Direction: After months of talent searching for an administrative assistant to…

2023

Direction: After months of talent searching for an administrative assistant to the president of the college, the applicants have been narrowed down to 5 — A, B, C, D, E. It was announced that the finalist would be chosen after a series of all-day group & personal interviews were held. The examining committee agreed upon the following procedure.

I. The interviews will be held once a week.

II. 3 candidates will appear at any all-day interview session.

III. Each candidate will appear at least once.

IV. If it becomes necessary to call applicants for additional interviews, no more than 1 such applicant should be asked to appear the next week.

V. Because of a detail in the written applications, it was agreed that whenever candidate B appears, A should also be present.

VI. Because of travel difficulties it was agreed that C will appear for only 1 interview.

If A, B and D appear for the interview and D is called for additional interview the following week, which 2 candidates may be asked to appear with D?

I. A

II. B

III. C

IV. E

  1. A.

    I and II

  2. B.

    I and III only

  3. C.

    II and III only

  4. D.

    III and IV only

Show answer & explanation

Correct answer: D

Concept:

In an attribute-based multi-variable arrangement puzzle, every stated rule is a hard constraint. Before asking who CAN join a session, first eliminate anyone who WOULD trigger a repeat, dependency, or quota violation under the given rules.

Rules that govern this puzzle:

  • Rule IV: at most one candidate who already appeared may be called back the following week.

  • Rule III: every one of the five candidates must appear at least once.

  • Rule V: whenever B appears, A must also appear.

  • Rule VI: C may appear in only one interview session in total.

Application:

  1. Week 1 session = A, B and D (given in the question).

  2. D is named as the one candidate called back for an additional interview in Week 2, so D occupies the single repeat slot Rule IV allows for that week.

  3. Because that repeat slot is already used by D, A and B — both already interviewed in Week 1 — cannot be called again; adding either of them would create a second repeat-candidate, breaking Rule IV.

  4. Rule III requires all five candidates to appear at least once. C and E have not appeared yet, so they must be the two who complete the 3-candidate Week 2 session alongside D.

  5. Checking the remaining rules: C appearing in Week 2 is C's only interview, so Rule VI holds; B is absent from Week 2, so Rule V (which is only triggered by B's presence) never applies.

Cross-check:

Any pairing that brings back A or B reintroduces a second repeat-candidate and fails Rule IV. Any pairing that leaves out C or E means a candidate is never interviewed, failing Rule III. The only pairing consistent with every rule at once is D together with C and E.

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