Logic Game Challenge #39: The Mixed Quartet Game

[wingedfeetxc]

Our latest Logic Game Challenge, The Singing Game, is live: http://www.manhattanlsat.com/logic-games-practice.cfm.

Post your answer explanations (or questions) questions here. Good luck!

[mkgraff]

Answering this problem set relies less on what is possible than what is not possible. There are too many permutations of possible answers for it to be time-efficient to list all the possibilities (at least for a problem set this small) and then compare those possibilities with the answers; the fastest way to complete the set, then, is to determine which answers are false.

Unfortunately, a direct comparison of the criteria only allows you to answer the first question really, with the rest requiring some extended reasoning. The key is to look at how each statement interacts with the others and reason out what the statements tell you that isn’t on the paper.

Going through each of the statements:

Statement #1 seems straightforward: J must outrank L. But, this also means that any time L gets a prize J will too, and L cannot #1 since J cannot outrank L if it is at #1.

Statement #4 is the same as #1, except for I and K.

Statement #3 says any answer than doesn’t involve I equaling 1st or 5th will be wrong. However, combined with statement #4, this means that if K gets a prize, I will be first.

The second statement is the most involved of the criteria to apply. First, taken inversely, it says that as long as H does not get a prize, there are no rules for G and K. The next step is to combine it with the other statements:
1. Combined with statements #3 and #4, if H gets a prize, I will always be first, since he must rank higher than K who now is also getting a prize.
2. Again combined with statements #3 and #4, if H gets a prize, four of the five slots are now immediately full; I first and then H, G, and K in some order where G outranks K.
3. Combined with statement #1 (and #3/4) , if H gets a prize and four slots are full: I, H, G, and K, then L cannot get a prize; if L gets a prize then so does J, and there isn’t room for both.

A general observation in looking at these, if H gets a prize it places the most restrictions on the answer and thus makes the number of possible answer much smaller. Conversely, if H does not get a prize, there a many, many more possibilities.

Going through each of the questions, the main tactic is to rule out the answers which violate one of the statements above.

In the first question each of the four wrong answers violates one of the four statements:
A is wrong because of statement 4: I must outrank K and does not.
B is wrong because of statement 2: if H gets a prize so do G and K, but K isn’t on the list.
D is wrong because of statement 3: I isn’t 1st or 5th.
E is wrong because of statement 1: L gets a prize when J doesn’t.

The second question tests the broader implications of statement #2 and #3:
If H gets a prize that means that four of the slots are filled and I is #1. If M is also getting a prize we know which five people are now in the top five. Because G must outrank K, G cannot outrank K at #2 if I is #1. Answer is D.

For the third question:
A is wrong because of the combination of statements #2 and #3: if H gets a prize, I must be first, but isn’t in this answer.
B is wrong for the same reason it was wrong in the previous question.
C requires some reverse thinking and the process of elimination. Per statement #1, if J does not get a prize, then L cannot either. Per statements #2 and #3, if I is 5th, then H cannot have a prize. And lastly, per statement #4, if I is 5th, K cannot get a prize either. All combined, J, L, H and K cannot have prizes in this scenario, which leaves only four possibles (F, G, I, and M) for five prizes.
D is wrong because of statements #1 and #2 (see implication #3 above). There isn’t room for Lenore if Horace gets a prize.

Once the statements are analyzed, question number four becomes fairly straightforward. If H is #2, we already know that I is #1, and G and K are ranked consecutively at 3/4, 3/5, or 4/5, making A possible.

To double check:
B is wrong because of statements #2, #3 and #4: I must be #1 (see above where this is explained).
C is wrong because of statements #1 and #2: if H gets a prize, then so do G and K, and I always get a prize. L cannot have a prize; if L has a prize then so does J, and there isn’t room for both.
D is wrong because G must outrank K per statement #2.
E is wrong because statements #2 and #3. If H is 2nd, K gets a prize. If K gets a prize and I must outrank K, I must be 1st, not G.

Question number five:
This is automatically B _ Horace ranking anywhere automatically places I at #1.

If you want to double check:
A is not necessarily true for the same reason the previous question was A.
C is not necessarily true since J must only rank higher than L. I ranking fifth is fine as long as H and K don't get a prize.
D is not necessarily true since even if L and H do not receive prizes, the other six are all still eligible.
E is not necessarily true since M has no stipulations, stated or implied, in any of the statements.

Question number six:
Please fix the typo _ G is for Grace, not Grant.
Since questions six provides three names of people who do not receive prizes, we want to look at the other five to determine what is possible.
A is wrong because H is not listed, therefore getting a prize, and G is, therefore not getting a prize. Statement #2 invalidates this.
B is wrong for the exact same reason.
C is wrong because L is not listed, therefore ranking above J, who is listed. Statement #1 invalidates this.
E is wrong because I is listed, therefore not getting a prize. Statement #3 invalidates this.

This leaves D.

Question number 7 (answer D contains a typo _ the = then; answer E contains a typo _ than = then) requires us to look at the effects of statement #2 and determine which is an exact substitute.

Statement #2 lists with the stipulations if H gets a prize, whereas answer C reverses the conditions and the stipulations, but gets them all:

If H receives a prize, then G and K both receives prizes and G outranks K.
vs.
If K outranks G or if either do not receive a prize, then H cannot get a prize.

It may be easier to process this question by elimination as well:
A is incorrect because this is only true if H receives a prize, otherwise it doesn’t matter what rank G and K are.
B is incorrect for the same reason A is. If H receives no prize, G and K’s order does not matter.
D says the same thing as B.
E is incorrect because it does not cover the stipulation about G outranking K.

[domenech.olivia]

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

[amucino]

Coming from just studying open grouping logic games and hybrids, this type of logic game is a breath of fresh air!

step one: Prepare for Battle

diagram the game. typical ordering game so 8 slots for 8 singers, best to worst. I always write in what direction best to worst goes in, so in this case best to worst is left to right:

Best __ __ __ __ __ I __ __ __ Worst

I also, drew a line between the 5th and 6th spot to symbolize prize winners and non prize winners

The rules are pretty straight forward:

J -- L

I1/ I5

I--K

** H - G -- K

** on my diagram I drew a box around the letters, to remind myself they ALL receive prizes. ALSO, I noticed an inference between three rules:
1. If H won a prize, then G must come before K
2. I must come before K
3. I is either 1st or 5th

THEREFORE: "I" must be in slot one if "H" wins a prize.
( I can't be 5th if H places, because if H places then both G and K place, and I must be before K, so it cannot be 5th)


Step Two: ATTACK!

1. My favorite type of question and the easier kind in my opinion. Process of elimination. Piece of cake

A)- impossible: K comes before I ( 4th rule)

B)- impossible: H won a prize therefore G and K must win prizes too..K is missing (2nd rule) OR you could spot that H won a prize and I is NOT in slot one ( inference)

C)- CORRECT YAY: alright H won a prize, I is in the right spot, both G and K also won prizes and G comes before K.

If it works, select it and move on! No need to see if D or E are right, because they are wrong ( because C is obviously correct)


2. ok so take a moment to see what you know so far:
- H is 4th, which means:
- G must come before K
- G and K must also win prizes
- I must be first

I always quickly scan the options and it worked in my favor on this one.
I know that G can't be first because I must be first. Therefore the earliest K can place is 3rd.

D stood out and was correct ( K finishes 2nd)

3. I again quickly scan the options, this one doesn't seem as obvious... so i use process of elimination to see which options I already know are wrong:

A) impossible- if H wins a prize then I must be first

B) impossible- K can't be second

C) impossible- There isn't enough room for the losers
- if I is 5th, H did not win ( 1/3 spots)
- I must come before K ( K must be a loser, 2/3)
- J must come before L, so niether won prizes ( 4/3 spots)

D) impossible- there isnt enough room for J in the top 5 ( J--L)

E) only one left. circle it and go!

4. Remember what you know:
- H is 2nd
- I is 1st
- G comes before K
- G and K both must place

take note that there are limited spots where G and K can go.

A) Correct. At first glance, it just seemed possible so I moved onto the next answers. it is a MUST BE TRUE question, so could be answers I do not eliminate.

B) impossible- H won a prize therefore I must be first

C) impossible- not enough room for L AND J ( remember, J must be before L)

D) impossible- H won a prize, therefore G must come before K AND both win a prize. G cannot be 5th

E) impossible- I must be first since H won a prize

A is the right answer!

5. Must be a true question. Quick scan of the options and this is so obvious! I don't even second guess because we have been using this inference for every question.

B) CORRECT! No matter what H places, as long as it does, I is 1st

6. Alright, time to give the losers some of the spotlight.
again, remember what you know. From the previous questions, its obvious the most useful rule we have is surrounded around H. So keep that in mind!

A) impossible- H isnt a loser, so G and K aren't either

B) impossible- same reasoning as A

C) impossible- J must come before L

D) Correct! Possible, move on

( if you must know, E cannot be correct because I must be 5th or 1st)

7. Rule rule question, I sometimes have trouble with these types of questions, so instead of figuring out what each rule does, I eliminate the answers that are obviously wrong.

but this one is pretty simple

C is correct


hope this helps!

Happy studying! If you need a break, this is a good laugh:

http://www.buzzfeed.com/jameskicksa/35- ... -lsat-b2tp

[frank4pepper]

It is really difficult..I am just amazed by the logic of this game..I hardly cross the intermediate level..

[rameshJPSB]

Set up is very important

Best I/_ __ __ __ _/I __ __ __ Worst
1 2 3 4 5 6 7 8

1. J > L

2. if H (1-5) then G>K (1-5) Set up (I) is 1st cannot be any other place (G & H) cannot be 5th (K) cannot be 1st or 2nd (Important Rule)

3. this should be before 2nd but its LSAT so I is 1st or 5th, I always gets prize

4. I > K

Floating Variables

F J(*) L M

Now Attack!

[christopherfarrelly]

Well, first time wiring this but since it's getting close to that December LSAT I thought, what the heck...

Set-up...

The first rule is quite simple being that J ranks better than L

J-L

Second: This is the one that will give us the answer to a majority of questions and I set it up as so..

If H-P then G-K (with a Prize Cloud above them)

Third: Ian ranks 1st or 5th... Easy just placed it into my diagram

1. I/ 5.I/

Fourth: Ian ranks better than Kramer (Huge Seinfeld fan here!)

I-K ...... This rule turns out to play a large role.

Big Pause: What do we see when we set this up. After about thirty seconds or so and about to give up I saw an inference. That if Horace is awarded a prize than Ian must be ranked 1st. It also fills up four of the five spots as well. Although, it might not be everything I should have seen, it sure helped.

The Q&A's

1. Correct - C
Incorrect: A - Violates the last rule of I-K... Simple, toss it.
B: Violates the rule in which both G&K receive prizes if Horace is awarded a prize.
D: Where's Ian?
E: Violates rule numero uno... J-K

2. Correct - D
How- If Horace is ranked and Maria is awarded a prize that means we have all five spots filled whether or not we know where they go is still a bit of a mystery. Although, if Horace is ranked 4th.. That means Ian must be ranked 1st and we still have the rule that G-K which means it would be impossible for K to rank second because I & G must come before it.

3. Correct- E
How - This was definitely for me one of the tougher questions..
A - Violates what we learned in the big pause!
B - Again! Violate was we learned in the big pause and question 2
C - Ok, if Ian is fifth then we know that H did not get a prize, and we know J as well was not awarded a prize. So, we now have 2 out and we know J-L which throws out another which makes it 3 in total. Finally we know that I-K and now we have 4 out which makes this, well, wrong...
D - If H is 2 then we know that I is first. Ok, then we know that G & K must also be in the top five as well which gives us four and we also know that L is fifth... and that gives us five.. Perfect, right? Actually, what about rule number 1? J-K ...

4. Correct - A
B - We ought to know why this is wrong by now... Ian must rank 1st is Horace is given a prize.
C- L being fifth just makes the top 5 a bit to crowded
D - Grace being 5th? Where would Kramer go?
E- Grace 1st? Nope, that's where Ian goes

5. Correct - B
I would right out why they are all wrong but if I wasn't able to spot this one immediately after all of these questions by now, I might want to take the Feb LSAT. Horace being ranked must mean Ian is first!

6. Correct - D
These questions to me are tough and would like some more practice with but here is how I got to the answer I did. Basically using my rules and what other crazy logic that is in my head I thought that if Horace was out than G or K must also have to be out which is filled by C and D.. Then in C I saw that J was out which in turn would make it incorrect because it would Violate J-K... So basically I thought that this would make it a possible complete and accurate list. Also, A & B don't have Horace in them but have Grace and E has Ian but I'm pretty sure he must receive a prize.

7. Correct - C
Again, not a fan of these questions but I think I choose (crossing fingers) the right one. I pick this answer because of the logic I had learned along the way. It was one of those question where what you put down on paper won't make any sense. I was just looking for something that seemed like to contrapositive and it just kind of made sense in my head. Weird, sorry I don't gave anything better, the answer just made sense.

Thanks!!

[c.r.passoni]

First thing I did was write out the diagram. I drew eight lines, labeling them 1-8. I put a dividing line between space 5 and 6 so that I remembered that the first five all receive prizes.

Then I wrote the rules and the contrapositives. For the sake of clarity, "<" means before, lowercase "p" means prize, lower case "np" means no prize. "-->" means a sufficient/necessary replationship
1. J < L
2. Hp --> Gp<Kp
2a. Contrapositive: K<G or Knp or Gnp --> Hnp (If Kramer is before Grace or Kramer gets no prize or Grace gets no prize, then Horace gets no prize). This is important for the last question.
3. I--> 1 or 5.
4. I < K

Next looking at the rules.
1. J cannot be last and L cannot be first. Also, L cannot win a prize unless J has also won a prize (Lp--> Jp)
2. Since Ian can only be 1 or 5, Ian has to win a prize.
3. Combining rules 2, 3, and 4, I see that if Horace wins a prize, then Grace and Kramer also win prizes. However, since Ian, who also wins a prize, must be before Kramer, Ian cannot be 5th (the last person to get a prize). Therefore If Horace wins a prize we know that Ian is first.
4. Combining Rule 2 with Inference 1, we see that if Horace wins a prize, L cannot win a prize. When Horace wins, we know that Ian, Horace, Grace, and Kramer all won prizes. This means only one more person can win a prize and L cannot win a prize unless J also wins a prize. Therefore, there is not enough room for both of them to win.

The questions:
#1: This is asking about who can be ranked 1-5. For these kinds of questions, go through and apply each rule to remove answers. Using Rule 1, we see that (E) cannot be the right answer because Lenore is 5th and Jezebel is not listed, meaning she is 6th, 7th, or 8th. Jezebel is not before Lenore, so this combination is not possible.

Using Rule 2 rules out (B). We see that Horace has won a prize. Consequently, Grace and Kramer should be in the list. However, we only see Grace.

Rule 3 means that (D) is wrong. Ian must be 1st or 5th. Here he is not in the list, meaning he is 6th, 7th, or 8th--none of which are acceptable.

Rule 4 says that Ian must be before Kramer. However, in answer choice (A), the opposite is true, making this answer incorrect.

Therefore, the correct answer is (C) by process of elimination.


#2) If Horace ranks 4th, then we know that Kramer and Grace get prizes. We also know that Ian must get a prize. The question tells us that Maria also receives a prize. Therefore, we know that Horace, Kramer, Grace, Maria, and Ian are the only people that will get prizes.

We know that Ian must be before Kramer, which means that Ian cannot be 5th. Consequently, Ian must be first. We also know that Grace must come before Kramer. Since Ian is first, the best Grace can do is second. This means that Kramer cannot be second. He must be 3rd, 4th, or 5th.

Looking at the answer choices, we see that (D) puts Kramer 2nd. We said that this is not possible, so it must be false, making it the right answer.

#3. For this question, use process of elimination. Using our previously stated inferences will make answering this question faster.

(A) Incorrect. According to Inference #3, If Horace wins a prize, Ian is first. Here, Horace wins a prize, but Ian is fifth. This is not possible.

(B) Incorrect. As we saw in the previous question, Kramer cannot be 2nd when Horace wins a prize. Horace has won a prize, so Ian is first. Grace must come before Kramer, also. The best Grace can do is 2nd, so Kramer can only be 4th or 5th.

(C) Incorrect. If Ian is 5th, then Kramer does not get a prize. If Kramer does not get a prize, then Horace cannot get a prize according to the contrapositive of rule 2. This means that only one other person cannot get a prize. If Jezebel does not get a prize, then neither can Lenore, since Jezebel must rank higher than Lenore. If this were true, not enough people would be awarded prizes. So it is wrong.

(D) Incorrect. If Horace is second, we know that Horace, Grace, Kramer, and Ian all won prizes. Only one more person can win a prize. If Lenore wins a prize, then Jezebel must win a prize. However, there is not enough room for both, so this cannot be true. This is also stated by our 4th inference: "If Horace wins a prize, Lenore cannot win a prize"

(E) Correct. Since none of the other options work, this must be the right one.

#4. Since this question gives you a condition, you should attempt to set it up.

Horace is 4th. This means that Ian is first and that Grace and Kramer win prizes. It also means that Lenore does not. We know nothing about Jezebel, Maria, or Frank). Additionally, we know that Grace cannot be 5th as she must come before Kramer. Therefore, she is 2nd or 3rd. Kramer cannot be second, because he must come before Grace. Therefore, he must be 3rd or 5th.

Essentially, our model looks like this:
1. I 2. G/J/M/F 3. G/J/M/F/K 4. H 5. J/M/F/K

Looking at our answer choices, we see that only (A) works, making it the correct answer.

#5. This is a global question. Using our inferences to find the correct answer and eliminate wrong answers is the best idea.

(A) Incorrect. If Ian is 1st, Kramer can be 2nd, 3rd, 4th, or 5th.

(B) Correct.Inference #3 states that if Horace wins a prize, then Ian is first. Since Horace ranks 3rd, he has won a prize. Therefore, Ian must be first.

(C) Incorrect. If Ian ranks 5th, Jezebel can rank anywhere between first and Forth.

(D) Incorrect. Think of the the contrapositive: If Horace does not receive a prize, then Lenore does. However, this is not necessarily true. Ian, Jezebel, Grace, Maria, and Kramer, for instance could be the winners. Consequently, neither Lenore nor Horace would get a prize. Remember: For global questions like this one, you only need one example to disprove the statement

(E) Incorrect. Like for (D), all you need to do is think of one example where this isn't the case. For instance, if Maria is 4th, there is no reason Horace cannot be 3rd. In this case, Ian would be first, Grace second, and Kramer 5th. This is an acceptable solution, but it proves (E) untrue.

#6. This is another global question. We want to use our inferences. You want to think about who has won a prize based on who hasn't.

(A) Incorrect. If Grace, Frank, and Lenore did not win prizes, then Ian, Horace, Maria, Jezebel, and Kramer did. If Horace won a prize, then Grace must win a prize. Therefore, this is wrong.

(B) Incorrect. If Grace, Jezebel, and Lenore did not win prizes, then Ian, Horace, Maria, Kramer and Frank did. Again, if Horace won a prize, Grace must also win a prize. Therefore this is wrong.

(C) Incorrect. If Horace, Jezebel, and Kramer did not win prizes, then Ian, Grace, Kramer, Lenore, and Frank did. This means that Lenore ranked higher than Jezebel. This violates a rule. Therefore it cannot be the correct answer.

(D) Correct. If Horace, Kramer and Maria are out. Ian, Jezebel, Lenore, Frank, and Grace are in. No rules are broken as Kramer comes after Ian and Lenore can come after Jezebel.

(E) Incorrect. If Horace, Ian, Kramer are out, then Ian cannot be ranked 1st or 5th. This violates a rule, making it incorrect.

#7. When substituting rules, your goal is to find a rule that produces the same results. The easier way of doing this is to search for the contrapositive. The other, and more frequent way, is to focus on the effects of the original rule and see which rule creates those same effects.

(A) Incorrect. According to the original rule, Kramer could rank higher than Grace as long has Horace didn't win a prize.

(B) Incorrect. This is an incorrect reversal of the original rule. Diagrammed it says G-K --> Hp. In addition it doesn't specify that if Horace wins a prize so must the other two.

(C) Correct. This is the contrapositive of the rule!

(D) Incorrect. This is an incorrect negation of the rule.

(E) Incorrect. This is the most appealing answer after the correct one. However, it does not specify that Grace must come before Kramer. The way in which Kramer's position was limited does not exclude the possibility that he ranks before Grace.

[ohthatpatrick]

Wow, great responses, everyone!

It was really difficult to pick a winner.

mkgraff's explanation was awesomely analytical, and sounded like how a very intelligent person would approach LSAT Games the first time he/she saw them.

amucino's and c.r.passoni's explanations were both more conducive to how most LSAT students learn/think about these games, so they work better as a "winning" explanation.

They really both deserve to win. Although c.r.passoni's explanation was more comprehensive (and had by far the BEST explanation of question 7), overall I thought amucino's was the most lucidly readable explanation. Plus, it had some infectious enthusiasm that reminds us that practicing Games should be fun.

So congratulations amucino!

Thanks to everyone for great contributions!