Logic Challenge #32 - The Graduation Game (Hard)

[noah]

Brave the cold harsh light of the public and write your explanation for this game.

Have fun!

[fshek030]

[Moderator note: It appears this explanation mixes up the order of some of the questions. Notes have been added to indicate which question the explanations correspond to.]

K,L,M,N,O,P,R (7)

Possible game distributions:

A)

2-1-1-1-1-1
L
O

or

B)

2-2-1-1-0
L
O

Note: with B) the years 2001 and 2006 must be filled by somebody (either M/P/R) because the "earliest [friend] graduated in 2001, and the latest in 2006".

The Rules:

1) K/O__O/K

2) PM or MP

3) O + L

4) [K] (means K is alone)

At this point, the K/O__O/K block can be placed in either 02 _ 04 or 04 _ 06.

Template 1:

R-----K/----- N-------/O+L---[M/P -in which ever order)

01----02------03-------04------05----06

Note: with the K __ O+L or O+L __ K block in 2 and 4, R has to be first and M and P (in which ever order) have to occupy 05 and 06.

Why?

M + P cannot be first because there is no room for the MP or PM block.

02 is taken up by either K or L+O - in both cases, no one can join them. Therefore, R is the only remaining variable that can be placed first.

It follows, then, that the only place that the MP or PM block can be placed is 05/06.

Template 2:

[M/P/R]--------N----/K-------------/O+L

01-------02----03----04-----05-------06

The M/P/R block here becomes important. We have the following options:

- R (01), M/P (01), M/P (02), Empty (05);
- R (01), M/P (02), M/P (03), Empty (05);
- M/P (01), M/P (02), R (02), Empty (05);
- M/P (01), M/P (02), R (03), Empty (05);
- M/P (01), M/P (02), R (05).

The Questions:

Which of the following could be an accurate accounting of when the friends graduated?

1)
A) Correct;
B) Violates rule 2: If P is in 2001, M must be in 2002;
C) Violates rule 3: L must be with O;
D) Violates the rule that requires N to graduate in 2003;
E) Violates the K/_L+O rule.


[This explanation corresponds to Question 3.]
2) Cannot be true question:
A quick look at both templates shows us that the 2004 must be occupied by either L+O or K (alone).

Thus, D is correct.


[This explanation corresponds to Question 4.]
3) Cannot be true:

Again, If 2004 must be occupied by either K or L+O alone (at most, 2 people can graduate per year), then R can never graduate in 2004


[This explanation corresponds to Question 5.]
4. Lets look at Template 2:

[M/P/R]--------N-------/O+L--------/K

01-------02-----03------04-----05----06



M can occupy the 1st, 2nd and 3rd spots (it can share with N).

It cannot be 4th because of the 0+L block; it cannot be 5th because there is no room for the MP or PM block and it cannot be last because K must be alone.

Thus, C is correct.


[This explanation corresponds to Question 6.]
5) Must be true question:

Could be false = not necessarily true; since this is an except question, the logical opposite of not necessarily true = must be true.

So, the 4 wrong answer choices are not necessarily true and the correct choice must be true.

A) is correct. Again, 2004 is occupied by either K or L+O (no one else).

This inference seems to be constantly tested in this game.

Also note that B and C are one in the same since K and L+O are pretty much interchangeable in this game because no other variable can join them.


[This explanation corresponds to Question 7.]
6. Which of the following conditions, if true, determines the two-year span during which P and M graduated?

This should be an easy one to answer if you have the two templates.

Template 1:

R-----K/----- N-------/O+L---[M/P -in which ever order)

01----02------03-------04------05----06

Template 2:

[M/P/R]--------N----/K-------------/O+L

01-------02----03----04-----05-------06



(B) K graduated in 2002 -

Yes, Template 1 confirms this. With K in 02, 0 + L Must be in 04; this leaves only 05 and 06 for the MP or PM block.


[This explanation corresponds to Question 2.]
7. If K graduated in 2002, which of the following must be true?

(A) R graduated in 2001.

You can use the last Q to answer this one. With K in 02, R must be in 01 because someone has to occupy 01. It cannot be MP or PM because K must be alone, so R becomes our only option.

[volambre]

in question seven why cant R be with P or M. i got the question right because i knew the others were wrong but i didn't feel like it was a sure answer.
is it implied only because it says the earliest a friend graduated was 2001 which implies that someone must be in 2001 and 2006. i didn't feel that when i was doing the questions but now its the only thing i can think of.

[cinderellarose14]

Here is my explanation. Hand written again so bear with my handwriting~~~

Enjoy

[cinderellarose14]

in question seven why cant R be with P or M. i got the question right because i knew the others were wrong but i didn't feel like it was a sure answer.
is it implied only because it says the earliest a friend graduated was 2001 which implies that someone must be in 2001 and 2006. i didn't feel that when i was doing the questions but now its the only thing i can think of.

Yes. When the stem said earliest was in 2001 and latest was in 2006 that implies that at least 1 person graduated in 2001 and 2006.

[cinderellarose14]

I am seriously thinking about making two explanations for each game next time. One is the traditional version like the one I posted here which spells out the inferences and states why every wrong answer is eliminated. The other one will be for more "advanced" players who don't want to read the obvious inferences regarding how they are reached and don't want to read through all the eliminations. So the "advanced" version will just go straight-forward and go the fastest routine --- basically pick the fastest way to tackle the questions, then jump and go.

What do you guys think?

[xbig_bangx]

Can the author mark the correct answer (or take down the incorrect one) among those that are submitted to avoid confusion and frustration for LSAT fellows?

[sidlaw46]

I have having difficulty understanding the correct answer for question five. According to the online correct answer, it is (C) that is correct, but I don't understand why it cannot be (D). For example,

M - P - N - _ - LO - _ - K (R is floater, within reason)
P - M - N - _ - LO - _ - K (R is floater, within reason)
R - _ - NM - P - LO - _ - K (P could be before N, too)
R - _ - NP - M - LO - _ - K

I can't see why one of these is incorrect. Explanation please?

[cutie_mattina]

Tough one!

why not

P-M-N-K-R-O&L? (P and M/ K and O&L interchangeable)

[christine.defenbaugh]

An excellent explanation by cinderellarose14 above!

I do have just a few tweaks to make, though, and a few comments about process, so I'm including some images and a small bit of supplementary explanation below.

First, I wholeheartedly endorse frames for this game! The tricksiest thing about setting up these frames is noticing that someone must go in 2001. That's why R ends up stuck in 2001 in Frames #1 and #2. Here are my frames (same as cinderellarose14's).


Question 1
Remember, orientation questions should be attacked not answer by answer, but RULE BY RULE!


Question 2
If K is in 2002, we know we're in Frame #1...

R must be in 2001 (A), and so can't be in 2006(B). M and P are in a cloud of ambiguity, so that eliminates (C), (D), and (E)!

Question 3
This is a must be false question with no hypothetical, so there's not much to go on. However, all of the answers are about where P can or can't go. So let's look at that:

Interesting! The only place P can never go in any frame is 2004! (D) matches!

Question 4
Four answers could be true, so one must be false. If M is immediately before N, that puts M in 2002. We know we're in Frame #2 or Frame #3.

The answer choices focus solely on R. Frame #3 forces R into 2001, but Frame #2 allows R to be anywhere except 2004 and 2006 - that leads us to (D). Interestingly, R cannot be in 2004 in any frame, regardless of the conditional.

Question 5
If K is last, we must be in Frame #2 or Frame #3...

M is in a small cloud of ambiguity in both frames - 2001-2002 in Frame #2, and 2002-2003 in Frame #3, for a total of 3 possible years. (C).

Question 6
The hardest thing about this question is realizing that there are 4 could be false answers, and one must be true. If P is in 2003, then we must be in Frame #3.

The K_/LO chunk is still ambiguous though, between 2004 and 2006, so none of (B), (C), or (E) have to be true. R is forced into 2001, so (D) is impossible.

But M is forced into 2002, which means the statement "M did not graduate in 2004" is correct, and must be true. Once again, it's interesting to note that M can never graduate in 2004, in any frame.

It's super easy to get turned around in all the double and triple negatives in this question! Be careful!

Question 7
We need something that forces us in to one and only one Frame to determine where the MP chunk goes. R in 2001 could happen in any Frame - not helpful. Similarly, anything about K/L/O in 2004 could happen in any Frame - again, useless.

Even something about K/L/O in 2006 would still leave us with both Frame #2 and Frame #3 - still not getting the job done. Only something about K/L/O in 2002 (B) would tell us for sure that we must be in Frame #1!


The only other way we could ever determine for sure what frame we were in would be R was NOT in 2001 - that would have forced us into Frame #2.

Remember, it's not enough to note that a thing can happen in a certain frame - you're looking for the thing that would require you to be in that frame.

I hope this helps!

[christine.defenbaugh]

why not

P-M-N-K-R-O&L? (P and M/ K and O&L interchangeable)

Thanks for posting, a user!

This looks like it's totally doable in Frame #2! Did you think it could not be? Or were you trying to figure out why it wouldn't work for a particular question?

I have having difficulty understanding the correct answer for question five. According to the online correct answer, it is (C) that is correct, but I don't understand why it cannot be (D). For example,

M - P - N - _ - LO - _ - K (R is floater, within reason)
P - M - N - _ - LO - _ - K (R is floater, within reason)
R - _ - NM - P - LO - _ - K (P could be before N, too)
R - _ - NP - M - LO - _ - K

I can't see why one of these is incorrect. Explanation please?

It looks to me like you have 7 slots in your diagram instead of 6! That extra slot is making you think you have more options for M than you actually do!

Can the author mark the correct answer (or take down the incorrect one) among those that are submitted to avoid confusion and frustration for LSAT fellows?

It looks like one of the explanation attempts got the question order a bit mixed up. I've added in a note to clarify for future readers!

[schultz.daniellek]

1) K/O__O/K

2) PM or MP

3) O + L

4) [K] (means K is alone)

[mattjwiener]

Where in this game do the rules specify that a friend must occupy each year, and that no year can be left unoccupied?

From my reading of the main paragraph and indented rules, I'm really having a hard time making this inference. For instance, in question #2, why can't R be paired with M or P in slot 5 or 6, leaving slot 1 empty?

Can someone also please clarify the wording of the first rule regarding K and O? I originally thought this meant K/O_ _O/K.

Thanks.

[MichaelW907]

One quick question:

Two years apart means just one year in between? not two years in between?

Had a problem of this and Question 1 made me to realize this problem.

[VincyM61]

this challenge is to hard and complicated for me




_____________________________
best assignment help

[Antariksha SinghT553]

Where in this game do the rules specify that a friend must occupy each year, and that no year can be left unoccupied?

From my reading of the main paragraph and indented rules, I'm really having a hard time making this inference. For instance, in question #2, why can't R be paired with M or P in slot 5 or 6, leaving slot 1 empty?

Can someone also please clarify the wording of the first rule regarding K and O? I originally thought this meant K/O_ _O/K.

Thanks.

Exactly my concern

Question 2 has no correct answer

We cannot assume "Every year has at least one friend" - as that is not assumed for most of the latter questions