I posted my Grouping: Selection / In-Out Logic Game on the blog a month ago, but that one was "Undefined," meaning that we didn't know how many variables were in (voted for) and how many were out (voted against).

The game I've written for this week, on the other hand, is "Defined," which means that we know exactly how many variables are selected and how many are not selected.

Please post your thoughts and questions in the comments!

***

Here's this week's Logic Game:

From among nine topics, a student will select six to debate at a tournament. The topics are organized into three categories. Of the topics, three-A, B, and E-are on politics, three-H, L, and O-are on religion, and three-S, T, and Y-are on war. At least one topic will be selected from each category. The student selects the topics according to the following conditions:

(A) A, B, E, H, L, O

(B) A, B, E, H, L, T

(C) A, B, E, H, O, T

(D) A, B, E, H, S, Y

(E) A, B, H, S, T, Y

2. If exactly one of the topics on religion is selected, then which one of the following is a complete and accurate list of the other topics that must also be selected?

(A) A, B, E, T

(B) A, B, E, H, Y

(C) A, B, L, T, Y

(D) A, B, E, S, T

(E) A, B, E, T, Y

3. Which one of the following must be true?

(A) A is selected.

(B) E is selected.

(C) T is selected.

(D) Of at least one of the three categories of topics, exactly two topics are selected.

(E) Of at least one of the three categories of topics, exactly three topics are selected.

4. If exactly two topics from each category are selected, then which one of the following must be true?

(A) B is selected.

(B) H is selected.

(C) Y is selected.

(D) L is not selected.

(E) T is not selected.

5. Each one of the following is a pair of topics that could be among the topics selected EXCEPT:

(A) A, Y

(B) B, H

(C) B, O

(D) S, T

(E) S, Y

6. Each of the following, if known, would fully determine the selection of the six topics EXCEPT:

(A) B and E are not selected.

(B) B and T are not selected.

(C) E and O are not selected.

(D) L and T are not selected.

(E) O and Y are not selected.

The text below contains the answers to the above Logic Game.

1. B

2. E

3. D

4. C

5. D

6. D

***

Can't figure out how to do the game? Not to worry - leave a comment!

See my tips on how to solve this game in Logic Game | Grouping: Selection Defined Diagram | Explanation.

***

For some LSAC-written Logic Games similar to this one, check out:

PrepTest 24, Section 4, Game 4 (page 213 in 10 More)

PrepTest 33, Section 4, Game 3 (page 178 in Next 10)

PrepTest 40, Section 2, Game 2

Photo by ennuiislife / CC BY-NC 2.0

The game I've written for this week, on the other hand, is "Defined," which means that we know exactly how many variables are selected and how many are not selected.

Please post your thoughts and questions in the comments!

***

Here's this week's Logic Game:

From among nine topics, a student will select six to debate at a tournament. The topics are organized into three categories. Of the topics, three-A, B, and E-are on politics, three-H, L, and O-are on religion, and three-S, T, and Y-are on war. At least one topic will be selected from each category. The student selects the topics according to the following conditions:

If S is selected, neither E nor L is selected.1. Which one of the following could be a complete and accurate list of the topics that the student selects?

If Y is not selected, L is selected.

At least one topic on war will not be selected.

(A) A, B, E, H, L, O

(B) A, B, E, H, L, T

(C) A, B, E, H, O, T

(D) A, B, E, H, S, Y

(E) A, B, H, S, T, Y

2. If exactly one of the topics on religion is selected, then which one of the following is a complete and accurate list of the other topics that must also be selected?

(A) A, B, E, T

(B) A, B, E, H, Y

(C) A, B, L, T, Y

(D) A, B, E, S, T

(E) A, B, E, T, Y

3. Which one of the following must be true?

(A) A is selected.

(B) E is selected.

(C) T is selected.

(D) Of at least one of the three categories of topics, exactly two topics are selected.

(E) Of at least one of the three categories of topics, exactly three topics are selected.

4. If exactly two topics from each category are selected, then which one of the following must be true?

(A) B is selected.

(B) H is selected.

(C) Y is selected.

(D) L is not selected.

(E) T is not selected.

5. Each one of the following is a pair of topics that could be among the topics selected EXCEPT:

(A) A, Y

(B) B, H

(C) B, O

(D) S, T

(E) S, Y

6. Each of the following, if known, would fully determine the selection of the six topics EXCEPT:

(A) B and E are not selected.

(B) B and T are not selected.

(C) E and O are not selected.

(D) L and T are not selected.

(E) O and Y are not selected.

The text below contains the answers to the above Logic Game.

1. B

2. E

3. D

4. C

5. D

6. D

***

Can't figure out how to do the game? Not to worry - leave a comment!

See my tips on how to solve this game in Logic Game | Grouping: Selection Defined Diagram | Explanation.

***

For some LSAC-written Logic Games similar to this one, check out:

PrepTest 24, Section 4, Game 4 (page 213 in 10 More)

PrepTest 33, Section 4, Game 3 (page 178 in Next 10)

PrepTest 40, Section 2, Game 2

Photo by ennuiislife / CC BY-NC 2.0

I hate to be a real stickler because I made a stupid comment about your last game, but I really think the answer to 6 is E.

ReplyDeleteWith choice D, having L and T out, you could either have ABHOSY with LTE out, or you could have ABEHOY with LTS out.

With choice E, having O and Y out, you know you need to have L in (Ynot -> L), which means S is out. Having OYS out means the only option is to have ABEHLT as the selected group.

Please tell me I'm right here... I need some good news!

Benjamin-

ReplyDeleteI think you might have misread the question? But your logic is right on...which is what really matters. Don't let those "excepts" trip you up and you will be unstoppable!

#6 asks for a situation where you AREN'T going to get the full solution (you aren't going to know all 6 of the topics picked) with the condition given in the answer choice (thus, the rest of the answer choices will force a complete solution...and be incorrect).

As you correctly noted, D still leaves you with two options: ABHOSY or ABEHOY. So you don't know the complete solution, and thus D is the right answer.

E, as you correctly stated, leads to a situation where you can only have ABEHLT, which IS a complete solution--and thus is not the right answer.

I'm sure you'll see as you work through A-C that they also give you complete solutions, and thus are incorrect.

:) Hope that helps.

Yeah, I'm retarded. My bad.

ReplyDeleteIs it:

ReplyDelete1. B

2. B

3. D

4. B

5. D

6. A

?

ok..I see why 2 is E and 4 is C and 6 is E...

ReplyDeleteI need to be more detail oriented but keep my love for games.. They're advanced brain twisters!

Amy,

ReplyDeleteSteve, the blog's author, includes the answers at the end of the post, but he does so using a white font. That's why you have to highlight them by moving your mouse to some point before them, such as at the end of the sentence about highlighting, and then click and drag over them to see them. In the event that that doesn't work for you, here are the answers: BEDCDD. Six is not E, btw, for the reasons described above by Ashley.

--Owen

Re: Question 4. Aren't answers C and D essentially the saying the same thing? It seems like if it must be true that Y is selected, then it also must be true that L is not selected. So how do you know the answer is C and not D?

ReplyDeleteTo put it a different way, I don't understand how there could be an interpretation of the rule "If Y is not selected, L is selected" that would allow for L to be selected if Y is selected. Or is it that L could be selected if Y is selected, but L definitely is selected if Y is selected?

Thanks for the fantastic puzzle and please keep them coming!

The last sentence of that comment should read "Or is it that L could be selected if Y is selected, but L definitely is selected if Y is NOT selected"

ReplyDeleteThanks!

Sara, I believe there was a post about this a few weeks ago.

ReplyDeleteBasically, the rule says: not Y -> L

the contrapositive: not L ->Y

What this means on a fundamental level is that there is always going to be one of L or Y. However, as you started to reason out, it could very well be that BOTH L and Y are selected without breaking the rule.

That being said, for #4 it is impossible to pick six with the condition given that leaves Y out, because if you left Y out you have to put L in (at least one of them has to be selected), but you also have to put the other two war topics in and you'd be left with a selection that includes both S and L, which would violate Rule 1.

For what it's worth you can plug L in (A B H L T Y for example) with no trouble as long as S is excluded.

Hope this helps.

Hi Sara,

ReplyDeleteI think the problem you are describing with "If Y is not selected, then L must be selected" and whether it then follows that "If Y is seleced then L cannot be selected" is called a mistaken reversal. I think what actually follows is that "Not L -> Y". It seems strange but you can reason this out by writing down the possibilities: YL, NotY L, NotL Y, Not L Not Y. The last choice, Not L Not Y demonstrates itself as impossible given the rule Not Y -> L. If you don't have Y then you have L, if you don't have L then you must have Y because if you didn't you would have L.

I'm not sure how others might approach question 4, but, assuming there is only one correct answer choice, the reason it has to be C, or "Y is selected", is because of the impossibility of not selecting Y. You must have exactly two choices from each group. From the war group's three choices there are 6 possible pairs: ST SY and TY. Of these ST is impossible because it pits the two global rules against each other. ST means there is no Y, if there is no Y then there MUST be an L, but because there is S, then there MUST NOT be L. So, that leaves two possible choices given the rules: SY and TY, both of which include Y. Therefore, Y must be one of the choices and therefore C must be the answer.

--Owen

I liked this a game a lot.

ReplyDeleteQuestions 4 and 6 confused me.

Why isnt the answer to #4 choice B?

As for #6, why is answer B wrong?

Maybe I'm on a 'B' kick.

But, it seems to me that B & T arent the most telling variables. Please enlighten me.

For 6, when you take b & t out, you're left with AE, HLO, SY. If you have S, you can't have E or L which means you don't have six variables. Therefore you must have Y as you have to have one from each category. In order to have six, you must have the rest of them, therefore taking B & T out means you get AEHLOY. You CAN have Y and L as the rule only states that if there is not a Y, then L must be chosen, not vice versa.

ReplyDeleteI understand the solution to #6, but does anyone have any suggestions as far as how to tackle a question like this QUICKLY? Trial and error is obviously too time-consuming, but I don't have a standard methodology for doing these quickly. Thanks!

ReplyDeleteIt took me some time to figure this out, but the easiest way to think about #6 is this. Since you know what the six topics selected will be if you can eliminate 3 and the answer choices already eliminate 2 for you, you can try to see if each choice will eliminate another topic. Also, since we know what topics must be selected if S is selected, if any of the choices do not match the "S-in" template, then S must be excluded --> therefore you eliminate 3 and know the full selection.

ReplyDeleteI hope that makes sense..

Just to finish my thought of the previous post --

ReplyDeleteA, B, C and E all do not match the "S-in" template and so must eliminate S. So D must be the answer!

N.B.

If "S-in" then ABHOSY selected

If ABHOSY not selected then "S-out" (contrapositive)

Natalie,

ReplyDeleteFrom the third condition we know that we can only select at most 2 War variables.

The first condition is: S -> ~E and ~L

Therefore S and E cannot be selected together and S and L cannot be selected together.

So, S -> ~E and S -> ~L

The second condition is ~Y -> L and the contrapositive is ~L -> Y.

Therefore if S is selected, then Y must be selected:

S -> ~L -> Y means that S -> Y

If only 2 war variables can be selected, then S and T cannot be selected together, because that would violate the rule that S -> Y.

Hope that made sense and helped!

A.D Young --

ReplyDeleteIt looks like C cannot be correct in choice 1 because there is no Y or L. Y or L or both must be present for it to be a complete and accurate list due to "If Y is not selected, L is selected." -- not Y -> L, Not L -> Y, which says that we must always have Y or L. Answer choice C does not have Y or L present, making it incorrect.

That is how I read it at least! Hope that helps a bit!

In response to "how to do #6 quickly"... My instinct in #6 was to try choice D first. How so? Knowing that A, B, H and O have no restrictions imposed on them by the rules, it makes sense that excluding just L and T (i.e., none of ABHO) would not likely provide sufficient information to fully determine the selection. On the other hand, choices A, B, C and E all excluded one of ABHO.

ReplyDeleteI want to ask about question #1.

ReplyDeleteI am torn between answer choice b and c

(B) A, B, E, H, L, T

(C) A, B, E, H, O, T

From these 2 choices, both L and O fit the criteria. So why is the correct answer b and not c?

sugarmouse

ReplyDeleteif you make the contrapositive diagram, you get a result that is

not y -> L -> not S

which means that if you dont have y included, you need L in there

Can someone please explain question #5? Why would you not be able to have S, T as a pair? Couldn't you have AB, HO, and ST? I don't think that violates any of the rules? Thanks!

ReplyDeleteHi! May I ask why C is incorrect in Q1?

ReplyDeleteThank you!

@Live, C is not correct because if L is not selected then Y is selected.

DeleteThis comment has been removed by the author.

ReplyDeleteI'm a bit confused on 4 as well. Couldn't it be true that A B H O S T are selected, meaning D would be the correct answer?

ReplyDeleteFor question 4 I chose D although the "correct" answer is C and I'm confused because for me they seem to be the same answer...~y means L and ~L means y...Can someone explain? Also I think I'm going to pass on doing anything other than LSAC games unless someone can convince me that doing hypothetical games is beneficial...I mean it would be if the course offered full explanations but this is the second made game I've attempted and then after hitting my head against the wall to not get clarity with each question given a thorough explanation just seems like a waste of time when there are so many other questions and tests to go through..Thoughts and feedback? I would however be interested in something like this if the course provided full explanations...

ReplyDeleteI would really appreciate an explination on #4. I know I'm doing something wrong

ReplyDeleteThank you. I realized a lot of things using this. Thank you for always writing good things.

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