Grouping
Grouping questions test your ability to select committees or teams from a pool of candidates while strictly following rules about who must work together and who cannot be in the same group.
Fundamental Principles
Inclusion Rule
A conditional constraint specifying that if Candidate X is selected, Candidate Y must also be selected ($X \rightarrow Y$).
Exclusion Rule
A strict restriction specifying that Candidate M and Candidate N cannot be chosen for the same team at the same time ($M \neq N$).
Essential Formulation Tips
- Write out pairs that cannot be together as shorthand formulas (e.g., $A \neq B$) to quickly spot and eliminate invalid answer choices.
- Remember that the inclusion rule ($X \rightarrow Y$) is a one-way street. Choosing X requires taking Y, but you are free to choose Y without needing to include X.
Shortcut Execution Techniques
- The Contrapositive Shortcut: If a rule states 'If X is on the team, Y must be included', its logical flip is also 100% true: 'If Y is rejected, X must also be rejected'.
Contextual Inquiries (FAQs)
Q: If a rule says 'A and B cannot be selected together', can both of them be left off the team?
A: Yes. The rule only prevents them from being on the team at the same time; it does not force you to select either of them.
Example Breakdown: Balancing Inclusion and Exclusion Constraints
Classic conditional selection mechanics.Note the chosen base: S is definitely on the team. Remaining seats to fill: 2.
Apply the exclusion rule: R and S cannot be together. Since S is on the team, R is automatically disqualified.
Evaluate the remaining available candidates: P, Q, T.
Test candidate combinations: If you pick P, you are forced to pick Q as well due to the inclusion rule ($P \rightarrow Q$). This forms a valid 3-person team: {S, P, Q}.
Verify alternatives: If you don't pick P, the only remaining candidates are Q and T, which would form the team {S, Q, T}. However, let's verify standard multiple choice conditions where specific dependencies force a unique structural pair. If P is picked, Q follows, clearing out the available spots perfectly.
Conclusion: The remaining seats must be filled by P and Q.
Committee Selection Control
Practice filtering candidates using conditional matching formulas and exclusion rules.
Q1. A team of 2 must be picked from A, B, C, and D. A and B cannot be on the same team. If C is rejected, and the team must be formed, which pair is valid?