LSAT Logic Games : Solving grouping games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #181 : Solving Grouping Games
Eight bakers-- A, B, C, D, E, F, G, H-- are distributing their pies to exactly three grocery stores-- store 1, store 2, and store 3. Store 1 and 2 will get three pies each; store 3 will get two pies. The following conditions apply:
1. Pie A must be distributed to store 1.
2. Pie B must be distributed to store 3.
3. Neither pie B nor E can be sent to the same store as pie G.
4. Pie D cannot be sent to the same store as H.
5. If pie C is distributed to store 1, pie H must also be distributed to store 1.
If pie F is sent to grocery store 1, which of the following pies must be sent to store 2?
D
G
E
H
C
C
Rule 1 tells us pie A must go to store 1, so if pie F is also in store 1, there is only one slot left in store 1. We know pie C cannot fill this slot because of rule 5. Pie C cannot go to store 3 either, because then there would be no way to ensure that pies D and H, as well as pies G and E are split up in different stores (rules 3 and 4).
Pie C must go to store 2, otherwise there is no room to spread out the mutually exclusive pairs of pies.
Example Question #182 : Solving Grouping Games
Eight bakers-- A, B, C, D, E, F, G, H-- are distributing their pies to exactly three grocery stores-- store 1, store 2, and store 3. Store 1 and 2 will get three pies each; store 3 will get two pies. The following conditions apply:
1. Pie A must be distributed to store 1.
2. Pie B must be distributed to store 3.
3. Neither pie B nor E can be sent to the same store as pie G.
4. Pie D cannot be sent to the same store as H.
5. If pie C is distributed to store 1, pie H must also be distributed to store 1.
If pie F is sent to store 3, each of the following is a pair of pies that can be sent to store 1 EXCEPT:
Pies C and H
Pies E and H
Pies D and E
Pies D and G
Pies G and H
Pies C and H
If pie F is occupying the remaining slot in store 3 (remember rule 2 states pie B must always go to store 3) the mutually exclusive pairs outlined in rules 3 and four need to be split between stores 1 and 2. It is helpful to draw out this information at this point.
In order to split up the mutually exclusive pairs of pies, the only place for pie C is store two. This will exclude any answer choice that places pie C in store 1.
Therefore, the correct answer is "Pies C and H."
Example Question #692 : Lsat Logic Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
Which one of the following could be the assignment of athletes to sports?
Basketball: Engstrom, Garcia
Rugby: Hooper, Dalton
Soccer: Carter, Franklin
Basketball: Carter, Dalton
Rugby: Engstrom, Garcia
Soccer: Franklin, Hooper
Basketball: Carter, Engstrom
Rugby: Dalton, Hooper
Soccer: Franklin, Garcia
Basketball: Garcia, Hooper
Rugby: Engstrom, Franklin
Soccer: Carter, Dalton
Basketball: Engstrom, Franklin
Rugby: Carter, Hooper
Soccer: Dalton, Garcia
Basketball: Carter, Engstrom
Rugby: Dalton, Hooper
Soccer: Franklin, Garcia
The correct answer choice is the only one that does not violate the listed conditions. The remaining answer choices violate at least one condition and thus fail to assign the athletes to the correct sports.
Example Question #693 : Lsat Logic Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
If Carter and Hooper do not play rugby, then which one of the following could be true?
Carter and Garcia play basketball.
Dalton and Engstrom play rugby.
Dalton and Garcia play rugby.
Carter and Dalton play soccer.
Dalton and Engstrom play soccer.
Carter and Dalton play soccer.
Carter and Dalton could play soccer under these circumstances. The remaining answer choices violate one or more conditions. Because Hooper would be forced to play basketball under these circumstances, Carter and Garcia could not play basketball. Dalton and Engstrom could not both play rugby, because this would force Garcia to play basketball with Hooper, and Garcia must play soccer if Dalton plays rugby. If Dalton and Engstrom play soccer, Carter has no sport to play without violating conditions. Finally, Dalton and Garcia can never both play rugby.
Example Question #694 : Lsat Logic Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
If Dalton plays rugby, what is the total number of players any one of whom could also play rugby?
Four
One
Two
Three
Five
Three
Exactly three players could play rugby with Dalton: Carter, Franklin, and Hooper. Garcia can never play rugby when Dalton plays rugby. Further, Engstrom cannot play rugby under these circumstances because if he did, Garcia and Hooper would have to play the same sport. But this is not possible, because Hooper cannot play soccer and Garcia must play soccer if Dalton plays rugby; therefore, they cannot play the same sport without violating a condition.
Example Question #695 : Lsat Logic Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
If Dalton and Engstrom play the same sport, each of the following could be true EXCEPT:
Engstrom plays rugby.
Garcia plays basketball.
Franklin plays rugby.
Dalton plays basketball.
Carter plays soccer.
Engstrom plays rugby.
If Dalton and Engstrom play the same sport, Garcia and Hooper must also play the same sport. However, Dalton and Engstrom cannot ever both play rugby. This is because Hooper cannot play soccer, yet Garcia would be forced to play soccer under those circumstances -- thus, pairing them in the same sport would be impossible without violating a condition. The remaining answer choices could be true under these circumstances.
Example Question #696 : Lsat Logic Games
Six athletes -- Carter, Dalton, Engstrom, Franklin, Garcia, and Hooper -- are assigned to play for local sports teams. Each athlete will be assigned to play one of three sports -- basketball, rugby, or soccer. Two athletes are assigned to play each sport, and no athlete may play more than one sport. The assignments are subject to the following constraints:
If Carter and Dalton play the same sport, Engstrom and Garcia play the same sport.
Hooper cannot play soccer.
If Dalton plays rugby, then Garcia does not play basketball or rugby.
Carter and Hooper may play the same sport only if Engstrom plays soccer.
Dalton and Engstrom may play the same sport only if Garcia and Hooper play the same sport.
If Hooper and Franklin both play rugby, which one of the following CANNOT be true?
Garcia plays basketball.
Dalton plays soccer.
Carter and Garcia play the same sport.
Engstrom and Garcia play the same sport.
Carter and Engstrom play the same sport.
Carter and Garcia play the same sport.
Under these circumstances, Carter and Garcia cannot play the same sport. This would force Dalton and Engstrom to play the same sport, which cannot occur unless Garcia and Hooper also play the same sport. With Hooper and Garcia already paired, this would be impossible. The remaining answer choices could be true under these circumstances.
Example Question #692 : Lsat Logic Games
Seven racecars—Black, White, Red, Yellow, Purple, Green, and Orange--finish a race. No two cars finish with the same time and no other cars compete in the race.
All of the following are true:
Purple finishes at some time before Green.
White finishes at some time after Red but at some
time before Orange.
Green finishes at some time after Yellow.
Orange finishes at some time after Yellow but at some time
before Black.
Which of the following could be the order in which the cars finish, from first to last?
Red, Purple, Yellow, White, Black, Green,
Orange
Red, White, Yellow, Green, Orange,
Purple, Black
Yellow, Purple, Red, White, Orange,
Black, Green
Purple, Red, Green, White, Yellow,
Orange, Black
Purple, Yellow, Red, Green, Orange,
White, Black
Yellow, Purple, Red, White, Orange,
Black, Green
Only the correct answer--"Yellow, Purple, Red, White, Orange, Black, Green"--doesn't violate one of the four pieces of information you are given about the order in which the cars finish. For instance, "Red, Purple, Yellow, White, Black, Green, Orange" violates the rule "Orange finishes sometime after Yellow but sometime before Black" since it has Orange coming in last. If you have trouble keeping track of the order, try making a list of the racecars systematically, using each piece of information in order to fill in gaps. Or go through each answer choice with the four rules you are given in mind, looking for any violations. You can dismiss an answer choice as soon as you see that it violates a single rule.
Example Question #183 : Solving Grouping Games
Seven racecars—Black, White, Red, Yellow, Purple, Green, and Orange--finish a race. No two cars finish with the same time and no other cars compete in the race.
All of the following are true:
Purple finishes at some time before Green.
White finishes at some time after Red but at some
time before Orange.
Green finishes at some time after Yellow.
Orange finishes at some time after Yellow but at some time
before Black.
Given the above information, all of the following could be true EXCEPT:
Orange finishes before Green.
Green finishes before Red.
Red finishes after Black.
Yellow finishes after White.
Black finishes before Purple.
Red finishes after Black.
All of the answer choices are possible given the information, EXCEPT for "Red finishes after Black," because that violates the rules "White finishes at some time after Red but at some time before Orange" and "Orange finishes at some time after Yellow but at some time before Black." Combining those rules, you will see that Orange finishes before Black and Red finishes before Orange, so therefore Red must finish before Black.
Example Question #694 : Lsat Logic Games
Seven racecars—Black, White, Red, Yellow, Purple, Green, and Orange--finish a race. No two cars finish with the same time and no other cars compete in the race.
All of the following are true:
Purple finishes at some time before Green.
White finishes at some time after Red but at some
time before Orange.
Green finishes at some time after Yellow.
Orange finishes at some time after Yellow but at some time
before Black.
If Yellow finishes fourth, which one of the following could
correctly list in what order some of the other cars finished?
Red second; Orange sixth
Red third; Black seventh
Purple first; White fifth
White third; Black fifth
Purple second; Orange third
Red second; Orange sixth
Only the answer choice listing "Red second; Orange sixth" does not violate any of the rules set by the question. If Yellow comes in fourth, Red could come before fourth and Orange after it, because of the rules "Orange finishes at some time after Yellow..." and "White finishes at some time after Red but at some time before Orange." (The latter statement implies that, regardless of the consecutive ordering of the cars, Red will always come before White, which will come before Orange, so Red will always come in ahead of Orange.) The other answer choices violate the rules set by the question and therefore are not correct.
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