LSAT Logic Games : Solving grouping games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #211 : Solving Grouping Games
Seven college football players—Fogel, Glenn, Hoskins, Innis, Wells, Xia, and Yates—have been drafted by a professional football team. One draftee is a kicker, three are offensive players, and three are defensive players. The following conditions apply in regards to which players fall within these three domains of the game:
- Hoskins and Yates play the same position
- Glenn does not play within the same domain as Fogel
- If Xia plays defense, then Wells plays offense
- Fogel plays offense
Each of the following could be an accurate partial list of the players who play defense EXCEPT __________.
Hoskins, Wells
Hoskins, Xia
Glenn, Innis
Glenn, Xia
Glenn, Yates
Glenn, Xia
The correct answer is the pair that CANNOT play defense together, while the wrong answers are legitimate potential pairs.
If Glenn and Xia play defense, then there is no room for Wells in the offense domain because the rules require that Fogel be there, along with Hoskins and Yates.
Example Question #212 : Solving Grouping Games
Seven college football players—Fogel, Glenn, Hoskins, Innis, Wells, Xia, and Yates—have been drafted by a professional football team. One draftee is a kicker, three are offensive players, and three are defensive players. The following conditions apply in regards to which players fall within these three domains of the game:
- Hoskins and Yates play the same position
- Glenn does not play within the same domain as Fogel
- If Xia plays defense, then Wells plays offense
- Fogel plays offense
If Fogel plays a position within the same domain as Xia, then each of the following could be true EXCEPT __________.
Innis plays defense
Glenn plays defense
Wells plays offense
Wells is a kicker
Hoskins plays offense
Hoskins plays offense
By rule, Fogel plays offense. The added rule from this question puts Xia on offense, too. That means Hoskins and Yates, who must stay together, must play defense; therefore, Hoskins cannot play offense, and that is the credited response.
Example Question #213 : Solving Grouping Games
Seven college football players—Fogel, Glenn, Hoskins, Innis, Wells, Xia, and Yates—have been drafted by a professional football team. One draftee is a kicker, three are offensive players, and three are defensive players. The following conditions apply in regards to which players fall within these three domains of the game:
- Hoskins and Yates play the same position
- Glenn does not play within the same domain as Fogel
- If Xia plays defense, then Wells plays offense
- Fogel plays offense
Which one of the following is a complete and accurate list of the players, each of whom CANNOT be drafted to play offense?
Innis
Fogel, Innis, Xia
Glenn
Glenn, Hoskins, Yates
Hoskins, Yates
Glenn
Fogel, Hoskins, and Yates can play offense. That fact eliminates all reponses, except the response specifying Glenn and the response specifying Innis. Innis could play offense if Hoskins and Yates play defense. But under no circumstances can Glenn play offense, by virtue of the rule that bars joining Glenn and Fogel.
Example Question #214 : Solving Grouping Games
Seven college football players—Fogel, Glenn, Hoskins, Innis, Wells, Xia, and Yates—have been drafted by a professional football team. One draftee is a kicker, three are offensive players, and three are defensive players. The following conditions apply in regards to which players fall within these three domains of the game:
- Hoskins and Yates play the same position
- Glenn does not play within the same domain as Fogel
- If Xia plays defense, then Wells plays offense
- Fogel plays offense
It can be determined in which domain each of the seven drafted players can play if which one of the following statements is true?
Innis and Wells are both drafted to play offense.
Innis and Xia are both drafted to play offense.
Innis and Wells are both drafted to play defense.
Fogel and Wells are both drafted to play offense.
Glenn and Yates are both drafted to play defense.
Innis and Wells are both drafted to play defense.
If we place Hoskins and Yates in the offense domain (note there are only two possibilities for H and Y—either in offense or defense—since they are required to be together), then we can deduce that Xia must be a kicker, since it is impossible for Xia to play defense under these circumstances. Why? Because if Xia plays defense, then Wells must play offense, but the offense slots are all taken (H,Y, F). With Xia in the kicker slot, and with Hoskins, Yates, and Fogel taking the offense slots, then we know that Wells, Glenn, and Innis occupy the defense slots.
Therefore, the credited reponse is "Innis and Wells are both drafted to play defense."
Example Question #215 : Solving Grouping Games
A successful recruiting drive by the local laser tag league has lead to the recruitment of seven new recruits-- P, Q, R, S, T, U, and V. After completing their initial training, they will all be assigned to one of the laser tag league's four teams-- Dragon, Salamander, Phoenix, and Rabbit. Their assignment to the teams must conform to the following conditions:
At least one new member is assigned to each of the four teams.
Q and T are not assigned to the same team if R and V are not assigned to the same team.
If T is not assigned to Dragon, then U is not assigned to Dragon.
P is always on a team with more new recruits than S.
Dragon gets more new recruits than any other team
Which of the following, if true, means that P must be assigned to Dragon?
S is assigned to Phoenix and U is assigned to Rabbit.
R is assigned to Phoenix and S is assigned to Rabbit.
U is assigned to Dragon and T is assigned to Dragon.
Q is assigned to Phoenix and S is assigned to Rabbit.
Q is assigned to Salamander and T is assigned to Salamander.
Q is assigned to Salamander and T is assigned to Salamander.
[Q is assigned to Salamander and T is assigned to Salamander.]
If this is the case, then P must be assigned to Dragon. This mostly tests your ability to deal with the ~(RV) --> ~(QT) rule, and its contrapositive, (QT) --> (RV).
d:
s: Q, T
p:
r:
To proceed from here, you really need to have written down the contrapositive mentioned above into your rules. With that contrapositive, you know that R and V must be on a team together. Since, Dragon must have the most new recruits, R and V must both go to Dragon, and there will be exactly one other new recruit that joins them there.
d: R, V, _
s: Q, T
p: _
r: _
T is not assigned to Dragon, so U cannot be assigned to Dragon. Let's just put U in Phoenix.
d: R, V, _
s: Q, T
p: U
r: _
That leaves S and P. S cannot be assigned to Dragon, because there would be no way for P to join a team with more new recruits. Thus, S must join Rabbit. That means that P must be assigned to Dragon.
d: R, V, P
s: Q, T
p: U
r: S
Example Question #216 : 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.
If exactly one racecar finishes between Green and Black,
with either Green finishing before Black or Black
before Green, any of the following could be true
EXCEPT:
White finishes second and Yellow finishes fourth.
Purple finishes first and White finishes third.
Red finishes first and Orange finishes sixth.
Red finishes second and Green finishes fifth.
Purple finishes first and Green finishes seventh.
Purple finishes first and Green finishes seventh.
In this question, all of the answer choices are possible except for "Purple finishes first and Green finishes seventh." If Green finishes seventh and there is exactly one car in between Green and Black, then Black must finish fifth. Putting Purple in the first position, that leaves positions 2, 3, 4, and 6 for the cars Red, Orange, White, and Yellow. But since the rules state that "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," no car could be in the sixth position, because Orange is can be inferred to be the last of the cars we have not yet positioned, but must be positioned "before Black."
Example Question #217 : 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.
Which of the following could NOT be the finishing position of one of the racecars?
Red first
Yellow fourth
Orange sixth
Black seventh
Green second
Green second
All of the finishing positions listed would be possible except for "Green second" because the rules state that "Purple finishes at some time before Green" and "Green finishes at some time after Yellow." This means that Green must be in third place at best, since Purple and Yellow both finish before Green.
Example Question #218 : 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.
Which of the following would contradict the given information?
Purple finishes before Yellow.
Black finishes before White.
Red finishes after Yellow.
Red finishes before Green.
Black finishes after Green.
Black finishes before White.
All of the answer choices are possible without contradicting the given information except for "Black finishes before White" because of 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 these rules, we can see that White finishes before Orange and Orange finishes before Black, so White must finish before Black.
Example Question #219 : Solving Grouping Games
A preschool intends to purchase exactly six items for its classroom. The items fall within three categories: Books, Puzzles, and Toys. The Books are identified as A, B, and C. The Puzzles are identified as K, L, and M. The Toys are identified as T, U, and Z. The selection of classroom items must meet the following conditions:
A and C cannot both be selected.
M and T cannot both be selected.
If C is selected, K is also selected.
If K is selected, M is also selected.
Which one of the following is an acceptable selection of items for the classroom?
A, B, K, M, T, U
B, C, K, L, U, Z
B, C, K, M, U, Z
A, C, K, M, U, Z
B, C, L, M, U, Z
B, C, K, M, U, Z
This is an acceptability question. By applying the rules one by one and eliminating, the correct answer emerges, as the other answer choices will be shown to violate one of the rules.
Example Question #220 : Solving Grouping Games
A preschool intends to purchase exactly six items for its classroom. The items fall within three categories: Books, Puzzles, and Toys. The Books are identified as A, B, and C. The Puzzles are identified as K, L, and M. The Toys are identified as T, U, and Z. The selection of classroom items must meet the following conditions:
A and C cannot both be selected.
M and T cannot both be selected.
If C is selected, K is also selected.
If K is selected, M is also selected.
If C and L are among the items purchased, which one of the following could be true?
Z is purchased.
F is purchased.
T is purchased.
Exactly two Puzzles are purchased.
Exactly one Puzzle is purchased.
Z is purchased.
L is a wildcard, so it doesn't tell us anything. But C tells us a lot if we use the conditionals and the contrapositives. If C is purchased, then A is out and K is in, which means that M is in. With M in, T is out. So this set of deductions eliminate all answers except: "Z is purchased."
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