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Objection’s LSAT Tips – “More/Less” Ordering GamesQuestion Type: More/Less Ordering Games Introduction Simple ordering games are just that – simple. There is a 1:1 ratio of variables to the number of slots. But you will often encounter a game where there are more variables than slots (e.g., six workers for four days) orfewer variables than slots (e.g., five babies for seven cribs). These can be tricky and complicated, but often have the potential to be broken wide open. Method As I said in the simple ordering games article, the two keys to logic games are making clear diagrams and making inferences. The “more/less” ordering games have one more key step: distributions. You must work out the possible numerical distributions for your setups. For example, if there are six workers for four days of work, and a rule states that each person works only one day, and each day has at least one person working, you would have the following potential distributions: 3111 The first distribution means you could have three workers on one day and one worker on the other three. The second says you could have two workers on two days and one worker on each of the other two. Rules often restrict your potential distributions. Let’s look at a second example. If there are five babies for seven cribs and the rules say nothing limiting the number of babies in each crib, you could have the following distribution of babies to cribs: 5000000 That is seven possible distributions. However, if the rules say no more than two babies per crib, you restrict the potential distributions to the bottom three distributions. Make sure you read all the rules prior to creating your distributions. Games are more easily taught by example. Let’s do an example of both a more game and a less game. Examples Four people – Q, X, Y, Z – have formed a party club to party together six days a week from Monday through Saturday. Each day, a party is hosted by exactly one of the people. The hosting schedule for any week must meet the following conditions: Each person hosts a party on at least one day. The first two rules should jump out you as restricting your distributions. In this case, our distributions will be number of times someone can host per week. Since each person must host at least once, you have the following two distributions: 3111 (one person hosts three times, the other three host once) 2211 (two people host twice, the other two host once) The rest of the rules are pretty simple to diagram. Here is the diagram I used:
Diagram rules (DR#) explanations: DR1. The distributions. Now, on to the questions! 1. Which one of the following could be a schedule of hosts for one week, for the days Monday through Saturday, respectively? A) X, Q, Z, Y, X, X How to Solve: Process of Elimination (Note: The rule numbers (DR#) correspond to the labels on my diagram.) A – Incorrect. Violation of DR2. 2. If during one week, Z hosts on Wednesday and Saturday only, which one of the following must be true of the week? A) Q hosts on Tuesday. How to Solve: Minidiagram plus Inference
Draw a minidiagram and put Z on Wednesday and Saturday. What does this mean? For starters, you’re looking at a 2211 distribution, but none of the answer choices deal with this. DR3 shows us that if Z is hosting Saturday, X cannot host on Monday. Since Z is only allowed to host on Wednesday and Saturday in this minidiagram, Z cannot host on Monday either. DR5 says that Q cannot host Monday. This means that Y must host on Monday. This is answer choice C. 3. If during one week X hosts on Monday and Saturday only, which one of the following must be true of that week? A) One other person besides X hosts on exactly two days. If X hosts on exactly two days, this means that you are looking at a 2211 distribution (DR1). This means that besides X, one person will host on two days. And… you can stop there. Answer choice A says this. 4. Which one of the following could be true of one week’s schedule of hosts? A) Q hosts on both Wednesday and Saturday. How to Solve: Process of Elimination (Note: “Could be true” means the wrong answers must be false.) A – Incorrect. Must be false because of DR4. 5. Which one of the following CANNOT be true of one week’s schedule of hosts? A) Q hosts on Tuesday and X hosts on Friday. How to Solve: Inference This one is tough. Process of elimination would be lengthy because of the difficulty of eliminating “could be true” answers. What you want to do is look for and start with answer choices that deal with two variables that tend to restrict each other or are used in a rule with each other. Answer choices B and C deal with variables X and Z, which are used together in DR3. In answer choice B, X is hosting on Monday (which, by DR3, means Z cannot host Saturday, which by DR4 means Z must host Wednesday). Answer choice B also specifies that Z is hosting Tuesday. We now have Z hosting on Tuesday and Wednesday, which is a violation of DR2. B is therefore the correct response. 6. If during one week Q hosts exactly twice but he hosts on neither Tuesday nor Wednesday, which one of the following could be true of that week? A) One person hosts exactly three times during the week. How to Solve: Process of Elimination plus MiniDiagram plus Inference If you haven’t noticed by now, it is usually easiest to solve “could be true” problems by process of elimination, while it is usually easiest to solve “must be true” problems by finding the answer directly using inferences. This problem is also aided by using a minidiagram:
If Q does not host on Tuesday or Wednesday, and by DR5 he cannot host on Monday, Q has three consecutive days (Thursday, Friday, and Saturday) to host twice. But since DR2 says he cannot host on consecutive days, Q must host on Thursday and Saturday. Further, Z must host on Wednesday, since by DR4 he hosts on at least one of Saturday and Wednesday. Remember, in “could be true” questions, the wrong answers all must be false. A – Incorrect. This must be false because if Q hosts exactly twice, the distribution is 2211. There is no room for someone to host three times.  Now let’s do a “less” game: During a single week, from Monday through Friday, tours will be given at three different houses – X, Y, and Z. Exactly five tours will be given that week, one each day. The schedule of tours for the week must conform to the following restrictions: Each home is toured at least once. This is a “less” game because you have three variables to fit into five days. Z is the limiting variable here. Before you read on, you should stop and try and figure out why this is key… The reason Z is key is twofold. First, Z can only be used twice. This means your distribution is 221. S and one other home can be toured twice and the third home only once. The second reason Z is key – and this really breaks the game wide open – is that Z must be toured consecutively; it must be in a block. This limits the placement of Z to four different twoday blocks: MT, TW, WTh, ThF. It also limits the entire game to four general templates. Here is the diagram:
Diagram rules explanations: DR1. This is the only possible distribution. Here are the four possible templates:
Template explanation: Off we go… 1. If in the week’s tour schedule the home that is toured on Tuesday is also toured on Friday, then for which one of the following days must a tour of home Y be scheduled? A) Monday How to Solve: Refer to Templates The home that toured Tuesday can also be on Friday in template three only. In template three, Y must be Monday. The answer is A. 2. Which of the following CANNOT be true of the week’s tour schedule? A) The home toured Monday is also toured Tuesday. How to Solve: Look for Template Violations You can answer this question pretty quickly by going through each answer choice and looking for clear violations of our rules and/or templates. Answer choice C can never happen in any of our templates. In templates one and two, Z is on Tuesday but cannot be on Thursday. In templates three and four, Z is on Thursday but cannot be on Tuesday. 3. If in addition to home Z, one other home is toured on two consecutive days, then it could be true of the week’s tour schedule both that A) Y is toured on Monday and X is toured on Thursday. How to Solve: Process of Elimination Remember, the wrong answers must be false. A – Incorrect. Y is toured on Monday in templates two, three, and four. In the third and fourth, Z is on Thursday. In the second, if X were to be Thursday, Y would be on Friday (as per rule two) meaning nothing else would be consecutive. 4. If in the week’s tour schedule the home that is toured on Tuesday is also toured on Wednesday, then which one of the following must be true of the week’s tour schedule? A) Y is toured on Monday. How to Solve: Templates At this point you’ve probably recognized how much easier the templates have made this game. The templates where the home toured Tuesday can be the home toured Wednesday are two and four. In both of those setups, Y is toured Monday. Answer choice A is correct. 5. If in the week’s tour schedule the home that is toured on Monday is not the home that is toured on Tuesday, then which one of the following could be true of the week’s schedule? A) A tour of Z is scheduled for some day earlier in the week than is any tour of Y. How to Solve: Process of Elimination Remember, wrong answers must be false. A – Incorrect. This must be false because Y is on Monday in each of the three possible templates (two, three, and four). (In template one, the ZZ block violates the rule introduced in the question.) Therefore, Z cannot come before Y. Notice that we didn’t really use our distribution rule in the second game as much as in the first, but it’s still nice to have. Final Notes “More” and “less” games are a little tougher than simple ordering games with their 1:1 ratio of variables to possible slots, but they are still manageable. Focus, find inferences, limit the game when you can. Look for those gamebreaking rules. Tackle each problem carefully. You will be fine. As usual, if you have any questions, please visit the TLS LSAT Prep forum at http://www.toplawschools.com/forums/viewforum.php?f=6 . 
Ken's Introduction to the LSAT Conquering the LSAT How I Scored a 180  Article #1 How I Scored a 180  Article #2 How I Scored a 180  Article #3 Retaking the LSAT Logic Fundamentals: A Lesson In Conditional Reasoning Objection’s LSAT Tips – “Describe” Questions (LR) Objection’s LSAT Tips – “Main Point” Questions (LR) Objection's LSAT Tips  "Must Be True" Questions (LR) Objection’s LSAT Tips – “Role” Questions (LR) Objection’s LSAT Tips – “Level Ordering” Games Objection’s LSAT Tips – “In/Out” Games Objection’s LSAT Tips – “More/Less” Ordering Games Objection’s LSAT Tips – Simple Ordering Games Objection’s LSAT Tips – Multiple Group Games LSAT Prep with Work and School 
