

MBF. Combined with Rules 2/5, that would require RSTV to be to the right of the corner, forcing us into the 2Top. That would leave MP above the cubicle, forcing Q into the corner, violating Rule 2.

(E) Q, R, S, and V are located to the right of the corner cubicle.

CBT. 2Top.

[orion]

Heehee, awesome sketches, superfilms.

[superfilms]

Thanks! & Grr @ my cell phone cam which is inappropriately blurry.

[superfilms]

Additional Q:

8. If S and T are to be placed as far apart as possible, who could be adjacent to the corner office?

A)M
B)R
C)V
D)T
E)S

[superfilms]

9. If S and T are not in the same parts of the L (ie, they are not in the same column or row), then each of the following could be false, EXCEPT:

(A) If R is not adjacent to Q then R is adjacent to T.
(B) Either Q is adjacent to S or Q is adjacent to T.
(C) Either P is not adjacent to S or P is not adjacent to Q.
(D) Either V is adjacent to Q or V is adjacent to S.
(E) If P is not adjacent to M then P is not adjacent to T.

[zhangstagangsta]

1.b
2. c
3.d
4.e
5.e
6.d
7.a

[lrthompson]

Answers as follows:
1 B
2 C
3 D
4 B
5 E
6 D
7 A


Reasoning:
1 a) no - R must be in the horizontal component
*b) yes - T is the corner, V and s are adjacent, making R separated by 2 cubicles from the corner (more than Q)
c) no - T and V are not adjacent
d) no - P is not in the vertical component
e) no - Q can not be the corner piece

2 a) Could be true, not a must
b) Could be true, not a must
*c) MUST be true - with T, V, M and P all in the vertical component, that leaves S as the corner piece, meaning Q must be next to it, for R to be farther away from the corner than Q
d) Can not be true, Q must be in horizontal component.
e) Could be true, not a must

3) a) Could be true... MP[S]TVQR (with [ ] representing the corner)
b) Could be true MP[V]TSQR
c) Could be true (see above for one possibility)
*d) Can not happen: with Q as the 3rd cubical above the corner, that leaves only two cubicles to separate R from the corner as well, and R needs to be farther away than Q. ex: QMP[S]TVR
e) Could be true: PMTV[S]QR

4 a) no - Again (as in question 3 d) Q can not be more than 1 cubicle away from the corner if in the verticle element, because that does not leave enough cubicles to separate R from the corner.
*b) Could be true: MQP[S]TVR
c) no - Q must be separated by at least one cubicle (no fewer) and R must be farther away than that (so 2 or more)
d) no - there are not enough cubicles available to do this if M,P and Q are all in the verticle element (one of S, T or V must be in the corner, leaving only two to separate R from the corner)
e)no - in order to separate R by two cubicles from the corner, There can only be 3 verticle cubicles not including the corner. they must be M, P and Q and Q must be the middle element. thus, P can either be adjacent to the corner, or separated by two cubicles.

5 a) no - one of S, T, or V must be in the corner
b) no - Ths would make V the corner element and place R adjacent to the corner, which would not be farther away than Q (R must always be separated by 1 or more from corner)
c) no - T and V must be adjacent (V is corner, since S and T are used in vertical element), placing Q at least at two above the corner (separated by one from corner) There are no cubicles left to separate R from the corner, so R is adjacent. Can not happen.
d) no - one of S, T or V must be corner.
*e) yes - ex: MP[T]VSQR

6 - MP (either order) S[V]T (can also be reversed) QR (must be like this)
a) yes, could be true : MPS[V]TQR
b) yes, could be true : MPS[V]TQR
c) yes, could be true : MPS[V]TQR
*d) no could not be true: Q must be closer to the corner than R, and if R separated by one from the corner (T in this case) and S is next to the other side of the corner, then Q would also be separated by one from the corner.
e) yes, could be true: MPT[V]SQR

7) MP (either order) [S]QRVT (must be in this order, because of the rules: T adjacent to V, R in horizontal element, and R farther away than Q)
this leaves one variable part with two elements: the beginning can be MP or PM.

There are 2 possibilities.

a) yes.

[dan]

Lots of great work here so far. We'll post the answers on our website
soon. Let me ask you guys...

What kind of game is this? It's an important question because if you
know the game type, you can create a very efficient diagram. Some
prompts to help you think about this:

1. What is the main challenge with this game?
2. What type of LSAT game commonly introduces this sort of challenge?
3. What type of diagram allows us to manage this challenge?

Superfilms is on the right track. Even if you think you got all the questions right, see if you can go back and shave some seconds, or even minutes, off of this game by
coming up with a clean diagram. Feel free to post here if you have any
ideas.

dan

[superfilms]

Really, it's an order game. Put

|1|2|3|4|5|6|7|

across the top of the diagram. The corner is the complicating component--but it's easier to draw a diagram if one thinks of it as things are either before or after the corner, with before representing the vertical component, and after representing the horizontal component. The setup says that there is at least one cubicle before and after the corner, so the corner can't be 1 or 7.

In the final diagram, some breakouts are not necessary if one can comfortably juggle the placement of two or three letters in one's head. That said, generally it's a smart move to break it out, and avoid any risk of an error.



Represent the corner with a circle in whichever box is the corner.



Rule 1. M & P are before the corner.
So now the corner can't be 1, 2, or 7.



Rule 2. Q & R aren't in the corner.



Q & R aren't in the corner.



Rule 3. T & V are adjacent.



Rule 4. R is farther from the corner than Q.
Rule 5. R is after the corner.



R can't be next to the corner, because that would force Q into the corner, violating the 2nd rule.



R is not adjacent to the corner.

That also means that there must be at least two boxes after the corner, so now the corner can't be 1,2,6 or 7. The corner could be 3, 4 or 5.



There are three models that describe the possible positions of the corner: 3rd, 4th, or 5th. Below the models are the breakouts for Q2.



The breakouts for the remaining Q's, answered in the best order (Q's with clues before Q's without additional information).

[dan]

Ah. So Superfilms is treating this as an ordering game (with a floating corner), and is tracking a few frames. Interesting thoughts! Thanks for posting those.

Any other ways of conceptualizing this?

[superfilms]

Trying both of the previous ideas I had out, I prefer the original (mapping) vs the new (ordering). The mapping only took about 6-7 minutes to set up and answer the questions.

Generally when I see a game like this, where a map, or arrangement, is described in the setup, typically with redundant information to guarantee a correct setup for the test-taker, I go with that and draw a picture as close as possible to the one described.

While I have no data other than the anecdotal/personal to prove this, I don't think LSAC has an interest in dreaming up ways to trick people into drawing a bad picture, and their games often have the redundant setup info as though they want the real challenge to be the deductions and not the diagram (in this game, for example, the two parts of the "L" are described as having at least one cubicle in addition to the corner, which can also be inferred from rules 1, 4, and 5).

Overall I prefer to map it. It makes it easier to answer the questions (for me) because what is described in the questions and answers matches what is in my head and in my diagrams.

[dan]

Thanks for sticking with this, Superfilms. Great ideas. I agree that mapping, or diagramming, is an effective approach.

In fact, for those who have taken our course, or studied our book, try creating a diagram using an open assignment approach. I think the biggest challenge for this game is that the number of cubicles in each section of the "L" is unknown. We can use open board symbols to track these uncertain numbers.

Hope that helps!

dan

[damita_chambers]

My Answers:
1. B
2. C
3. D
4. B
5. E
6. B
7. A

[gpvarsity58]

My Answers:

1. E
2. C
3. D
4. A
5. E
6. D
7. A

[gpvarsity58]

Whoops, I meant this was my answer.
My Answers:

1. B
2. C
3. D
4. A
5. E
6. D
7. A

[dan]

Hey everyone,
You can view the answers to this game by clicking the following link, scrolling to the bottom, and clicking "view answer."

http://www.atlaslsat.com/Logic_C_view.cfm?ChallID=17

dan

[mikburger44]

The problem reflects linear ordering

Draw a symmetric L - Make the corner available for STV (rules dictate)

And the rest follows recognizing that TV being connected
doesnt preclude one acting as the corner slot and the other
going either verticle or horizontal