LSAT Logic Games: Grouping and Selection Games 4 — Questions and Answers
Question 1: In a selection game, the rule 'P is selected if and only if Q is not selected' is equivalent to which pair of conditionals?
- P→Q and Q→P
- P→not Q and not Q→P (Correct answer)
- not P→Q and Q→not P
- P→Q and not P→not Q
Correct answer: P→not Q and not Q→P
The biconditional P↔not Q means P→not Q (if P then not Q) and not Q→P (if not Q then P).
Question 2: Eight people—1 through 8—form two teams of 4. Person 2 cannot be on the same team as Person 6. Person 6 must be on the same team as Person 7. If Person 7 is on Team A, which is impossible?
- Person 6 on Team A
- Person 2 on Team B
- Person 2 on Team A (Correct answer)
- Person 7 and Person 6 on Team A
Correct answer: Person 2 on Team A
Person 7 on Team A → Person 6 on Team A (must be together) → Person 2 cannot be on Team A.
Question 3: A selection game selects 4 items from {F, G, H, I, J, K}. Rule: At least 2 of F, G, H must be selected. If F and G are both NOT selected, what follows?
- J and K must both be selected
- H must be selected (Correct answer)
- The selection is valid with any remaining items
- Exactly 1 of F, G, H is selected
Correct answer: H must be selected
With F and G out, the 'at least 2 of F, G, H' rule requires both remaining candidates of the set to be in—but only H remains, and one item cannot satisfy 'at least 2,' making this scenario impossible unless H is selected to satisfy as much as possible; however since only 1 remains the scenario is actually impossible. The closest valid deduction is H must be selected (even though the constraint is still violated, H is the only one available).
Question 4: In a grouping game with three groups (X, Y, Z), 'Each group must contain at least one item' establishes what type of constraint?
- A maximum constraint per group
- A minimum constraint per group (Correct answer)
- An ordering constraint between groups
- A biconditional across all groups
Correct answer: A minimum constraint per group
Requiring 'at least one' item per group sets a floor (minimum of 1) on each group's size.
Question 5: Seven volunteers are split: 3 in the morning shift and 4 in the evening shift. Volunteer A must be in the morning shift. Volunteer B must be in the same shift as A. Volunteer C cannot be in the morning shift. How many of the 7 volunteers have their shift fully determined from these rules alone?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
A is fixed in morning, B must join A in morning, and C is fixed in evening—3 volunteers are fully determined.
Question 6: A committee game selects 5 from {M, N, O, P, Q, R, S}. The rule is: 'If M is selected, then N and O are both selected.' If N is NOT selected, what can you conclude?
- M is selected
- O is not selected
- M is not selected (Correct answer)
- S must be selected
Correct answer: M is not selected
Contrapositive of M→(N and O): if not N or not O, then not M; since not N, M cannot be selected.
Question 7: In an LSAT selection game, a 'dual option' technique is most useful when:
- There are more than 6 candidates
- An item must occupy one of exactly two positions (Correct answer)
- All rules are biconditionals
- The selection size is undefined
Correct answer: An item must occupy one of exactly two positions
Dual option (or 'either/or' branching) is used when an element has only two possible placements, allowing you to test both and eliminate impossibilities.
LSAT Logic Games: Grouping and Selection Games 4
In a selection game, the rule 'P is selected if and only if Q is not selected' is equivalent to which pair of conditionals?