LSAT Logic Games : Grouping Games
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #11 : 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 cannot be true?
Q is assigned to Dragon and U is assigned to Dragon.
S is assigned to Salamander and Q is assigned to Salamander.
S is assigned to Salamander and T is assigned to Rabbit.
P is a assigned to Dragon and U is assigned to Dragon.
R is assigned to Phoenix and T is assigned to Dragon.
Q is assigned to Dragon and U is assigned to Dragon.
[Q is assigned to Dragon and U is assigned to Dragon.]
If U is assigned to Dragon, then T must also be assigned to Dragon. This is the contrapositive of the rule that U is not in Dragon if T is not in Dragon.
Dragon: Q, U, T
Salamander:
Phoenix:
Rabbit:
If Q and T are together, then R and V must also be together. This is the contrapositive of the rule that if R and V are not together, then Q and T are not together. Now, we can't put both R and V in Dragon, because then there wouldn't be enough recruits to distribute to other teams. For now, let's put them in Salamander.
Dragon: Q, U, T
Salamander: R, V
Phoenix:
Rabbit:
We must still deal with P and S. P must be in a group with more new recruits than S, so it it would have to go in Dragon or Salamander. Unfortunately, that would mean that either Phoenix or Rabbit would be left without a recruit, which is unacceptable.
Thus, we know that Q and U cannot both be in Dragon together.
Example Question #12 : 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.
If Q and T are both assigned to the same team and only one new recruit is assigned to Rabbit, then which of the following is a complete list of the recruits that could possibly be assigned to Rabbit?
S
R, S, U, V
S, U
U
S, U, V
S, U
If Q and T are paired together, then R and V must be paired together, thanks to the contrapositive to the rule regarding those pairs. If that's the case, then we know that P is assigned to one of the two teams to which R and V and Q and T are assigned, of which one is Dragon. Since Rabbit is only getting one new recruit, then we know that P, Q, T, R, and V are not going to be available to be assigned to Rabbit. That leaves only S and U, neither of which are restricted in this case from being assigned to any particular teams, only from being assigned to the teams that are already made full by the QT and RV pairs.
Example Question #11 : 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.
If P is assigned to Salamander, which of the following must be false?
Q is assigned to Dragon and V is assigned to Salamander.
R is assigned to Dragon and S is assigned to Phoenix.
R and U are on separate teams.
Q is assigned to Phoenix and S is assigned to Rabbit.
T is assigned to Dragon and U is assigned to Dragon.
Q is assigned to Dragon and V is assigned to Salamander.
If P is assigned to Salamander, then you know you're dealing with a 3/2/1/1 distribution of the recruits. Furthermore, you know that Q and T can never be placed in the same team, because there would be no place to put R and V. S must be on one of the teams that only recruits one person, meaning it is not on Dragon nor is it with P (although P and S are never together anyway).
d: _ _ _
s: P, _
p: S
r: _
This means we need to deal with Q, R, T, U, and V. We know that U cannot be in Dragon unless T is. That means we're going to have two separate diagrams-- one with T and U in Dragon and one where that is not the case.
d: R, U, T
s: P, V
p: Q
r: S
However, when we actually attempt to make a diagram without both T and U in Dragon, we run into a problem.
d: Q, R, U?
s: P, V
p: S
r: T
d: Q, R, T?
s: P, V
p: S
r: U
U cannot be in Dragon if T is not in Dragon. If U is not in Dragon, then either T or V must take up the slack. However, putting T in Dragon is problematic, then you have a QT pair which requires you to do R, V, which is impossible given the constraints.
Thus, the diagram without T and U in Dragon looks like the following:
d: Q, R, V
s: P, U
p: S
r: T
There are some slight variations in these diagrams, but, when you compare it against the answer choices, you'll see that [Q is assigned to Dragon and V is assigned to Salamander.] is an impossibility. In order to place those, you're forced into a situation where Q and T are on the same team, but there is no way to put R and V together, since P and V ae already together.
Example Question #521 : Lsat Logic 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.
If V and P are assigned to Rabbit, then which of the following could be true?
T is assigned to Salamander.
R is assigned to Salamander.
U is assigned to Phoenix.
Q is assigned to Phoenix.
Q is assigned to Dragon.
Q is assigned to Phoenix.
If V and P are both assigned to a non-Dragon team (in this case, Rabbit), then the rest of the diagram gets more or less fully filled in (non-Dragon teams are generally interchangeable).
For example:
d: T, U, R
s: V, P
p: S
r: Q
The essential aspect of that diagram is that T, U, and R are assigned to Dragon. If V and P are together, then we know that Q and T must be separated. S, again, must be one of the one-recruit teams. Thus, in order to fill in Dragon, we're going to NEED three of Q, T, U, and R. If Q and T can't be together, then we have a choice between T, U, and R and Q, U, and R. If U is a Dragon though, then T must be a Dragon. Thus the T, U, R assignment to Dragon is necessary. Thus, incorrect or false answer choices must interfere with the T, U, R assignment to Dragon.
If you compare the answer choices versus the diagram above, then the correct answer becomes obvious.
Example Question #13 : Solving Grouping Games
A company sells gum in eight sticks per pack. Each pack contains at least one of the company's four gum flavors, which are apple, grape, watermelon, and lychee. Each individual stick is wrapped in either green, red, or yellow paper. For every pack of gum, the following conditions are met:
1. Apple and grape are only wrapped in green or red
2. Watermelon is never wrapped in green
3. If there are more than three reds in a pack, there must be at least two yellows
4. The number of sticks of watermelon is always less than the number of sticks of lychee
Which of the following could one potentially find if they bought a pack of gum from this company?
3 red lychee, 2 green apple, 1 red watermelon, 1 green grape, 1 yellow watermelon
3 yellow lychee, 2 yellow watermelon, 1 red grape, 1 green watermelon, 1 red apple
2 green lychee, 2 red apple, 2 yellow watermelon, 1 green grape, 1 green apple
3 yellow watermelon, 2 red grape, 1 green apple, 1 yellow lychee, 1 green grape
2 green apple, 2 red lychee, 1 red watermelon, 1 green grape, 1 yellow lychee, 1 yellow watermelon
2 green apple, 2 red lychee, 1 red watermelon, 1 green grape, 1 yellow lychee, 1 yellow watermelon
This is the only combination that satisfies all the premises: the apple and grape are only wrapped in green or red, watermelon isn't ever wrapped in green, there are at least two yellow since there are at least three red, and there are less watermelon than there are lychee.
Example Question #11 : Grouping Games
A company sells gum in eight sticks per pack. Each pack contains at least one of the company's four gum flavors, which are apple, grape, watermelon, and lychee. Each individual stick is wrapped in either green, red, or yellow paper. For every pack of gum, the following conditions are met:
1. Apple and grape are only wrapped in green or red
2. Watermelon is never wrapped in green
3. If there are more than three reds in a pack, there must be at least two yellows
4. The number of sticks of watermelon is always less than the number of sticks of lychee
If a pack contains 3 green, 3 red and 2 yellow, what is the minimum number of watermelon in the pack?
2
3
Cannot be determined
5
1
1
This problem can be solved by simply testing to see if 1, the absolute minimum, is possible. One possible scenario is the following: 2 green apple, 2 yellow lychee, 2 red grape, 1 green apple, 1 red watermelon
Example Question #12 : Grouping Games
A company sells gum in eight sticks per pack. Each pack contains at least one of the company's four gum flavors, which are apple, grape, watermelon, and lychee. Each individual stick is wrapped in either green, red, or yellow paper. For every pack of gum, the following conditions are met:
1. Apple and grape are only wrapped in green or red
2. Watermelon is never wrapped in green
3. If there are more than three reds in a pack, there must be at least two yellows
4. The number of sticks of watermelon is always less than the number of sticks of lychee
All of the following are true EXCEPT:
It would be possible to have a pack with only green and red wrappers.
It would be possible to have a pack with 6 yellow wrappers.
It would be possible to have a pack with 7 green wrappers.
It would be possible to have a pack with 7 red wrappers.
None of the above
It would be possible to have a pack with 7 red wrappers.
It is impossible to have 7 red wrappers in a pack because, according to the third premise, if there are more than three red then there must be at least two yellow. If there are 7 red, that means there are more than three red but there's only one left. Therefore, there cannot be two yellows.
Example Question #16 : Solving Grouping Games
A company sells gum in eight sticks per pack. Each pack contains at least one of the company's four gum flavors, which are apple, grape, watermelon, and lychee. Each individual stick is wrapped in either green, red, or yellow paper. For every pack of gum, the following conditions are met:
1. Apple and grape are only wrapped in green or red
2. Watermelon is never wrapped in green
3. If there are more than three reds in a pack, there must be at least two yellows
4. The number of sticks of watermelon is always less than the number of sticks of lychee
If a pack contains 3 red watermelon, which of the following could be true?
There are 2 yellow watermelon
None of these
There are 3 red apple
There is 1 green watermelon
There are 3 green grape
None of these
There couldn't be 3 red watermelon and 3 green grape because there would be only 2 remaining, meaning there would be less lychee than watermelon, which violates the fourth Premise. Additionally, since at least 1 of the remaining sticks would have to be apple, then that stick would have to be either green or red, meaning only one stick would be yellow. This violates the third premise.
The couldn't be 3 red watermelon and 1 green watermelon because according to the second premise you can't have green watermelon. Additionally, there would only be 4 left, and since 1 would have to be apple and 1 would have to be grape there could only be a maximum of 2 lychee, which is less than the number of watermelon, which violates the fourth premise.
There couldn't be 3 red watermelon and 3 red apple because of the 2 remaining, 1 would have to be lychee and the other would have to be grape. Since grape can't be yellow, there would be 6 red and 1 yellow, which violates the third premise.
There couldn't be 3 red watermelon and 2 yellow watermelon because there would be 5 watermelon. No matter what, in this case there would be more watermelon than lychee, which violates the fourth premise.
Example Question #13 : Grouping Games
A company sells gum in eight sticks per pack. Each pack contains at least one of the company's four gum flavors, which are apple, grape, watermelon, and lychee. Each individual stick is wrapped in either green, red, or yellow paper. For every pack of gum, the following conditions are met:
1. Apple and grape are only wrapped in green or red
2. Watermelon is never wrapped in green
3. If there are more than three reds in a pack, there must be at least two yellows
4. The number of sticks of watermelon is always less than the number of sticks of lychee
If a pack contains 2 red and 3 green, which of the following MUST be true?
The pack contains at least 2 watermelon.
It is possible for the pack to contain 3 yellow watermelon.
The pack contains 4 yellow.
None of these
It is possible for both of the red to be apple.
It is possible for both of the red to be apple.
Both of the reds could be apple because we are able to come up with a scenario in which this is true and no premises are violated, e.g.: 2 red apple, 2 green lychee, 2 yellow watermelon, 1 green grape, 1 yellow lychee.
Example Question #11 : Solving Grouping Games
The chef at a La Maison, a popular French restaurant, is famous for making nine different dishes: three beef dishes - A, B and C; three poultry dishes - L, M and N; and three fish dishes - X, Y and Z. La Maison's special tasting menu always consists of exactly five of its chef's famous dishes. Each month, the chef changes the dishes on the tasting menu, choosing from among his famous dishes in accordance with the following conditions:
There must be exactly one fish dish on the menu.
If Z is not on the menu, A cannot be on the menu.
No more than two beef dishes can be on the menu.
If both L and Y are on the menu, B cannot be on the menu.
If A is on the menu, N cannot be on the menu.
Unless both C and X are on the menu, M cannot be on the menu.
Which one of the following could be La Maison's tasting menu for the month of February?
B, C, L, N, Z
A, B, C, L, Z
B, C, L, N, Y
A, C, N, Y, Z
A, B, M, X, Z
B, C, L, N, Z
All of the incorrect answers violate at least one condition.
The first condition eliminates {A, B, M, X, Z} and {A, C, N, Y, Z}. Each has more than one fish dish.
The third condition eliminates {A, B, C, L, Z}, as it has more than two beef dishes.
The fourth condition eliminates {B, C, L, N, Y}, which contains B, L and Y on the same menu.
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