Logic Games Challenge #25 Pat the Party Planner

[ManhattanPrepLSAT2]

Hi everyone --

Here's the latest -- http://www.manhattanlsat.com/logic-games-practice.cfm

Go ahead and post your explanations here.

We'll select a best explanation, and also randomly select someone with the correct answers (which can be submitted directly on the game page). Winners in both categories can receive either $200 off of a live course, or a free strategy guide. You can win up to 3 times. After that, you are officially good at these.

Like many scary games that appear on the LSAT, this one is actually just a paper tiger. Give it your best shot!

By the way, if you're wondering why this is #25, we decided to replace an old game that we felt was a bit too close for comfort to a real LSAT game...

[drterri]

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

M _ O _ K (chain of 5 or more)
N-P-L
R, Q
Because there is a band member in common with each of M and O and K, there must be at least one band that plays between M and O, and at least one band that plays between O and K. Because of common band member, R cannot play before or after N, and before or after L.
1--you can immediately eliminate C, D and E because of the MOK rule. Then you can eliminate B because R is placed next to L. That leaves A.
2--O has at least 2 bands perform before it, so it cannot perform 2nd, making A the correct answer.
3--If M performs 4th, then we know 0 is 6th and K is 8th. The 5th and 7th bands are unknown at this point. P cannot be the 7th band because there would be no slot left for L which must come after P. So answer C is correct because P must be before O.
4--With N after K, we know M is 1, O is 3, K is 5th, N is 6th, P is 7th and L is 8th and R and Q must occupy either the 2nd or 4th slots. R and Q may occupy either 2nd or 4th slots, creating two correct orders of the bands, answer B
5--When we know that L performs 3rd, that means N must be 1st and P must be 2nd. That leaves 5 slots for our M_0_K chain, making M the 4th, O the 6th and K the 8th. R and Q occupy either 5th or 7th slots. Answer E creates the same setup, by requiring L to perform before M.
6--If R is immediately before M, the minimum of 5 chain now becomes a minimum of 6.
RM_O_K
N-P-L
Q
The only answer that could not be true is d because it would place N immediately before R which is a violation of the rules.

[cyruswhittaker]

I agree with the above answers/explanations.

1) (A) is the only choice that doesn't violate the constraints.

2) O cannot perform second because that would force M into slot 1, and violate rule 5.

3) M in forth forces O in 6 and K in 8th. Since P precedes L, the earliest that P can go is slot 5.

4) For this problem, create a sequencing chain:

M--O--K--N--P--L

Only Q and R remain, and they must fill a slot between M/O and O/K to prevent violation of the 5th rule. Either Q or R can fill either slot, so there are two possibilities.

5) If L performs immediately before M, then we have the following chain:

N--P--LM--O--K

Only Q and R remain, and similair to number 4, must occupy spaces between M/O and O/K to prevent violation of rule 5. As a result, 5 bands must come after L and hence L is forced into position 3.

6) R immediately preceding M produces RM--O--K, with at least one element between M/O and O/K to prevent violation of rule 5. That means that the above chain contains at a minimum 6 elements. Thus if spaces one or two are not filled by either R or M, then this chain will occupy spaces 3-8. Thus immediately search for a choice that forces this positioning while causing a rule violation. Choice D produces this violation. If Q, N occupy 1,2 respectively, then R is forced into slot 3, and this violates rule 5.

Note: I was rushed so I couldn't elaborate on the incorrect answer choices but I will when I get some more time.

[interestedintacos]

First we need to get a grasp on the combination of the rules, which seems like a difficult task at first, but isn't:

First the simple ones:

# O performs before K but after M.
# P performs before L but after N.

So we get: M-O-K and N-P-L. I prefer to simply use a line to represent these. It's natural to think from left to right and use your eyes to put it together. I don't think it's helpful to use ">," "<," etc.

Here's the "tricky" part:

* At least one person in band M is in both bands K and O.
* At least one person in band R is in both bands N and L
# No musician can perform in consecutive time slots.

Combining what we got before with our first simple rule we realize that M-O-K is actually M_?_O_?_K because there must be at least one musician in band M who also plays in K and O, and no one musician can play consecutive time spots. In other words, there must be other bands in between M, O and K.

We can't do as much with the rule that R, N and L can't play consecutively, but we must obviously keep it in mind. It plays an important role in solving the last question. We also know that N will come before L because of the simple rule of N-P-L from before. We don't know how many spots will separate them, nor we do know if R will come before or after or how many spots separates it.

Also we should quickly note that Q has no constraints.

The next thing you have to understand if you haven't already is that there will be 8 time slots: 8pm to midnight = 4 hours--multiply by 2 (2 30 minute slots each hour) and you get 8.

1. This comes from the easiest variety of logic game questions: can be true. All we have to do is apply the rules we've gathered: M_?_O_?_K, N-P-L, and R/N_?_N/L/R_?_L/R. (I apologize for the difficulty in expressing the last one via plain text--I would just put a cross through NRL) We apply each rule to each of the answer choices in order to eliminate the answer choices that can't be true.

Applying our first rule we find that we can eliminate answer choice C, because K comes before O, answer choice D because there is no band between O and K, and answer choice E because K comes before M and O. So now we just have A and B. We can't eliminate anything with our N-P-L rule, but with our last rule we can eliminate answer choice B because there's no band between L and R. So we are left with answer choice A, our correct answer.

2. Again we can use our 3 rules and think quickly about how they apply to O. Knowing O is involved in the middle of one of our rules we ought to do this and not get into something more murky. With our rule M_?_O_?_K we know at least two bands must come before O. So we know O can't go second, which happens to be answer choice A, our first choice...not bad.

3. Now we can benefit from a diagram with 8 time slots. Having used the M_?_O_?_K rule so much we should quickly realize putting M in slot 4 means we'll instantly know the positions of O and K because at least one band must split each of them apart. So we know O will be 6 and K will be 8. Now we ought to check the answer choices and see if that's enough: it's not. Now we should do a negative test--let's falsify each answer choice that might involve another restriction, and if we find that falsifying it means we can't reach a solution within the rules, we've found our answer--a simple "must be true" strategy. Doing this to answer choice C obviously proves it's the answer--there's only one spot for P if O comes before it--slot 7. And that means there's no room for L, which we know must come after P. So C is the answer.

4. We have to use a diagram again on this one. Placing N after K immediately gives us permanent spots for M, O, K, N, P and L. Q and R are left in the air in slots 2 and 4. Either Q in 2 and R in 4 or R in 2 and Q in 4 works, clearly. So the answer is B.

5. First we have to understand what this slightly strange question is asking. "The same effect" means literally the same placement of bands, not for instance, shifting one band 2 slots or shifting a couple bands a few slots--it means exactly the same positioning. Placing L in slot 3 gives us a certain lineup of bands, and we need to know what other action would give us the exact same lineup.

First we learn that placing L in slot 3 puts N in slot 1 and P in slot 2: NPL. That doesn't leave much room for our M_?_O_?_K block: M must go in slot 4, O in 6, and K in 8. R and Q are again left out as variables that fit into 5 or 7 respectively. Now we have to try answer choices that seem most potentially affected by restrictions or we can just try each choice. Answer choice A doesn't necessarily give us the same result because placing N first doesn't mean we can't move around P and L. Answer choice B fails for the same reason because we can still move around L, even if NP remain in place. Answer choice C is wrong from the start because R doesn't necessarily occupy slot 5--it could be in slot 7, so obviously putting it in slot 5 will give us a more specific result, not the matching result. Answer choice D doesn't work because we can put the new PL block later on in the night, separating it from N and the original NPL block. Answer choice E is now correct by elimination. Also we could have picked it first because if M is going to come right after L, the NPL block must stay intact at the beginning of the night, and the M must stay in place as well because the M is constrained so much by the big M_?_O_?_K block.

6. Placing R immediately before M gives us a bigger chain than before. We simply have to look at the various options with our new enlarged chain: RM_?_O_?_K. Now, again thinking about our rules, we'll find an opportunity for our last rule to play a big role. Answer choice D should stick out. With Q in slot 1 it can't help break up the RNL grouping restriction, and with N in slot 2 and the big 6 space RM_?_O_?_K block we realize this one necessarily violates our rule. R and M must go in slots 3 and 4. Then slot 5 must be P (part of the N-P-L block), and slot 7 and 8 either R or L. We'd be forced to put R next to L, which violates the rule. So D is in fact the answer.

[rimamehr]

1) A
2) A
3) C
4) B
5) A
6) D

[swwestley]

interestedintacos's guide is near-definitive, however I thought I'd give this a whirl too.

First we must create a representation of the situation.

Before even viewing the rules, we must realize that this game is based on fitting eight items, in various orders, into eight slots.

Rule 1, combined with Rule 5, tells us that M, O, and K cannot be placed next to each other.
Rule 2, combined with rule 5 tells us the same about R, N and L
Rule 3 gives us the sequence M-O-K
Rule 4 gives us the sequence N-P-L

Now, before looking at the questions, we need to realize the following:

We can combine Rules, 1, 5, and 3 to get a relatively restrictive stipulation that could be represented M_?_O_?_K, meaning there must be at least one other group (but possibly more) in between M and O, and O and K.

The next most important rules concern N-P-L and the placement of the R. N's inability to be placed next to L is immaterial because of the the N-P-L sequence

Q has no restrictions.

It would be a reasonable strategy for each of the following questions to begin by dealing with the M_?_O_?_K group, then moving on to N-P-L and R, and leaving the easily disposed of Q to be considered last.

1. For this relatively easy question we can use the "comb" technique, applying rules or deductions one by one until only one answer is left. Naturally, we want to start with our most restrictive deduction, that concerning the M_?_O_?_K group. This immediately allows us to eliminate [C],[D],and [E] as possibilities. Next we look at R. In answer [B], it is placed next to L, violating rules 2 and 5. Thus we eliminate [B] and choose [A].

2. This question about "O" should immediately cause us to focus on the M_?_O_?_K group again. Our prior deductions allows us to see that the earliest O could possibly appear is in the third slot. Thus, [A] is impossible, and our correct answer.

3. This is the first question for which a diagram consisting of our eight slots is useful. Using our previous deductions about the M_?_O_?_K group, we can immediately see that O must fall into the 6th, and K into the eighth slots.

The "Must be true" formulation can be confusing. There are two ways we can proceed. The "brute force" approach would involve attempting to find a counterexample (that is, a complete ordering that follows the rules and yet falsifies the answer) for each answer. The answer which cannot be falsified will be the correct one. While unfailingly accurate, this is potentially quite time consuming.

Therefore, it would be still more appealing to discover an elegant logical solution, and luckily, one is apparent in this case: Without even trying different combinations and simply from applying rule 4, we can see that P could never be in the first or seventh (last of the remaining available) spots. If one of the answers were to express this, we could immediately select it as the winner. Answer [C], "O performs after P", given what we already know, may as well say "P can never be in the seventh place". Thus we can select [C] as our answer.

To describe the second approach in an easily generalizable way: We first found a positive statement (P can never be in the first or seventh place) about the possible ordering and then checked to see if any of the answers matched it.

Choosing to approach the problem in this way represents a calculated risk. While in this case it was much faster than the "brute force" method, it would of course have been possible that none of the answers would have expressed the deduction we made, and we would have been forced to return to the brute force method with an additional time handicap.

4. A diagram will once again be useful in order to make the necessary deductions. In fact, if one diagrams the problem correctly M_O_KNPL, the question practically answers itself. The remaining bands can appear in either place, thus there are two possibilities and our answer is [B].

5. This kind of question can be confusing. Two approaches follow, but they both begin the same way: First, make all possible deductions based on the knowledge that L is third. This gives is NPLM_O_K.

From here, we once again face a choice between a "brute force" negative approach, and a more intuitive, "positive" method.

Using the brute force method would require asking of each potential answer, "Does this information, if applied to the original ruleset, allow me to deduce exactly NPLM_O_K?"

Or to put it negatively, "is there any other possibility than NPLM_O_K given this answer?

A quick glance at the possible answers shows us that [C] cannot possibly be true, as the original knowledge that L is third does not tell us the exact location of R.

[A] can be eliminated, because M could immediately follow N
[B] can be eliminated, because M could immediately follow P
[D] can be eliminated because as we saw in question three, the entire NPL formulation could be after the M_O_K group

Therefore [E] must be correct.

The positive, intuitive approach to this question is more difficult to describe but might happen as follows. The most distinguishing factor of the NPLM_O_K ordering seems to be that the entirety of the NPL sequence is before M_O_K, and additionally, that this is the only possible ordering if that is true. Thus any potential answer that lets us know that NPL comes before M is true will be our solution. [E] fits the bill.

6. Adding R to our much-used M_?_O_?_K group tells us that R must be in one of the first three spaces.

Keeping in mind the that we are now looking for an answer that CAN'T be true, our approach is the following:

Looking at our answers, there is one where [R] appears in the first space, and it is immediately followed by M, which checks out, so we can eliminate [A]

Looking again at the answers, there is one that places R in the second place, preceded by Q. This is also possible, so we can eliminate [E]

All of our remaining possible answers require that R be in the third place. Thus, if any were to contain N or L in the second place, they would be impossible and thus correct. Answer [D] contains N in the second place, and is therefore our correct answer.