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CAT 2023 Slot 1 · DILR · Scheduling and Rosters · medium

CAT 2023 Slot 1 DILR: Seven-Day Store Roster

A small retail store is open all seven days of the week (Monday through Sunday) and is staffed by seven employees: A, B, C, D, E, F and G. Exactly one employee is off duty on each day of the week, and each employee gets exactly one day off during the week (i.e., the days off form a one-to-one mapping between employees and days).

The following is known about the roster:
1. A is off duty on Monday.
2. E is off duty on Wednesday.
3. G is off duty on Saturday.
4. B is off duty exactly two days after F (counting days of the week in order Monday=1 to Sunday=7).
5. D is off duty exactly two days after C.
6. F's day off comes earlier in the week than C's day off.

Question 1

Single correct option

Which employee is off duty on Thursday?
  1. A. B
  2. B. C
  3. C. D
  4. D. F
Show answer and solution

Answer: (A) B

The days Mon, Wed and Sat are taken by A, E and G respectively, leaving Tue, Thu, Fri and Sun for B, C, D and F. Testing pairs with B = F+2 (in day-number) and D = C+2 among {Tue=2,Thu=4,Fri=5,Sun=7}: F=Tue(2), B=Thu(4) works (diff 2); then C, D must come from {Fri=5, Sun=7}, and D=C+2 gives C=Fri(5), D=Sun(7). (The alternative F=Fri,B=Sun,C=Tue,D=Thu is ruled out by clue 6, since it would put F's day off after C's.) So B is off on Thursday.

Question 2

Single correct option

Which employee is off duty on Sunday?
  1. A. B
  2. B. C
  3. C. D
  4. D. F
Show answer and solution

Answer: (C) D

From the deduction above, the full roster is: Mon–A, Tue–F, Wed–E, Thu–B, Fri–C, Sat–G, Sun–D. So D is off on Sunday.

Question 3

Single correct option

Which employee is off duty on the day immediately after C's day off?
  1. A. B
  2. B. D
  3. C. F
  4. D. G
Show answer and solution

Answer: (D) G

From the full roster (Mon–A, Tue–F, Wed–E, Thu–B, Fri–C, Sat–G, Sun–D), C is off on Friday. The day immediately after Friday is Saturday, on which G is off duty.

Question 4

Single correct option

Whose day off falls exactly midway (chronologically) between B's day off and G's day off?
  1. A. A
  2. B. C
  3. C. D
  4. D. F
Show answer and solution

Answer: (B) C

B is off on Thursday (day 4) and G is off on Saturday (day 6); the day exactly midway is Friday (day 5), on which C is off duty.

Question 5

Numerical answer

Numbering the days Monday=1 through Sunday=7, what is the sum of the day-numbers on which B, C and D are off duty?
Show answer and solution

Answer: 16

B is off on Thursday (4), C is off on Friday (5), and D is off on Sunday (7). Sum = 4+5+7 = 16.
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Original question written in the CAT 2023 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake