Logic Challenge #13 - Dolphins

[lsatlifer]

Hi Folks, Attached are my explanations for this game. Feedback welcome

[bouakedojo]

I'm not an LG expert at all, but I must say that I'm with you until the last question.

O may only be chosen if F and G are not chosen. But it isn't required to be chosen if F and G are chosen. You seem to have made that assumption in choosing B.

However, the next choice (C) is GPO meaning F and O are both chosen.

According it your contrapositive rule, F or G --> ~O.

Therefore, C is correct. (I think.. )

[lsatlifer]

I'm not an LG expert at all, but I must say that I'm with you until the last question.

O may only be chosen if F and G are not chosen. But it isn't required to be chosen if F and G are chosen. You seem to have made that assumption in choosing B.

However, the next choice (C) is GPO meaning F and O are both chosen.

According it your contrapositive rule, F or G --> ~O.

Therefore, C is correct. (I think.. )

Thanks for the follow-up! Admittedly, I'm a little perplexed about what you're referring to here. Are you suggesting that the diagram for the new rule is wrong or that the scenario I provided for the answer B is wrong? In either case, I don't follow because I'm not sure how it would be.

"ONLY IF" always introduces a necessary condition (except in the case of "if and only if", where it introduces both a sufficient and necessary condition. ex: A if and only if B: A ---> B and B ---> A). Thus, I can't see how the diagram fails.

As for the scenario I came up with for B:

The partial scenario tells us that F G and O are all OUT, so we're left with figuring out who else can be OUT (everyone else, by design, are IN).

In: __ __ __ __
Out: F G O __

F and G are both adults, and Rule 1 says that two adults must be selected (IN), so that only leaves H and I adults for selection. So now we have:

In: H I __ __
Out: F G O __

But since H is in , Rule 4 says N must be out. This is the only spot left for the OUT group:

In: H I __ __
Out: F G O N

So, all that's left for selection are M and P. And this is impossible to have, according to Rule 5 because we already have I. We can't have I M and P selected. This is why the partial OUT group given to us can't work, in my opinion. It has nothing to do with O F and G because these were already UNselected for us.

Now for C:
In: _ _ _ _
Out: G P N _

There are a couple scenarios that wouldn't violate the new rule or the remaining other rules. Notice how F and G are not always opposite of O (and sometimes they are):

In: F M I H
Out: G P N O

In: O M I H
Out: G P N F

The key to make this scenario work is to notice that O and F cannot be in the same group. There isn't enough room for them both in the OUT group. And if we put them both in the IN group, this violates the new rule, which is that O is chosen ONLY IF F AND G is not selected.

Hope this helps some.

[asood]

6. The question is unclear. if you say Orpheus performs only if Francis and Griseus do not perform (as in both together don't perform) then both A and E can be right, by taking the same combination in both - F I O M (i am using the first letter of the name only) and thus there are 2 right answers.

If you take the other case, that either of them should not perform for O to perform then anyways 4 options become invalid and then C is correct.

[lsatlifer]

6. The question is unclear. if you say Orpheus performs only if Francis and Griseus do not perform (as in both together don't perform) then both A and E can be right, by taking the same combination in both - F I O M (i am using the first letter of the name only) and thus there are 2 right answers.

If you take the other case, that either of them should not perform for O to perform then anyways 4 options become invalid and then C is correct.

With regard to you FIOM reference, You came up with 2 scenarios that definitely don't work, and you had to violate a rule in order to get there. You don't leave open the possibility that there is still a scenario that does work for both A and E, namely the ones that I posted:

A)
IN: HMPG
OUT: FION

E)
In:HGIP
Out: FOMN

If you're looking for something impossible, your best approach is to look for a way to make what you're given possible, so you can eliminate it. It's not enough to violate a rule in order to come up with a way to make it not work, it has to be impossible as is.

For A), you start off with:
IN:
Out: F I O

G has to be IN because of Rule 4 which prohibits H and N being selected together. If G were OUT, then H and N would be forced into selection. So we have:

IN: G H/N __ __
Out: F I O H/N

And this leaves M and P for selection:

IN: G H/N M P
Out: F I O H/N

For E), you start off with

In:
Out: F O M

Since M is out, H must be in (Rule 2). So we have:

In: H
Out: F O M

Since H is in, N must be out (Rule 4). So we have:

In: H
Out: F O M N

This leaves I G and P for selection:

In: H I G P
Out: F O M N


With regard to your alternative interpretation: Even with your interpretation, C is still possible:
In: O M I H
Out: G P N F and if it's possible, then it is, by definition not the choice we're looking for.

[timmacgougan]

It's true that O doesn't need to be in if F and G are out, but B is still the correct answer.

If FG are out, then HI are in (at least 2 adults needed). So N is out, and MP are in. Leaving:

In: HIMP
Out: FGON

But I and P can't both be in when M is in.

[bouakedojo]

It's true that O doesn't need to be in if F and G are out, but B is still the correct answer.

If FG are out, then HI are in (at least 2 adults needed). So N is out, and MP are in. Leaving:

In: HIMP
Out: FGON

But I and P can't both be in when M is in.

That makes sense now Tim. Thanks.

[bbirdwell]

Excellent discussion, all! For the record, (B) is the correct answer to #6 because it violates the m/p/i rule. LSATLIFER's original post regarding this game includes a sound strategy for this question, I believe:

Throw out the old rule and be sure to also rule out any deductions or inferences made with it. Then symbolize the new rule O ---> ~F & ~G, contra: F or G --> ~O, and go from there. Unfortunately there is no viable option other than plug and chug.

Start with (A) and follow the logic chain as far as it will DEFINITIVELY go -- that is, if you come to a point where the logic chain ends and all of the elements have still not been placed, STOP. Don't make an arbitrary decision and base your answer choice eliminations on that. If the scenario definitely violates a rule, choose it and get on with your life. If, up to the point of uncertainty, the scenario has not violated a rule, do not choose it and do not eliminate it, either. Move on to the next choice and evaluate it the same way.

For example, (A). If F and I are OUT, H and G must be IN. If H is IN, N is OUT. Therefore P and M are IN, which violates no rules.

When you get to (B), you'll see that if F and G are OUT, H and I must be IN. If H is IN, N is OUT. If N is out, M AND P must be IN. This violates a rule, thus the scenario can't be true and you need go no further.

Now, let's pretend (E) was actually the first choice, instead of (A). If O and M and N are all OUT, P must be IN. Also, if M is OUT, H must be IN. We now have:
IN: H p
OUT: o m n

Here the logic chain stops. We have our one necessary juvenile and we've violated no rules. The three remaining adults could potentially work in several ways. STOP HERE! This scenario does not explicitly violate any rules! Don't waste time exploring the options too deeply. Move on to another choice, where it is highly likely you will encounter a scenario that clearly and definitively violates a rule. If for some reason that does not happen, then you can re-visit this choice as necessary to find potential missed deductions.

Hope that helps. Keep up the good work!

^b

[zagreus77]

Liked the game. And my only problem with question 6 was that it didn't trade on the rule change , it was invalid because it moved N to the out group and thus created a conflict with the M P I rule. Overall though, a well thought out game.

[calgmathis]

Question 5 might have a wording issue with it. If Ignacio and Plato are not chosen than that ensures that H is not chosen due to it being impossible to choose Mambo. Additionally, Nelly can no longer be chosen because H is chosen. So while you know three of the Dolphins performing (which is the listen answer) you know that two additional dolphins cannot perform (M and N) so you have 5 known positions by the way the question is worded. I might be misreading and it would be good to know.

(I know I am a few years late on this)

Never mind, I see it says "other dolphins" this is what too much studying does to your mind.

[MylesB926]

To order the Rules in LG #13 I created THREE schemas. The Symbolic Logic (SL), an In-Out Chart (IOC), AND two Templates. The game math creates TWO possibles "worlds" or Templates, neither of which are too helpful in this game:

Template 1 = AAAJ and Template 2 = AAJJ. The Templates reflects Rule 1 "no more than 2 juveniles".

Symbolic Logic: The Given Rules. Below is a representation of the explicit game rules.

~M ->H
F&G -> ~0
N -> ~H
M -> I or P ~IP
O -> F or G

Below that, I added the contrapositives, and identified the most powerful logic chain.

N -> ~H -> M -> ~PO

IF N & M are included then Template 2, AND J is filled, hence ~PO. A powerful logic chain with relevance to Q4 [eliminate]/Q5[answer]. IF M & N are selected -> MNIG.

Q1. (A) No, can't have H & M. (B) No, cant have three juveniles "MOP". (C) No, H & M rule broke again. (D) Correct. (E) No, F & G requires O.

Q2. Any could be true or could not be true answer choice to a "must be true" question is wrong. (A) No, could be true [see Q1]. (B) No, [see Q1]. (C) No, FGOH, etc, is possible, consequently eliminate (D). (E) Correct, AA is required in both Templates, or process of elimination.

Q3. (A) Correct. The contrapositive of Rule 1 is ~H -> M activating rule Rule 4 I or P, can't be both.

Q4. Wrong answers to could be true questions cannot be true or must be false. (A) No. Without NH only 2 adults FG left but O removes one of them which is an impossible Template. (B) No. M or H must be selected. (C) The powerful logical chain from the beginning comes in handy here, N rules out O. If N -> M + O, too many Js. (D) No, tough. FGH & MN remain. M removes H forcing F&G which remove 0, no. N removes 0 too, no. FG removes O too, no. (E) Correct.

Q5. (B) Correct. Again, a contrapositive of the initial powerful logic chain is P -> ~N therefore, PO -> ~MN and M -> H.

Q6. (B) Correct. A painful tongue twister. The new rule is O -> ~FG. The question asks for a list of dolphins who could NOT be selected EXCEPT. In other words, which list of dolphins could not all be not selected, or, which list of dolphins not selected must be false. The new rule directly contradicts option (B). O performs only if FG don't so ~FG -> O therefore ~FGO is impossible.

[JamesB833]

With regard to you FIOM reference, You came up with 2 scenarios that definitely don't work, and you had to violate a rule in order to get there.