Logic Game Challenge #38: The Mixed Quartet Game

[wingedfeetxc]

Our latest Logic Game Challenge, The Mixed Quartet Game, is live: http://www.manhattanlsat.com/logic-games-practice.cfm. Post your answer explanations (or questions) questions here. Good luck!

[rwayersiii]

[rwayersiii]

Sorry, those picture don't look too good. I have my explanation for this game in a pdf but I am not sure how to upload it. The pictures are the best I can do for now.

[khaleesiwantstodolaw]

I have the same problem. I have my explanations ready in a pdf document but don't have the option to attach documents.

[khaleesiwantstodolaw]

I couldn't find a way to attach documents. So, I'm sharing a URL that opens up the pdf copy of my explanations. https://www.dropbox.com/s/8gsj36h34vsuhxo/Logic%20Game%20Challenge%2038%20-%20khaleesiwantstodolaw.pdf

[GburtR]

See link
https://docs.google.com/file/d/0B8ll_1k ... sp=sharing

[Mingyuns]

I encountered a dilemma when I first tackled this one. Later, I figured it out that I misrepresent one condition and by correcting that, it becomes much easier.

Four musicians: F, H, J, K;
Six instruments: o, p, r, t, v, x;

Since each of the musicians plays one or more of the instruments, and each instrument by at least one of the musicians, we choose musicians as our base:

1. J is the only musician who plays exactly one instrument: J=1, F>=2, H>=2, K>=2;
2. The musician who plays the most instruments plays exactly four instruments: J=1, 2<=F, H, K<=4; and one of F, H, J must be 4;
3. F and H do not play and of the same instruments: F=/= H;
4. F is the only member of the ensemble who plays the t: H, J, K, does not play t;
5. Any musician who plays r or p plays both instruments: r ---> p; p ---> r; with their contraceptive conditions: ~p ---> ~r; ~r ---> ~p, we know that r and p must be played together by one musician; Therefore, J only plays one instrument, so J cannot play r or p;

Thus, the final representative figure is as below:

_............._.............x.............._

_ ............._.............x............._

✡.............✡.............x.............✡

✡(t).........✡.............✡(o/v/x).....✡

F.............H.............J.............K

.............~t.............~t.............~t

.............................~p

.............................~r

Question 1:
(Condition 1). Nothing to be deleted;
(Condition 2). Delete B;
(Condition 3). Nothing to be deleted;
(Condition 4). Delete A;
(Condition 5). Delete C;
Only D and E are left. We must not forget that "each instrument by at least one of the musicians", and then we can delete E.
So the correct answer is D.

Question 2:
First of all, "could be true EXCEPT" means "must be false".
The additional conditions tells that no one else plays any instrument that J plays. Since J=o/v/x, and J only plays one instrument, we know that all three other musicians should play all other five instruments, other than the one J plays. By using the total of 5, and F=/= H, we know that only K can play 4 instruments. (Actually o/v/x is exchangeable, we can assume J=o to tackle this question if needed)
(A) F>H: F=3, H=2, J=1 and K=4. No other assignments have interferences. Sounds good;
(B) F>K: F=3, K=2, J=1 and H=4. WRONG: only K can play 4;
(C) F and K shares 2 instruments: since K=4, and K=/= t, so F should play 3; F=/=H, so H could play 2; (remember the total is 5 now);
(D) H, K both plays x: then J=o/v, but no other assignments have interferences. Sounds good;
(E) K plays o&v: then J=x, but no other assignments have interferences. Sounds good.
So the correct answer is B.

Question 3:
The additional condition tells that each of four musicians plays a different number of instruments, which means that four of them play 1, 2, 3, 4, respectively.
We already know J=1 and the maximum is 4. If we could know anyone plays 2 or 3, it would be very helpful and determine all four of them.
(A) J=1, plus K=4: we could not determine F/H for â…”;
(B) J=1, plus J, H, K all play o:
(C) J=1, plus H = p&r only: J=1, H=2, Since F=/=H, the maximum of F is 4. We cannot determine F/K to be 4;
(D) J=1, plus K=3: then F/H are â…”. But could we determine which one is 2 and which is 3? We only know F plays t, and H does not play t. There is no way for use to know who plays 2 and who plays 3;
(E) J=1, plus F=3: Since F=/=H, and the total is 6, so H cannot be 4. Then K must be 4, and H plays 2.
So the correct answer is E.

Question 4:
First of all, "could be false EXCEPT" means "must be true".
The additional condition is F plays p&o, which means that F plays p,r, t&o, with the maximum instruments played by one musician.
Since F=/=H, and H>=2, so H must play v&x. So the correct answer is A.

Question 5:
(A) H plays the same number of instruments as J and K combined. It indicates two options:
(1) H=4, and since J=1, K=3, which makes F=2. Sounds good.
(2) H=3, and since J=1, K=2, which makes F=4. WRONG: H+F=7>6.
(B) o,x&v are each played by exactly two of the musicians: for example: J=o, K=x,v,p&r, F=t,x&v, H=o,p&r. Sounds good.
(C) No other musician plays any of the same instruments as F: for example: F=p,r,t&o, H=v&x, J=o, K=p&r. Sounds good.
(D) No other musician plays any of the same instruments as K: since 2<=K<=4, and K=/=t, we can know that K plays at least 2 out of (o, p, r, v, x). There are two options:
(1) K=4, since H=/=t, K=/=t, H>=2, so H+K+t>=7. Wrong;
(2) F/H=4. Then F+H=6. Then there must at least one same instruments F/H plays as K plays. WRONG.
(E) Only one of the musicians plays p: for example: F=o,t,v&x, J=p&r, J=x, K=o&v. Sounds good.
So the correct answer is D.

Question 6:
If one of the instruments is removed, the total number of the instruments is 5. Since F=/=H and the each F/H at least plays 2 instruments, so neither F or H can play 4. Since J=1, so only K could play 4. We can assume to remove o. Since K=/=t, so K=p,r,v&x.
(A) F/H=2/3, J=1 and K=4. Sounds good;
(B) K plays p&r: CORRECT as shown in the inferences.
(C) Three of the musicians play violin: K=p,r,v&x, J=v, F=t&v, H=p&r. Sounds good.
(D) K plays exactly one more instrument than F: K=p,r,v&x, F=3, H=2, J=1. No other assignments have interferences. Sounds good.
(E) J is the only musician that does not play r: WRONG since F=/=H.
So the correct answer is B.

[ohthatpatrick]

Hey, everybody.

Thanks to everyone for a truly impressive set of submissions to the explanation contest! It was incredibly hard to pick a winner this time around, since you all provided really effective explanations.

I don't like to pick based on length, since sometimes the most effective explanations are shorter/sweeter.

And I don't like to pick based on exhaustive up-front deductions, because in reality when we play a game a tough game like this we often only have a partial sense of what's going on when we get into it (I loved rwayersiii's sentiment during the setup of "There are other hidden inferences, but this is all we need for now").

But I gotta go with Gregory.Rudin for the overall winner. I thought he provided the best balance of realistic up-front insight and easy-to-read/digest explanations, even if his diagram looks nothing like Manhattan LSAT's typical open board.

I'm sorry there can only be one winner this time, but congratulations Gregory!

[csunnerberg13]

Where can I find a clear set-up and explanation for this game? These explanations are really not that helpful if you're totally lost in the set up. Is there a slide or pdf somewhere?