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CAT 2023 Slot 2 · DILR · Allocation and Selection · hard

CAT 2023 Slot 2 DILR: Relay Swim Team Selection

A swimming coach must select 4 swimmers from a squad of 6 (A, B, C, D, E, F) to form a 4×100m medley relay team, with each of the 4 selected swimmers assigned to exactly one of the four strokes — Backstroke, Breaststroke, Butterfly and Freestyle — and no swimmer assigned to more than one stroke. The table below shows each swimmer's personal-best time (in seconds) for each stroke.

| Swimmer | Backstroke | Breaststroke | Butterfly | Freestyle |
|---|---|---|---|---|
| A | 32 | 34 | 30 | 30 |
| B | 35 | 31 | 33 | 30 |
| C | 30 | 36 | 32 | 31 |
| D | 33 | 30 | 31 | 28 |
| E | 31 | 33 | 29 | 32 |
| F | 34 | 32 | 35 | 33 |

The coach selects the team and stroke assignment that minimises the team's total relay time (the sum of the times of the 4 chosen swimmers in their assigned strokes).

Question 1

Numerical answer

What is the minimum possible total relay time (in seconds) for the team?
Show answer and solution

Answer: 118

Checking all feasible assignments, the minimum total is achieved with C on Backstroke (30), B on Breaststroke (31), E on Butterfly (29) and D on Freestyle (28): total = 30+31+29+28 = 118 seconds. No other assignment of 4 swimmers to the 4 strokes gives a lower total.

Question 2

Single correct option

In the optimal team, which swimmer swims the Butterfly leg?
  1. A. A
  2. B. C
  3. C. E
  4. D. F
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Answer: (C) E

In the minimum-time assignment (C-Backstroke, B-Breaststroke, E-Butterfly, D-Freestyle), swimmer E swims the Butterfly leg with a time of 29 seconds — E's best time among all swimmers for that stroke.

Question 3

Single correct option

Which two swimmers are NOT selected for the optimal relay team?
  1. A. A and F
  2. B. B and F
  3. C. A and C
  4. D. D and F
Show answer and solution

Answer: (A) A and F

The optimal team uses C, B, E and D (for Backstroke, Breaststroke, Butterfly and Freestyle respectively). The two swimmers left out of the squad of six are A and F.

Question 4

Numerical answer

What is the time recorded by the swimmer who swims the Freestyle leg in the optimal team (in seconds)?
Show answer and solution

Answer: 28

In the optimal assignment, D swims Freestyle with a time of 28 seconds, which is the fastest Freestyle time in the table and part of the overall minimum-time combination.

Question 5

Numerical answer

If swimmer D becomes unavailable, what is the new minimum possible total relay time (in seconds) using the remaining five swimmers?
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Answer: 120

With D unavailable, checking all feasible assignments among A, B, C, E, F gives the minimum at C-Backstroke (30), B-Breaststroke (31), E-Butterfly (29), A-Freestyle (30): total = 30+31+29+30 = 120 seconds.
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Original question written in the CAT 2023 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake