LSAT Logic Games : Two-Variable
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #101 : Two Variable
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If D is assigned to the fifth slot, then which of the following must be assigned to the sixth slot?
F
E
A
C
B
B
With D in the fifth slot, E and F must be in the first two slots. If A is in the third slot, and since B must come after C, this leaves C in the fourth slot and B in the sixth slot. If C is in the third slot, and since B and C cannot be consecutive, again B must be in the sixth slot.
Example Question #102 : Two Variable
A human resources manager must schedule a round of interviews during a particular day. Six different time slots are available in the afternoon and are numbered one through six in sequential order. Six candidates - Joe, Jim, Mary, Bob, Jess, and Sue - must be scheduled during the afternoon. Only one candidate can occupy each interview slot. The assignment of interview slots is subject to the following restrictions:
- Either Mary or Bob must occupy the second time slot.
- Joe must occupy the sixth time slot.
- Mary and Bob cannot occupy consecutive time slots.
- Jim and Mary must occupy consecutive time slots.
- Sue must be interviewed before Jess.
If Jim is assigned to the fourth slot, which of the following must be true?
Sue must occupy the third slot.
Mary must occupy the fifth slot.
Jess must occupy the first slot.
Bob must occupy the third slot.
Mary must occupy the third slot.
Mary must occupy the fifth slot.
The only restriction that involves Jim is that he and Mary must occupy consecutive slots. Therefore, if Jim occupies the fourth slot, Mary must occupy the third or fifth slot. Since Mary can't be in the second slot, Bob must be assigned to this slot. Lastly, Mary and Bob cannot occupy consecutive slots. So if Bob is in the second slot, Mary cannot be in the third slot. Mary must be in the fifth time slot. Now the 2nd, 4th, 5th, and 6th slots are all accounted for. Finally, since Sue must be interviewed before Jess, Sue must be 1st and Jess must be 3rd.
Example Question #103 : Two Variable
A talent show contest must schedule a round of preliminary auditions to be aired on television. The show will be broken up into six segments, and each contestant will occupy a different segment. Six contestants - lettered A, B, C, D, E, and F to prevent bias - will be scheduled for the contest. Only one contestant can occupy each audition segment. The assignment of auditions is subject to the following restrictions:
- E and F must occupy consecutive time slots.
- Either A or C must occupy the third time slot.
- A must audition before D.
- B must audition after C.
- B and C cannot occupy consecutive time slots.
If C is assigned to the third time slot, then which of the following must be true?
A must be assigned to the second time slot.
F must be assigned to the fifth time slot.
B must be assigned to the sixth time slot.
E must be assigned to the fifth time slot.
A must be assigned to the fourth time slot.
A must be assigned to the fourth time slot.
The only statement that must be true is that A must be assigned to the fourth time slot. B cannot be consecutive with C but must come before C, which leaves only the fifth or sixth slots for B. Because E and F must be consecutive, they must be in slots one and two. Since A must come before D, D must either be fifth or sixth. Therefore, A must be in the fourth slot.
Example Question #371 : Linear Games
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
Which of the following is a complete and accurate order in which the packages could be delivered?
B, F, D, E, C, A
F, A, C, E, D, B
A, D, E, C, B, F
D, E, C, A, B, F
F, A, D, B, E, C
D, E, C, A, B, F
F must be first or last, which eliminates one answer. D must come before C, which eliminates another. E must be immediately surrounded by D and C, which eliminates yet another. And the last we take out because A cannot be first.
Example Question #372 : Linear Games
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
Which of the following must be true?
If Package B is delivered third, then Package E is delivered fifth
Package A cannot be delivered last
Package B must be delivered sometime before Package C
Package B cannot be delivered first
If Package F is delivered first, then Package A is delivered last
If Package B is delivered third, then Package E is delivered fifth
If Package B is delivered third, then the only place the DEC block can fit is in spots four, five and six, respectively. Therefore we know the only place E could go is in spot five, which means it must be true.
Example Question #373 : Lsat Logic Games
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
If Package A is delivered second, which of the following could be true?
Package E is delivered third
Package B is delivered fourth
Package B is delivered first
Package C is delivered fourth
Package D is delivered fifth
Package B is delivered first
If Package A is delivered second, there are only two spots where the DEC block can fit: either in spots three, four and five, or four, five and six. Leaving us with two possible set ups:
_ A D E C _ OR _ A _ D E C
Leaving us to place F and B. In the first solution, F and B are interchangeable - since the only rule we are working with is that F must go either first or last. In the second solution, F must go first, leaving us with only one way to solve. Therefore, the following three solution are the only possibilities:
F A D E C B; B A D E C F; F A B D E C
Example Question #373 : Linear Games
A Postman has six packages to deliver: A, B, C, D, E and F. He must deliver all of the packages, and each package is delivered to a different address. The order in which he delivers the packages must conform to the following restrictions:
- Package E must be the only package delivered between packages C and D
- Package A cannot be the first, third or fifth package delivered
- Package D must be delivered sometime before Package C
- Package F must be either the first or last package delivered
Which of the following, if true, would determine the order in which every package must be delivered?
Package E is delivered fourth
Package F is delivered first
Package C is delivered third
Package A is delivered last
Package F is delivered last
Package C is delivered third
If Package C is third, the we know that package D and E must be second and third, respectively.
_ D E C _ _
Package A cannot go first or fifth, so we must place it last.
_ D E C _ A
F must then go first, and we fill in B in the second spot.
F B D E C A
Example Question #101 : Two Variable
A photographer is hanging six portraits on the wall in a straight line. The portraits are of six family members: Lily, Mildred, Nancy, Owen, Peter and Quentin. The order in which the portraits are hung must conform to the following restrictions:
Mildred's portrait must be either first or last
There must be exactly one portrait between Nancy and Quentin
Nancy's portrait must come after Lily's but before Quentin's
If Mildred's portrait is first, which is a complete and accurate list of all the possible portraits that could appear second?
Nancy, Owen Peter, Lily
Owen, Peter
Nancy, Owen, Peter
Owen, Lily, Peter
Owen, Lily
Owen, Lily, Peter
Knowing that Mildred's portrait comes first lets us plot out the possible locations for the Nancy/Quentin block. They can either go in spots three and five or four and six, respectively. (Nancy cannot go in spot two, because Lily has to come before her.) This creates two possibilities for solutions. The first, with Nancy and Quentin in spots three and six gives us Lily in two, and either Peter or Owen in four and the other one in six. The second possibility with Nancy and Quentin in spots four and six gives us the option of Peter, Lily or Owen for spots two and three, and then whomever is left of Peter and Owen for spot five. Therefore, considering both possibilities the only people who could occupy the second spot when Mildred is in the first spot are Owen, Lily and Peter.
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