Manhattan LSAT Logic Game Book - Page 2
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Manhattan LSAT Logic Games Strategy Guide Excerpt
How Did You Do?
Check your work against the following explanations. Read through the ENTIRE explanation for each question, even if you got the question correct. We've included many general tips and takeaways that you may find useful.
1. Which of the following could be the order of the performances from first to last?
(A) Plethora, Truth, Orbit, Moonshot, Rewind, Simpleton, Victim, Nonesuch
(B) Truth, Nonesuch, Moonshot, Plethora, Simpleton, Orbit, Victim, Rewind
(C) Plethora, Truth, Nonesuch, Orbit, Moonshot, Victim, Simpleton, Rewind
(D) Truth, Plethora, Nonesuch, Orbit, Simpleton, Moonshot, Victim, Rewind
(E) Truth, Nonesuch, Orbit, Simpleton, Plethora, Rewind, Moonshot, Victim
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The correct answer is (D).
Most Logic Games sets start with a question like this one, an Orientation question. These questions ask you to choose one possible complete outcome from five choices. If our Tree is right, the String Technique is the easiest approach:
Looking at our Tree, we see a P-O-M-V string. These four letters must come in that order (not necessarily consecutively, but certainly in that order). So, let's start by eliminating any answer choices that do NOT contain the P-O-M-V string. (B) has M-P-O-V. Eliminate it. (E) has O-P-M-V. Eliminate it. Now let's take another string: S-V. Let's eliminate any choice that does NOT contain the S-V string. Eliminate (C). Lastly, we'll evaluate the S-R string. Eliminate (A). We're left with (D).
We could also use the actual text versions of the constraints in a systematic manner to eliminate incorrect answers:
First constraint: Truth and Plethora both perform before Orbit.
Examine each answer choice, beginning with (A), and look for any violations of this constraint. The ordering in answer choice (E) does not comply with this constraint. Eliminate (E).
Second constraint: Simpleton performs before Rewind.
Start with answer choice (A) once again, and look for violations of this constraint. The ordering in answer choice (A) does not comply with this constraint. Eliminate (A). On Orientation questions, a given constraint will rarely eliminate more than one answer choice. Knowing this, we should immediately move on to the next constraint.
Third constraint: Truth performs before Nonesuch.
Since we've already eliminated both (A) and (E), we'll start with answer (B). Examine the answer choices and look for violations. This particular constraint doesn't allow us to make any eliminations.
Fourth constraint: Victim performs after Simpleton.
(C) does not comply with this constraint. Eliminate (C). Again, we'll move on immediately since the likelihood of eliminating a second answer with this constraint is low.
Fifth constraint: Moonshot performs before Victim but after Orbit.
Examine the remaining choices, (B) and (D), and look for violations. The ordering in answer choice (B) does not comply. Eliminate (B). You may be tempted to verify answer (D), but this will only waste valuable time. If you've confidently eliminated the other four choices, (D) must be correct. Trust yourself and move on!
2. Which one of the following must be true?
(A) At least four bands perform at some time after Plethora.
(B) At least four bands perform at some time after Truth.
(C) At least two bands perform at some time after Moonshot.
(D) At least two bands perform at some time before Nonesuch.
(E) At least two bands perform at some time before Rewind.
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The correct answer is (B).
Starting with (A), let's analyze the choices using our Tree diagram. Our diagram shows that O, M, and V must perform at some time after P (we can trace continuous, one-directional paths from P to O, P to M, and P to V), but that's all we know about P. We can't be sure that there are at least four bands after P. Eliminate (A).
Analyzing answer choice (B), we see that indeed N, O, M, and V must all come at some time after T (we can trace continuous, one-directional paths from T to N, T to O, T to M, and T to V). Thus, the correct answer must be (B). During the actual exam, you may be tempted to analyze the remaining answer choices to be sure they're wrong, but that would be a waste of valuable time. Only one answer can be correct. If you're confident in your Tree setup, and if you're confident in the inferences you've made, choose (B) and move on to the next question!
That said, you should take the time to analyze each and every answer choice as you are reviewing your practice work. As an example, take a few minutes now to analyze (C), (D), and (E). Can you see why these need not be true? Use the Tree to convince yourself, and even write out a few possibilities if you're unsure.
This in-depth analysis will sharpen your instincts and build your confidence. Do the hard work of verifying now so that you'll have the confidence to choose (B) and move on during the exam.
3. If Plethora performs fifth, then each of the following could be true EXCEPT:
(A) Rewind is the sixth band to perform.
(B) Nonesuch is the fourth band to perform.
(C) Simpleton is the second band to perform.
(D) Truth is the third band to perform.
(E) Rewind performs at some time before Nonesuch but at some time after Truth.
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The correct answer is (A).
This is an "If" question. "If" questions introduce an additional constraint that is to be applied only for this question. In this case, the additional constraint is that P performs fifth. Next to the question, we set up an "If" diagram that incorporates this additional information (we don't want to write over our original Tree because we'll need the original form for future questions). From our Tree, we can quickly see that O, M, and V must all come at some time after P, and in that order. So, O, M, and V must perform sixth, seventh, and eighth, respectively.
Note the word EXCEPT in the question, printed in all caps. This must be important! You will see four kinds of EXCEPT questions on the Logic Games section. It is crucial that you understand exactly what you are being asked for in these situations. Here's a quick translation guide:
| EXCEPT WORDING | Translation |
| ...each of the following could be true EXCEPT: | Which one must be false? |
| ...each of the following must be true EXCEPT: | Which one could be false? |
| ...each of the following could be false EXCEPT: | Which one must be true? |
| ...each of the following must be false EXCEPT: | Which one could be true? |
Notice that the translation always involves changing "could" to "must" and "must" to "could." Also notice that "true" goes to "false" and "false" goes to "true."
For these tricky questions, it is very important that you anticipate (before you start analyzing the choices) the nature of the five choices. For this particular question, we translate to "Which one must be false?" Thus, four choices could be true and one must be false. Get that straight before anything else!
We start with choice (A) and we can immediately see from our "If" diagram that R cannot possibly perform sixth. No need to check the remaining answers; move on! For the purposes of your review, however, this is a good time to verify that the remaining answer choices could indeed be true.
4. If Moonshot performs fourth, then which one of the following must be true?
(A) Victim is the sixth band to perform.
(B) Truth performs earlier than Plethora.
(C) Nonesuch performs earlier than Victim.
(D) Simpleton performs earlier than Nonesuch.
(E) Simpleton performs later than Orbit.
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The correct answer is (E).
The additional constraint in this "If" question is that M performs fourth. Our "If" diagram incorporates this new information. The Tree clearly shows that O, T, and P must all come at some time before M, with T and P preceding O. Thus, O must be third. Notice that the order of T and P is unknown. We'll use a circle to symbolize this uncertainty. While we don't know exactly who performs first, T or P, we do know that the first four spaces are occupied. This leaves the remaining four spaces for N, S, V, and R, not necessarily in that order.
In a situation like this, the incorrect choices will usually attempt to define the relationships for elements that have uncertain relative positions. For example, we don't know which comes first, P or T. We can expect an answer or two that will attempt to order these two bands. Also, the last four slots will be filled by N, S, V, and R, but their relative positioning is uncertain (aside from the fact that V and R must come after S). Be wary of answers that attempt to provide some fixed order in the last four positions.
Answer choice (A) is a good example. Again, we don't know the ordering of the last four elements. After all, N and R are floaters. Eliminate (A).
Answer choice (B) attempts to define the relationship between P and T. All we know about P and T is that they must come at some time before O. Which comes first is anybody's guess at this point. Eliminate (B).
In (C), we again see an attempt to define the position of a floater. N could potentially occupy any one of the last four slots. Eliminate (C).
Same thing in answer choice (D). The position of the floater N relative to S is unknown. Eliminate (D).
We see that answer choice (E) must be correct. If you're confident in your work up to this point, you can move on without verifying. A quick check proves easy enough, however, and we see that S must indeed perform later than O, since all the spots before O are filled.
Are you thinking that you could have done without the "If" diagram? As you get more practice reading the Tree, you'll find yourself "moving" the parts of the Tree in your mind as you answer questions like these. You'll be able to check the answer choices against the Tree without actually needing to draw out the "If" diagram. In this case, a quick examination of the Tree tells us that the first four spots will be filled by T, P, O, and M, making it impossible for S to come anywhere before O. If you're not there yet, don't worry. Keep working on it!
5. Each of the following could be true EXCEPT:
(A) Victim performs earlier than Nonesuch.
(B) Rewind performs earlier than Truth.
(C) Nonesuch performs earlier than Plethora.
(D) Simpleton performs later than Orbit.
(E) Moonshot performs earlier than Plethora.
The correct answer is (E).
We quickly note the EXCEPT language (it's hard to miss!) and translate to: "Which one must be false?" Again, before we do anything else, let's anticipate the nature of the choices: four could be true, one must be false.
Answer choice (A) attempts to define the relative positions of N, a floater, and V. Remember, N could go anywhere, except before T! Thus, V could certainly perform earlier than N. Eliminate (A).
Answer (B) tries the same trick. The floater R can go anywhere except before S! Thus, R could certainly perform earlier than T. Eliminate (B).
The floater N could certainly perform earlier than P. Eliminate (C).
The position of S relative to O is unknown, so S could potentially perform later than O. Eliminate (D).
Answer (E) is the correct answer. We see from the diagram that M must always come somewhere after P. Thus, the statement that Moonshot performs earlier than Plethora must be false.
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6. If the condition that Victim performs at some time after Simpleton is replaced with the condition that Victim performs at some time before Simpleton, and if all other conditions remain in effect, then which of the following must be false?
(A) Rewind performs last.
(B) Nonesuch performs last.
(C) Simpleton performs seventh.
(D) Victim performs fifth.
(E) Moonshot performs sixth.
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The correct answer is (E).
This is a unique type of "If" question in that instead of introducing an additional constraint it actually alters one of the existing constraints. These questions are rare, but if you encounter a question such as this on an LSAT game it will most likely be the last question in the set. These are difficult questions that are designed to be time-intensive. Generally, they require that we create a new diagram, in this case a new Tree, that incorporates the altered constraint. As we do for all "If" questions, we'll draw a new diagram next to the question text in our test booklet.
Let's anticipate the nature of the choices: four could be true, one must be false.
We can see from our new Tree that R could indeed perform last. Eliminate (A).
As we analyze (B), we must keep in mind that the floater N can go just about anywhere (except before T), including after R. N could potentially perform last. Eliminate (B).
S performs seventh whenever the floater N performs somewhere before S. Eliminate (C).
V performs fifth whenever the floater N performs somewhere after V. Eliminate (D).
M must be followed by at least three bands, V, S, and R (and potentially a fourth, N). Thus, the latest M could perform is fifth. The statement that Moonshot performs sixth must be false.
Question-Specific Approaches
What Did We Learn?
Let's summarize the main takeaways from the preceding six questions. You will find that many of these takeaways cut across all game types. We will be revisiting many of these concepts and approaches as we uncover the details of the remaining game types.
1. On Orientation questions, apply the constraints, one at a time, to the answer choices. Eliminate answers that violate the given constraint, and then move on to the next constraint. On Tree games, use the String approach to tackle these questions.
2. On Orientation questions, it is rare that any one constraint will eliminate more than one answer choice. Therefore, once you find an answer that violates a particular constraint, eliminate it and immediately move on to the next constraint.
3. As soon as you find a correct answer, choose it and move on! Don't bother with proving the others to be incorrect. There can only be one correct answer.
4. As you are reviewing your work after completing a game for practice, do take the time to verify all correct answers and disprove all incorrect answers. This will sharpen your instincts and build your confidence.
5. "If" questions add a new constraint. If you need to create a new diagram or abbreviated sketch, do it next to the text in your test booklet. DO NOT write over the original diagram!
6. Be comfortable interpreting questions with "EXCEPT" language:
| EXCEPT WORDING |
Translation |
| ...each of the following could be true EXCEPT: | Which one must be false? |
| ...each of the following must be true EXCEPT: | Which one could be false? |
| ...each of the following could be false EXCEPT: | Which one must be true? |
| ...each of the following must be false EXCEPT: | Which one could be true? |
7. On tricky EXCEPT questions, anticipate the nature of the choices before you start (for example, four could be true, one must be false).
8. As you become more comfortable with the Tree, you'll be able to "move" the elements of the Tree in your mind as you consider the question at hand. This is something to shoot for as it will save you time.
9. Always watch out for the floaters! The floaters will come into play on just about every question.
Putting it All Together
Here's your chance to put all the pieces together on a new game. Give yourself 8 minutes to complete the following game. We'll work through the setup and solutions together on the pages to come.
October 2008 exam, Section 4, Game 3
Mercotek carried out a study to compare the productivity of its night shift with that of its day shift. Every week the company's six crews—F, G, H, R, S, and T—were ranked from first (most productive) to sixth (least productive). There were no ties. For any given week, either G and T were the two night-shift crews or else S and H were—the four other crews were the day-shift crews for that week. The following relationships held for every week of the study:
F is more productive than G.
R is more productive than S.
R is more productive than T.
S is more productive than H.
G is more productive than T.
13. Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given week of the study?
(A) F, G, T, R, S, H
(B) F, R, G, T, H, S
(C) G, R, T, S, H, F
(D) R, F, G, S, H, T
(E) R, S, H, T, F, G
14. If F is ranked third for a given week of the study, then which one of the following could also be true of that week?
(A) G ranks second.
(B) H ranks fourth.
(C) R ranks second.
(D) S ranks fourth.
(E) T ranks fourth.
15. Which one of the following CANNOT be the crew ranked fifth for any given week of the study?
(A) G
(B) H
(C) R
(D) S
(E) T
16. For any given week of the study, the ranking of all the crews is completely determined if which one of the following is true?
(A) F ranks second that week.
(B) G ranks fifth that week.
(C) H ranks third that week.
(D) R ranks third that week.
(E) S ranks third that week.
17. If the night-shift crews rank fifth and sixth for a given week of the study, then which one of the following could also be true of that week?
(A) G ranks fourth.
(B) H ranks fifth.
(C) R ranks third.
(D) S ranks fourth.
(E) T ranks fifth.
18. Which one of the following is a complete and accurate list of the crews that CANNOT be ranked third for any given week of the study?
(A) G, H, S
(B) R, T
(C) F, T
(D) G, T
(E) T
The Setup
Let's start by setting up our diagram. In this case, we see many of the characteristics that define a relative ordering game: "ranking" the crews from 1st to 6th, "no ties," and all relative contraints ("X is more productive than Y"). So, we want to set up a Tree diagram. First, we'll get all our letters in one place, and we'll make note of the fact that the night-shift crews are either G/T or H/S:
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STEP 1: Start with the first constraint, drawing a line between any two letters for which the relative positioning is known.
F is more productive than G.
R is more productive than S.
R is more productive than T.
S is more productive than H.
G is more productive than T.
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STEP 2: Then find the next constraint that can be connected to any part of the existing diagram.
R is more productive than S.
R is more productive than T.
S is more productive than H.
G is more productive than T.
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STEP 3: Repeat until all constraints have been used.
R is more productive than S.
R is more productive than T.
S is more productive than H.
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R is more productive than T.
S is more productive than H.
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R is more productive than S.
R is more productive than T.
S is more productive than H.
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Solutions
Check your work against the following explanations. Read through the ENTIRE explanation for each question, even if you got the question correct. We've included many general tips and takeaways that you may find useful.
13. Which one of the following could be an accurate ranking of all the crews, in order from first to sixth, for a given week of the study?
(A) F, G, T, R, S, H
(B) F, R, G, T, H, S
(C) G, R, T, S, H, F
(D) R, F, G, S, H, T
(E) R, S, H, T, F, G
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The correct answer is (D).
This is an orientation question. We'll use the String technique to eliminate answer choices. Our diagram tells us that we must have an F - G - T string in any correct arrangement of letters. While F, G, and T need not be adjacent to each other, they do have to come in this order.
(C) G - T - F. Eliminate it.
(E) T - F - G. Eliminate it.
We also know that any valid arrangement will have an R - S - H string.
(B) R - H - S. Eliminate it.
Finally, our diagram tells us that R must come before T.
(A) T - R. Eliminate it.
While you wouldn't need to verify (D) on the exam, take a second now to verify that (D) could in fact be a correct ordering.
14. If F is ranked third for a given week of the study, then which one of the following could also be true of that week?
(A) G ranks second.
(B) H ranks fourth.
(C) R ranks second.
(D) S ranks fourth.
(E) T ranks fourth.
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The correct answer is (B).
This is an "If" question that puts F in the third spot. We'll use our Tree to make some inferences. If F is third, two letters must come before it. These must be R first and S second (notice that we can't put H before F in this case because that would put three letters, R - S - H, before F). Thus, G, T, and H will occupy the last three spots, but we don't know in what order. G must come before T, but H could go in any of those last three spots. Our "If" diagram above represents this uncertainty with a circle.
We can eliminate (A), (C), and (D) right off the bat. (E) can't be true because G must come before T. The earliest T could come is fifth.
15. Which one of the following CANNOT be the crew ranked fifth for any given week of the study?
(A) G
(B) H
(C) R
(D) S
(E) T
The correct answer is (C).
Anticipate the nature of the choices: four answers can be fifth, one CANNOT be fifth.
Fifth is second to last. Thus, any letter that MUST have at least two letters after it cannot be fifth (there's room for only one letter after the fifth). T, S, and H must all come after R. So, R cannot be fifth.
16. For any given week of the study, the ranking of all the crews is completely determined if which one of the following is true?
(A) F ranks second that week.
(B) G ranks fifth that week.
(C) H ranks third that week.
(D) R ranks third that week.
(E) S ranks third that week.
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The correct answer is (C).
This question is designed to be more time consuming, so we shouldn't feel bad about taking our time to get it right. Let's look at the choices one at a time.
(A) If F ranks second, R would have to be first. But what about S and H? We're not sure. For example, here are a few possibilities:
R F S H G T
R F S G T H
R F G T S H ... and so on. Eliminate (A).
(B) If G ranks fifth, T would have to be sixth. But what about R, S and H? We're not sure. For example, here are a few possibilities:
F R S H G T
R S H F G T
R S F H G T ... and so on. Eliminate (B).
(C) If H ranks third, R must be first and S must be second. And since F - G - T must come in that order, we'd have:
R S H F G T
Done! On the exam, you'd move on to the next question. Just for practice, go ahead and take the time now to show that (D) and (E) are not correct.
17. If the night-shift crews rank fifth and sixth for a given week of the study, then which one of the following could also be true of that week?
(A) G ranks fourth.
(B) H ranks fifth.
(C) R ranks third.
(D) S ranks fourth.
(E) T ranks fifth.
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The correct answer is (C).
Ah. We were just wondering why they hadn't yet asked us anything about the night-shift crews. Remember back at the start of our setup we made a note that the night-shift crews could either be G/T or S/H. Let's note that again here to remind ourselves.
If the night-shift crews rank fifth and sixth, there are two possibilities. It has to be one of these two:
CASE #1: G is fifth and T is sixth
CASE #2: S is fifth and H is sixth
We can eliminate (B) immediately. H could be sixth (in case #2), but in neither case could H be fifth. We can also eliminate (E) immediately. T could be sixth (in case #1), but in neither case could T be fifth.
Let's look at (A) more closely. If G is fourth, S would be fifth and H sixth (case #2). So we'd have:
_ _ _ G S H
But wait! We know that T must come after G. There's no room for T. Eliminate (A).
We can use similar logic on (D). If S is fourth, G would be fifth and T would be sixth (case #1). So we'd have:
_ _ _ S G T
But wait! We know that H must come after S. There's no room for H. Eliminate (D).
We can quickly verify that (C) is correct. If R is third, F must be first and G must be second (remember, we know that T, S, and H must all come after R, so the only two that could come before R would be F and G). Since G is second, this would be a case #2 scenario. S would be fifth and H would be sixth. So, we'd have:
F G R T S H
This could certainly be true.
18. Which one of the following is a complete and accurate list of the crews that CANNOT be ranked third for any given week of the study?
(A) G, H, S
(B) R, T
(C) F, T
(D) G, T
(E) T
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The correct answer is (E).
Which ones could never be third? Notice that T is listed in four of the five choices. T must be an obvious letter that CANNOT be third. Let's verify: we know that F, G, and R must all come before T. Thus, the earliest that T can come is fourth. T can't be third. So, T must be on our list! Eliminate (A) immediately.
Can R be third? Yes! Remember all that work we did on #17 to verify answer (C)? We could have F G R T S H. So, R can't be on our list. We're looking for a list of letters that could NEVER be third. Eliminate (B).
We can also eliminate (D) immediately! Look back at #13, the orientation question. Note that the correct answer had:
R F G S H T
Thus, G could be third. We're looking for a list of letters that could NEVER be third. Eliminate (D).
So it's down to (C) and (E). The only question left is whether F could be third. Look back at #14! They give us a scenario where F is third! Eliminate (C).
As you get down to the last few questions of the set, remember to look back at the work you've done on previous questions. Often, this previous work will allow you to eliminate some answers very quickly.
In Conclusion
Advantages of the Tree
You've learned to recognize Relative Ordering games, set up the Tree, allocate your time wisely on Relative Ordering games, draw inferences from the Tree diagram, and apply question-specific approaches while attacking the problems. A few advantages of the Tree system:
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1. It is a repeatable process. The process of diagramming the branches of the Tree is easy to understand, easy to practice, and perhaps most important, easy to execute under the pressure of the real exam.
2. It uncovers implicit relationships. By strictly diagramming the explicit relationships given in the constraints, we automatically arrive at relationships that are implicit in the rules given. For example, in the Tree above we can easily see that V comes after P, even though that particular relationship was never explicitly mentioned in the constraints.
3. It effectively manages the uncertainty. There will always be some uncertainty in Relative Ordering games. The key is managing the uncertainty so that you know exactly where it exists (mostly in the floaters!). For example, the only thing we know about N is that it comes somewhere after T. The position of N relative to the other elements is uncertain. By using the Tree to recognize floaters, we can effectively manage the uncertainty of their position. The key is being certain about the uncertainty!
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