LSAT Logic Games : Determining sequence in linear games
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Example Questions
Example Question #51 : Determining Sequence In Linear Games
During a period of six consecutive days (day 1 - day 6) each of exactly six restaurants will be inspected by the department of health. During this period, each of the restaurants will be inspected exactly once, one restaurant per day. The schedule for the inspections must follow these conditions:
A is inspected on either day 1 or day 6.
D is inspected on an earlier day than E is inspected.
E is inspected on the day immediately before F is inspected.
If B is inspected on day 3, then E is inspected on day 5.
Which one of the following must be false?
The inspection of C is scheduled for day 6.
The inspection of F is scheduled for day 2.
The inspection of E is scheduled for day 3.
The inspection of B is scheduled for day 4.
The inspection of D is scheduled for day 4.
The inspection of F is scheduled for day 2.
The statement 'The inspection of F is scheduled for day 2' must be false because according to the conditions, E must be inspected immediately before F, and D must be inspected some time before E is; thus D < EF. If F is scheduled for day 2, there is no room for D and E to be placed before F in the schedule.
All of the other statements are possible, and thus are incorrect because they do not necessarily false. The correct choice will be the statement that cannot be true in any circumstance.
Example Question #51 : Determining Sequence In Linear Games
During a period of six consecutive days (day 1 - day 6) each of exactly six restaurants will be inspected by the department of health. During this period, each of the restaurants will be inspected exactly once, one restaurant per day. The schedule for the inspections must follow these conditions:
A is inspected on either day 1 or day 6.
D is inspected on an earlier day than E is inspected.
E is inspected on the day immediately before F is inspected.
If B is inspected on day 3, then E is inspected on day 5.
The inspections scheduled for day 3 and day 5, respectively, could be those of:
B and F
B and C
C and B
F and D
F and C
F and C
The inspections for day 3 and 5 can only be F and C, respectively, of the answer choices.
B and C is incorrect because if B is 3rd, then E must be 5th.
B and F is incorrect because if B is 3rd, then E must be 5th.
C and B is incorrect because if C is 3rd and B is 5th, then the only spots for E and F are 1st and 2nd, since E must be immediately before F. However, since D must be before E and F, there is no room for D to be scheduled.
F and D is incorrect because if D is scheduled 5th, then there is no room for E and F to be scheduled after D.
Example Question #52 : Determining Sequence In Linear Games
During a period of six consecutive days (day 1 - day 6) each of exactly six restaurants will be inspected by the department of health. During this period, each of the restaurants will be inspected exactly once, one restaurant per day. The schedule for the inspections must follow these conditions:
A is inspected on either day 1 or day 6.
D is inspected on an earlier day than E is inspected.
E is inspected on the day immediately before F is inspected.
If B is inspected on day 3, then E is inspected on day 5.
The inspection of F is scheduled for the day immediately before the inspection of A, which one of the following must be true about the schedule?
The inspection of either B or D is scheduled for day 1.
The inspection of either C or D is scheduled for day 3.
The inspection of either B or C is scheduled for day 1.
The inspection of either C or D is scheduled for day 4.
The inspection of either B or D is scheduled for day 2.
The inspection of either C or D is scheduled for day 3.
If F is scheduled before A, then we combine the condition that D must be some time before E and that E must be immediately before F to create the condition that D must be before E, F, and A, or D < EFA (EFA being in consecutive order). Since A must be either in the 1st or 6th position, we can now only place it in the 6th position.
_ _ _ E F A
1 2 3 4 5 6
If B were placed in the 3rd position, then the 5th position would have to be E. Since the 5th position is not E, B cannot be placed in the 3rd position. Thus, only the remaining letters C and D can be placed in the 3rd position.
Example Question #53 : Determining Sequence In Linear Games
During a period of six consecutive days (day 1 - day 6) each of exactly six restaurants will be inspected by the department of health. During this period, each of the restaurants will be inspected exactly once, one restaurant per day. The schedule for the inspections must follow these conditions:
A is inspected on either day 1 or day 6.
D is inspected on an earlier day than E is inspected.
E is inspected on the day immediately before F is inspected.
If B is inspected on day 3, then E is inspected on day 5.
If the inspections of B and C are scheduled, not necessarily in that order, for days as far apart as possible, which one of the following is a complete and accurate list of the restaurants that any one of which could be scheduled for inspection for day 1?
A, D
A, B, C, D
A, B, C
B, C, D
B, C
A, B, C
For B and C to be as far as possible, we can try to place them at the 1st and 6th positions. However, this is not possible because A must be in either the 1st or 6th position. Thus, B and C can either be in the 1st and 5th positions or in the 2nd and 6th positions (non-respectively), and A must fill the available 1st or 6th position.
B/C _ _ _ C/B A
or
A B/C _ _ _ C/B
Without having to do any more work, we can already see from these hypotheticals that only A, B, or C can be scheduled for day 1.
Example Question #54 : Determining Sequence In Linear Games
During a period of six consecutive days (day 1 - day 6) each of exactly six restaurants will be inspected by the department of health. During this period, each of the restaurants will be inspected exactly once, one restaurant per day. The schedule for the inspections must follow these conditions:
A is inspected on either day 1 or day 6.
D is inspected on an earlier day than E is inspected.
E is inspected on the day immediately before F is inspected.
If B is inspected on day 3, then E is inspected on day 5.
If the inspection of B is scheduled for the day immediately before the inspection of E, then which one of the following could be true?
The inspection of F is scheduled for day 3.
The inspection of D is scheduled for day 2.
The inspection of E is scheduled for day 4.
The inspection of B is scheduled for day 5.
The inspection of C is scheduled for day 6.
The inspection of D is scheduled for day 2.
If the inspetion of B is scheduled immediately after the inspection of E, then we combine the condition that D must be inspected some time before E and that E must be scheduled immediately before F to create the condition that D < BEF.
The inspection of B cannot be scheduled for day 5 because E and F have to be scheduled after it; there is no room for this.
The inspection of H cannot be scheduled for day 6 because A would have to be scheduled 1st, which leaves the hypothetical: A D B E F H. If B is scheduled 3rd, then E must be scheduled 5th. That is not the case here.
The inspection of E cannot be scheduled for day 4 for the same reason; this would leave a similar hypothetical: _ _ B E F _ , since B must be immediately before E and F must be immediately after E. IF B is scheduled 3rd, then E must be scheduled 5th.
The inspection of F cannot be scheduled for day 3 because D < BEF; the closest satisfaction of this condition would be D B E F _ _ . Thus, F must be scheduled at day 4 or later.
Example Question #55 : Determining Sequence In Linear Games
A mailman will deliver exactly seven packages: T, U, V, W, X, Y, Z. Each will be delivered one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions:
X must be delivered either first or seventh.
The mailman delivers V at some time after delivering T.
The mailman delivers Z at some time after delivering U.
The mailman delivers exactly one package between delivering T and delivering W, whether or not T is delivered before W.
The mailman delivers exactly one package between delivering U and delivering X, whether or not U is delivered before X.
Which one of the following is an order in which the mailman could make the deliveries, from first to seventh?
W, Y, T, V, U, Z, X
T, V, Y, W, U, Z, X
X, Z, U, Y, T, V, W
X, V, U, Y, W, Z, T
U, Z, X, Y, T, V, W
W, Y, T, V, U, Z, X
W, Y, T, V, U, Z, X satisfies all conditions and doesn't violate any of them.
T, V, Y, W, U, Z, X is incorrect because T must have only one package between it and W.
U, Z, X, Y, T, V, W is incorrect because X must be in either the 1st or 7th position.
X, V, U, Y, W, Z, T is incorrect because T must be in an earlier position than V.
X, Z, U, Y, T, V, W is incorrect because U must be in an earlier position than Z.
Example Question #56 : Determining Sequence In Linear Games
A mailman will deliver exactly seven packages: T, U, V, W, X, Y, Z. Each will be delivered one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions:
X must be delivered either first or seventh.
The mailman delivers V at some time after delivering T.
The mailman delivers Z at some time after delivering U.
The mailman delivers exactly one package between delivering T and delivering W, whether or not T is delivered before W.
The mailman delivers exactly one package between delivering U and delivering X, whether or not U is delivered before X.
Which one of the following could be true?
Z is delivered second.
Y is delivered seventh.
V is delivered first.
Z is delivered first.
U is delivered fourth.
Y is delivered seventh.
Only Y can deliver seventh as it does not violate any of the conditions.
V cannot be delivered first because T must be delivered before it.
Z cannot be delivered first because U bust be delivered for it.
Z cannot be delivered second because it must be delivered after U, and U can only be delivered either third or fifth in order to have exactly one package between it and X.
U cannot be delivered fourth because it must be delivered either third or fifth in order to have exactly one package between it and X.
Example Question #52 : Determining Sequence In Linear Games
A mailman will deliver exactly seven packages: T, U, V, W, X, Y, Z. Each will be delivered one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions:
X must be delivered either first or seventh.
The mailman delivers V at some time after delivering T.
The mailman delivers Z at some time after delivering U.
The mailman delivers exactly one package between delivering T and delivering W, whether or not T is delivered before W.
The mailman delivers exactly one package between delivering U and delivering X, whether or not U is delivered before X.
If V is delivered fourth, which one of the following could be true?
Y is delivered first.
T is delivered first.
U is delivered third.
W is delivered fifth.
T is delivered second.
T is delivered first.
Only T could be delivered first as it does not violate any of the conditions or inferences.
T cannot be delivered second because if it were, W would have to be delivered fourth in order to satisfy the condition that one package be between T and W. V is taking the position that W would have to take.
U cannot be delivered third because then X would have to be delivered first. T would then have to be delivered second to be delivered before V (one of the conditions), and W would have to be delivered fourth. However, V is already taking the fourth position.
W cannot be delivered fifth because then T would have to be delivered third in order to be delivered before V (one space must be between T and W, so T must be third or seventh -- it cannot be seventh if it must be delivered before V). If T is delivered third, then U would have to be delivered sixth, since U must be delivered either third or sixth in order to have one package between it and X (X must be first or seventh). If U is delivered sixth, then X must be delivered fourth. However, V is taking the fourth spot in this question.
Y cannot be delivered first because then X would have to be delivered seventh (X must be first or seventh). If X is seventh, U is fifth, since one package must be between U and X. This gives Y _ _ V U _ X. There is no room for T and W to have exactly one package between them.
Example Question #57 : Determining Sequence In Linear Games
A mailman will deliver exactly seven packages: T, U, V, W, X, Y, Z. Each will be delivered one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions:
X must be delivered either first or seventh.
The mailman delivers V at some time after delivering T.
The mailman delivers Z at some time after delivering U.
The mailman delivers exactly one package between delivering T and delivering W, whether or not T is delivered before W.
The mailman delivers exactly one package between delivering U and delivering X, whether or not U is delivered before X.
If Z is delivered fourth, the seventh package delivered must be:
X
W
Y
T
V
W
If Z is delivered fourth, then U must be delivered third - this is because U can only be third or fifth in order to have one package between it and X (X must be first or seventh). If U is third, then X is first: X _ U Z _ _ _
There is only space for T and W to have one package between them in the fifth and seventh spots. Since T must be delivered before V, T cannot be in the seventh spot, so W must be in the seventh spot to satisfy all conditions.
Example Question #60 : Determining Sequence In Linear Games
A mailman will deliver exactly seven packages: T, U, V, W, X, Y, Z. Each will be delivered one at a time, not necessarily in that order. The seven deliveries must be made according to the following conditions:
X must be delivered either first or seventh.
The mailman delivers V at some time after delivering T.
The mailman delivers Z at some time after delivering U.
The mailman delivers exactly one package between delivering T and delivering W, whether or not T is delivered before W.
The mailman delivers exactly one package between delivering U and delivering X, whether or not U is delivered before X.
If the mailman delivers U some time after delivering W, the fifth package delivered could be one of the following EXCEPT:
V
U
T
Y
Z
T
U can only be in one of two positions: the third and the fifth, since it must have exactly one package between it and X (and X can only be in the first or seventh position). Therefore, two hypotheticals exist:
X _ U _ _ _ _
_ _ _ _ U _ X
In the first hypothetical, W must be second in order for U to be delivered after W (U>W).
X W U _ _ _ _
T must be fourth, since there must be one package between W and T.
X W U T _ _ _
The fifth package in this hypothetical can be either one of Z, Y, or V because any of these wouldn't violate any of the stated conditions; all conditoins are currently satisfied.
In the second hypothetical, U occupies the fifth position, and can thus be delivered fifth. Only T is not eliminated, so T cannot exist in the fifth position.
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