I've enjoyed forcing you to think about a spaceship with 8 monkeys and 7 Greek deities in a power struggle as you completed my first two LSAT Logic Games.However, it's time to get back to the real world, at least for a little while, so the Logic Game I've written for this week has a more standard topic.
Please post your thoughts and questions in the comments!
***
Here's this week's Logic Game:
On Wednesday, a legislator remembers that she must vote on seven bills-defense, environment, free trade, gun control, health care, immigration, and judicial activism-by the end of the week. Because the legislator wants to align herself with a major political party, she will vote on the seven bills in accordance with the following conditions:
She votes for the gun control bill only if she votes against the environment bill.1. Which one of the following could be a complete and accurate list of the bills the legislator votes against?
Unless she votes against the judicial activism bill, she will vote for the immigration bill.
She will vote for either the environment bill, the judicial activism bill, or both.
She votes for the gun control bill if she votes for both the health care bill and the defense bill.
(A) free trade, gun control, immigration, judicial activism
(B) defense, free trade, gun control, health care, immigration
(C) free trade, health care, immigration, judicial activism
(D) environment, gun control, health care, judicial activism
(E) defense, environment, gun control, health care
2. If the legislator votes against the judicial activism bill, then which one of the following CANNOT be true?
(A) She votes against both the defense bill and the gun control bill.
(B) She votes against both the gun control bill and the health care bill.
(C) She votes for both the health care bill and the defense bill.
(D) She votes for both the health care bill and the environment bill.
(E) She votes for both the environment bill and the free trade bill.
3. Which one of the following CANNOT be true?
(A) The legislator votes for neither the gun control bill nor the immigration bill.
(B) The legislator votes for neither the environment bill nor the immigration bill.
(C) The legislator votes for neither the gun control bill nor the health care bill.
(D) The legislator votes for neither the health care bill nor the free trade bill.
(E) The legislator votes for neither the free trade bill nor the immigration bill.
4. If the legislator votes against the immigration bill, then which one of the following is the minimum number of the seven bills she must also vote against?
(A) one
(B) two
(C) three
(D) four
(E) five
5. If the legislator votes for the gun control bill, then which one of the following must be true?
(A) She votes for the health care bill or the defense bill.
(B) She votes against the health care bill or the defense bill.
(C) She votes against the judicial activism bill.
(D) She votes for the immigration bill.
(E) She votes against the immigration bill.
6. If the legislator votes against the judicial activism bill, then each of the following could be true EXCEPT:
(A) She votes against the health care bill and the defense bill.
(B) She votes for the health care bill and the defense bill.
(C) She votes against the health care bill and the gun control bill.
(D) She votes against the free trade bill and the gun control bill.
(E) She votes for the environment bill and the free trade bill.
7. Suppose the condition is added that if the legislator votes for the free trade bill, then she will vote against the judicial activism bill. If all other conditions remain in effect, then each of the following must be true EXCEPT:
(A) If she votes for the free trade bill, then she votes against the gun control bill.
(B) If she votes against the environment bill, then she also votes against the free trade bill.
(C) If she votes against the immigration bill, then she votes for the free trade bill.
(D) If she votes against the judicial activism bill, then she also votes against the gun control bill.
(E) If she votes against the immigration bill, then she also votes against at least three other bills.
The text below contains the answers to the above Logic Game.
1. E
2. C
3. B
4. C
5. D
6. B
7. C
***
See my tips on how to solve this game in Logic Games Selection | In-Out Diagram Explanation.
***
If you want to try several LSAC-written Logic Games that are similar to the one above, check out the first category of games in 7 LSAT Logic Games That Repeated on Future PrepTests.
The 3rd game listed in 10 Hardest Logic Games is a similar Grouping: Selection / In-Out game as well.
Photo by rexandsharkey / CC BY 2.0 (from the Schoolhouse Rock song "I'm Just a Bill")"
Hi, I have a question about #4. Why is the answer C instead of D? If she votes against Immigration, doesn't she also have to vote against J, G, and one of H or D?
ReplyDeleteYup.
Deletethe key for quest 4 is " minimum number of the seven bills she must ALSO vote against?" meaning besides that one in the question "I" how many others are there. Yes there are 4 in total with the inclusion of I, but the answer is 3 other ones she must vote against
DeleteIf I is out, then J, G and at least one of H/D (but not necessarily both) have to be out. E is in. I originally misread it as 4 additional myself, until I realize I accidentally counted H and D together.
DeleteNot sure if this helps, but that was my experience.
Steve--
ReplyDeleteI finished the game and have two questions:
1. How common is it to see a double negative in a logic game? I have never seen something like "unless not J then I," though of course "Not A unless B" is somewhat common (from what I've seen).
2. How did you arrive at C)three for question 4? From what I can tell:
- Not/against I forces not/against J
- Because one of J/E must be always in the "for" bin, E must now be in the "for" bin.
- Because of rule 1 (G-->~E), putting E in the "for" bin forces G and at least one of H/D into the "Against" bin.
And that makes at least FOUR total, which is answer D.
Thanks!
In response to the first post and part two of the post above, the question asks the minimum number of bills she must ALSO vote against. So you don't coun't Immmigration. If she votes against I, then she must ALSO vote against J, G and either H or D. The key is the word also. She must ALSO vote against at least three others. There is no mention of TOTAL bills voted against. The devil is in the details, as is so often the case on the LSAT!
ReplyDeleteVery enjoyable, as the other games have been :)
ReplyDeleteI had problems with the entire problem set. Could someone break down each condition? Once I understand th rules, I can tackle the problems again with better understanding. Thanks!!!
ReplyDeleteSteve--
ReplyDeleteNice game, BUT:
Q1: Nowhere do you mention a rule that restricts the legislator from voting against free trade, so answer B could incude free trade in the list.
Q7: The correct answer (supposedly C) includes the actual new rule, introduced by the question. I have not see this done on an actual exam, plus it is true, although the mandatory rule is turned into a tentative. If the legislator votes for free trade, she must vote against judicial, which means she will vote against immigration, too.
Please elaborate.
Q1 asks for a complete and accurate list. We know F (free trade) is a 'floating' or unrestricted variable.
DeleteAnswer choice B is incorrect because it asks what the legislator votes against. If she votes against I (immigration) she MUST also vote against J (Judicial Activism).
Q7 is a must be true except. A, B test your application of this new condition to the previously established conditions. Namely the 1st, 2nd and 3rd rules combined with the new condition. Choice D just takes the 1st and 3rd rules and tests them. Choice E is a regurgitation of question 4.
Hope that helps! I know Steve already posted a breakdown prior to my post.
These are all CONDITIONAL rules. It is important to remember that these "if" conditions are UNIDIRECTIONAL (that's why they're written with an arrow that points in one direction).
DeleteFor Q7, remember the diagram is (NotI)--> (NotJ)--> E--> (NotG)--> [and any of the following three possibilities: (NotH + NotD) or (NotH + D) or (H + NotD)]. The new rule can then be represented by [F--> NotJ]. To get the contrapositive of the new rule, you flip and negate it: [J--> NotF]. See the diagrams he links to at the bottom of the page for the complete contrapositive diagram. On to the answer choices:
Option A can be rewritten as: F--> NotG. Looking back at the diagram this is true.
Option B can be rewritten as: NotE-->NotF. Looking back at the contrapositive diagram, this is true.
Option C can be rewritten as: NotI-->F. This does NOT have to be true. There are no arrows pointing from a NotI to a positive F on the diagram. The new rule (F--> NotJ) begins at F; it does not affect I. Voting against J does not guarantee that I will be voted against. For conditionals, remember to always move forward with the arrow--not against.
Option D can be rewritten as: NotJ-->NotG. This is true.
Option E can be rewritten as NotI--> at least 3 OTHER Not-votes. This is true because NotI--> NotJ--> NotG--> [and at LEAST a NotH or NotD, but both NotH and NotD are possible]. The number three comes from NotJ, NotG, and either NotH, NotD, or both (the word OTHER (other than NotI is purposeful).
This is the way I understand it. Don't let contrapositives trick you into thinking that conditionals (i.e. "If..., then...) are bidirectional. The arrow symbols are chosen for a reason; don't fall into the trick of going backward and thinking that conditional rules are unconditional.
Smoked it, Mr. Schwartz. In/Out game. Money for 2 sessions well spent. Thanks, Steve.
ReplyDeleteRe: Ina's post
ReplyDeleteq1: One of the problems with B is that it would involve the legislator (a woman! yaaaay Steve!) voting FOR only EJ. This violates rule #2 (which diagrams as notI -> notJ, the converse of which is J -> I.) It helped me to write out what she was voting FOR next to the answer choice for the last few answers.
q2: Lots of logic games introduce a new rule in the very last question (or suspend an earlier rule). I am not 100% sure I understand your question, but I think that your understanding of rule #2 is flipped (it's that if she votes against I she will also need to vote against J, not the other way around). In any case, C doesn't have to be true, because if she votes against the immigration bill, she could also vote for the free trade bill (since J would already be a bill that wasn't selected when she voted against the immigration bill). However, the rest of the conditions must be true, assuming that you use the new rule, and a lot of the questions test your understanding of the "either E or J or both" condition. Take A, for example. If she votes against the free trade bill, then we know that she can't vote for J--that's right there in the new rule. However, we know that this means that E must be included. But if E is included, we know she can't vote for G (the contrapositive of the first rule). So A must be true, and given the "EXCEPT", we know it can't be the right answer.
Ok, I'm stumped on #1. I put C. Free trade can stand alone, health care can stand alone (it is not necessary that G is out as well.. -G-->-H ) Immigration, and judicial activism.
ReplyDeleteWhat did I miss here?????? :>(
I got them all right but Q1. How can it be E? The first rule says that if she votes against the Enviromental Bill then she can vote for the G bill. Can someone explain? Thanks!
ReplyDeleteQ1: read the question carefully--the choices are lists of bills she votes AGAINST
ReplyDeleteHa ha. I did the same as the previous person on Aug 24. Got them all right except Q1; didn't carefully read the question!!
ReplyDeleteQ1: can someone explain how rule 2 gets diagrammed not I -> not J
ReplyDeletethe "unless" makes "not J" the necessary condition thus giving I -> not J.
Am I completely off the mark on this? I don't see E beign the right answer - especially with the legislatore voting for FIJ which would be against my diagramming of rule 2.
the sufficient is negated in an "unless", thus giving the not I-> not J. (J->I)
ReplyDeleteE is the right answer when you fix the mistake.
Hey there,
DeleteThe unless is in front of J, so wouldn't it be "if not J" and this would be the sufficient modeling the "if-then"?... "if not J then I" since the question does not say it won't vote for I?
Q5: Because she must vote for Environment or Judicial Activism, or both, AND she cannot vote for Gun Control and Immigration at the same time, this question is insolvable.
ReplyDeleteIf she votes for Gun Control, then she does not vote for Environment. If she does not vote for E, then she MUST vote for J. 'D' says she votes for Immigration. This does COULD BE TRUE, but needn't be true to guarantee that the E v J condition is met. Further, when she votes for G, she can only vote for I, if she ALSO votes for J. Again, J could be true, but needn't be.
What does everyone think?
I completed the Power Score Bible chapter on Grouping Games and am finding these remarkably challenging.
ReplyDeleteSame for this game. I'm trying to determine if I need to diagram contrapositives or not.
I'm struggle with drawing inferences once I hit Rule #3.
Could someone layout the rules and associated inferences?
Thanks!
Are the answers for this game provided? Please excuse me if this is an obvious question; I'm new to this blog. Many thanks, SB
ReplyDeleteHi SB,
ReplyDeleteI included the answers at the end of the blog post.
Question one seems fairly ambiguous. What is the likelihood of running into this on a test? I couldn't tell is it was asking what are the bills it was simply possible to vote against, or if I were to assume she did vote against all of the listed bills, and thus select which list could be correct if she did so given the conditions(hope that made sense?). Please advise.
ReplyDeleteIt's not ambiguous at all. This is a fairly common question. The likelihood is high enough. See the first question of PrepTest 33 (December 2000), Game 2, for something similar.
ReplyDeleteIt's the latter (second interpretation you mentioned).
for question 1, I am confused. Doesn't the third rule NOT E --> J disprove the answer (E). If she votes against E how does she also vote against J?
ReplyDeleteThanks!
Choice E does not contain J in its list.
ReplyDeleteI am stumped by question one as well. Rule #1 says "She votes for the gun control bill only if she votes against the environment bill."
ReplyDeleteDoesn't this mean those two bills can never be voted on in the same way? Answer E contains both gun control and environment, but since these two can't have the same outcome, how can answer E be a list of bills she votes against?
Appreciate any help!
Please read previous comments and my explanation for the game.
ReplyDeleteI read both multiple times before initially posting and am still confused :(
ReplyDeleteIf she votes for G, then she doesn't vote for E.
ReplyDeleteTherefore, she cannot vote for both. She can vote for one, the other, or neither (meaning she CAN vote against both).
To say otherwise would be to confuse necessary and sufficient conditions.
Looking at my diagram in the explanation, keep in mind that you can only follow an arrow in the direction it points. You can't go backwards.
I think this game is most easily solved by making three separate scenarios: one with E in, another with J in, and another with both E and J in.
ReplyDeleteHere's the setup:
J out/E in:
In: E
Out: J,G,D/H
Remaining: F,I,D/H
J in/E out:
In: J,I,
Out: E
Remaining: D,H,G,F
J in/E in:
In: E, J, I
Out: G, D/H
Remaining: F, D/H
Using this setup, I breezed through the questions on this game, which, incidentally, strongly reminded me of the Birds game on PT33.
Maybe I am having a moment, but like others that have posted comments - question 1 has thrown me for a loop. I thought for sure that the answer was B, not E.
ReplyDeleteIn trying to grasp the concept of why E is the most correct answer - it is because of rule 1: "she votes for the gun control bill only if she votes against the environment bill" doesn't work when reversed??
Sorry.. about brain-dead at this hour but frustrated I got this wrong!
I got thrown off with the first rule because for whatever reason I incorrectly jotted it down as:
ReplyDelete-E > G (orig.)
-G > E (contr.)
She could have voted for at least one of the two, or for both (which rules out voting against both).
After reading the comments, I realized my error and it should correctly be:
G > -E
E > -G
In this situation, she could have voted against at least one, or possibly against both.
OMG, it is so cold right now and all I can do is be face down in LSAT prep. My fingers are aching to type and I am in bloody Virginia right now -- not the North! Weather gods, deliver me!
ReplyDeleteHumor and trembling fingers aside, THANK YOU for the clarification and suggestion regarding double arrows. I strongly advise against using the double arrow symbol in one's work (even through several test prep companies employ them). For myself, I found double arrows to be confusing, both in authorship and employment .... this was affecting my translations .... which clearly affected my ability to answer questions correctly. Not good. Using 1 arrow direction allows crystal clear legibility and greatly simplifies reading one's diagram -- a time save (which is always appreciated) and more importantly allows one to actually GET to the question stems with the correct diagram in place.
Second, thank you also for your explanation regarding "A or B or both must be present" conditional statements. I found the inclusion of "both" to initially be a stumbling block in my diagramming. But I am now on the right track. Awesome. You rock!
This is a great site and a great contribution!
For Question #1, why is the answer E and not D? The answers are mostly the same, except that she votes against J in the latter. Because there are no rules stating that she cannot vote for I and against J at the same time, I don't understand why E,G,H,J cannot be a complete/accurate list of the bills that she votes against.
ReplyDeleteI don't understand question 7 at all. I don't understand why the answer is C. If she votes against the immigration bill, then she MUST vote FOR the free trade agreement according to the contrapositive chain, right? Is there something I'm missing? Please help because this is really bothering me!
ReplyDeleteNathaly,
DeleteYou're looking for something that COULD BE FALSE (must be true except).
the new rule is If F --> ~J or J --> ~F. Ans choice C has a sufficient condition that does not trigger anything else in the rules. Voting AGAINST Immigration does not advance anything. So, F does not HAVE to be in. She could vote DEJ and not violate any rules.
I think you may have an error with your translations
I have a question on question 6. According to the diagram, how is the answer A possible? Because doesn't ~J>E>~g>~H or ~d instead of ~H and ~d? Someone please answer my question. Thank you.
ReplyDelete
ReplyDeleteWhat is confusing in both Q1 and Q7 is how to correctly infer the contrapositives. I made the same mistake on both…
RULE 1 states that the senator votes for the gun control bill only if she votes against the environment bill.
The implication of this to me was that the senator must vote against EITHER E or G. SHE CANNOT VOTE AGAINST THEM BOTH. (I assumed)
The correct answer to Q1 was found in the possibility of the senator voting against BOTH of these bills. NOT G AND NOT E
Similarly in Q7 the NEW RULE stipulated that,
“ if the legislator votes for the free trade bill, then she will vote against the judicial activism bill.”
Again, the implication of this to me was that the senator votes against EITHER F or J. It is unclear that she can vote AGAINST BOTH.
Yet again, the correct answer to Q7 is found in the possibility of the senator voting against BOTH F and J (and by extension I).
From what I have studied so far, I have not come across any LSAC Logic Games that require one to make this kind of backward contrapositive inference.
Well, Steve, you must be onto something because I found the following similar logical reasoning deduction in the very next question in your 3 month study guide.
ReplyDeleteThis is taken directly out of KAPLAN's Study guide.
PREPTEST 36 #1
Rule 1’s contrapositive reads “If the stand carries pears then it doesn’t carry kiwis,” which means
that the rule boils down to “I can never choose both pears and kiwis,” or “NEVER KP” in your nearby
scratchwork. Note that the rule doesn’t mean “one or the other” (the rule permits us to choose neither
kiwis nor pears), but simply that the moment we pick one of the two fruits, the other is to be tossed out.
I am following your 3 month study guide religiously, btw...
ReplyDeleteI don't mean to beat a dead horse but I still do not understand how 7(c) can be false. None of the other posts are making this clear to me! If immigration is out, judicial activism is out as well. If judicial activism is out, then the necessary condition of the new rule (free trade in, judicial activism out) is satisfied, thus making the necessary condition satisfied as well. Should I not take the contrapositive of the new rule (if J is in F has to be out)? Steve, I even looked at your explanation and using those diagrams I still understand I being out if F is in. Heeelp! I'm dying with these grouping games, I've actually given up and just moved on to LR because I'm so frustrated.
ReplyDeleteWait! I think I got it. It's because I'm screwing up necessary and sufficient, aren't I? If F is in then J is out, but that doesn't make J being out necessary for F to be in. If it said
Delete"If F is in then J MUST be out" THEN (c) would have to be true. Is that right?
This comment has been removed by the author.
ReplyDeleteOk so I read the "unless,without,until,except" blog post but there seems to be some discrepancies. Your instruction was to replace the phrases above (unless,excepts, etc) with "if not".
ReplyDeleteHere's the rule from the problem:
Unless she votes against the judicial activism bill, she will vote for the immigration bill.
So this is "unless" not J then I because she never says she will not vote for I.
If you replace the "unless" phrase with "if not" its "if not J then I".
In the blog post regarding this rule it says "Not B unless A". The "unless" gets replaced by the "if not" and it is rewritten " Not B if not A" but then this can be rewritten to match the "if-then" template as " If NOT A then NOT B"
but the difference between the blog explanation in the rule in the game is that one says NOT and the other doesn't. It is not stated in the rule that she will not vote for the immigration Bill.
Even in the other example in your blog about the turkey:
It's not Thanksgiving (B) unless there's turkey (A). (I know it's not Thanksgiving for a few weeks, but I'm hungry for turkey and stuffing now.)
With "if not" replacing "unless":
It's not Thanksgiving if there's no turkey.
AGAIN the NOT id clearly stated, so someone please make sense of this for me.
Well I definitely enjoyed studying it. This information provided by you is very practical for good planning.
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