Fall Start Eligibility Under Conditional Admissions Rules
A specialized master's program admits students to a fall or spring start. The rules are: (1) an applicant is admitted only if they have both a quantitative background (Q) and an English certification (L); (2) an admitted student who lacks an internship (I) must complete a summer bridge course (B); (3) any student who takes B starts in spring, while all other admitted students start in fall; (4) exactly two of the four applicants have an internship.
The applicants are: Anna - Q yes, L yes, I no; Ben - Q yes, L yes, I yes; Carla - Q no, L yes, I yes; Dan - Q yes, L no, I no. The program has one fall seat available beyond Ben and is considering several rule changes, but for now the rules above are fixed.
1. Under the fixed rules, who is admitted, and who starts in fall? Explain how each rule applies.
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Admission requires both Q and L.
- Anna: Q yes, L yes → admitted. She lacks I, so rule 2 requires bridge course B; under rule 3 she starts in spring.
- Ben: Q yes, L yes → admitted. He has I, so no B; he starts in fall.
- Carla: Q no → not admitted, even though she has L and I.
- Dan: L no → not admitted, even though he has Q.
Only Ben starts in fall. Anna is admitted but deferred to spring by the bridge requirement, and Carla and Dan fail the admission condition. The fact that exactly two applicants have an internship (Ben and Carla) does not change the outcome, because Carla is not admitted.
2. The director proposes giving Dan an English certification so that the program will have exactly two fall starters. Does that change achieve the goal? Justify your answer using the rules.
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No. Giving Dan L makes him Q yes and L yes, so he becomes admitted. But Dan still has I no. Rule 2 therefore requires Dan to take B, and rule 3 sends any B student to a spring start. The fall starters remain only Ben (and possibly Anna if Anna's internship status changes, but the proposal does not touch Anna).
To create a second fall starter, the change must either (a) remove the bridge requirement for an admitted student who lacks I, or (b) admit a student who already has I. For example, giving Anna an internship would let Anna start in fall; alternatively, relaxing the Q requirement for Carla would admit Carla, who has I and would not need B. Giving Dan L alone does neither.
3. Suppose rule 1 is relaxed so that applicants lacking Q but holding I may be admitted conditionally, and conditional admits are exempt from the bridge course. Who then starts in fall?
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Under the relaxed rule, Carla is admitted conditionally because she lacks Q but has I. Conditional admits are exempt from B, so Carla starts in fall. Ben remains admitted with Q, L, and I, so he also starts in fall. Anna is still admitted but lacks I, so she must take B and starts in spring. Dan still lacks L and does not qualify for the conditional route because the relaxation applies to applicants lacking Q, not applicants lacking L; he remains not admitted.
Fall starters: Ben and Carla. Spring starter: Anna. This yields exactly two fall starters without changing Ben's or Anna's records.