CAT 2021 Slot 2 · DILR · Question 1

CAT 2021 Slot 2 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.

Reasoning Based DIDATA INTERPRETATION -High LevelType in the answer (TITA)Medium

Set 1: Orders Booked and Dispatched in September — this question belongs to a set. Read the full set with all 4 questions →

The different bars in the diagram above provide information about different orders in various categories (Art, Binders, ….) that were booked in the first two weeks of September of a store for one client. The colour and pattern of a bar denotes the ship mode (First Class / Second Class / Standard Class). The left end point of a bar indicates the booking day of the order, while the right end point indicates the dispatch day of the order. The difference between the dispatch day and the booking day (measured in terms of the number of days) is called the processing time of the order. For the same category, an order is considered for booking only after the previous order of the same category is dispatched. No two consecutive orders of the same category had identical ship mode during this period.

For example, there were only two orders in the furnishing category during this period. The first one was shipped in the Second Class. It was booked on Sep 1 and dispatched on Sep 5. The second order was shipped in the Standard class. It was booked on Sep 5 (although the order might have been placed before that) and dispatched on Sep 12. So the processing times were 4 and 7 days respectively for these orders.

How many days between Sep 1 and Sep 14 (both inclusive) had no booking from this client considering all the above categories?
Answer & solution

Answer: 6

Category

Orders (ship mode: booked → dispatched, processing days)

Number

Average

Art

Std 1→3 (2), 2nd 3→4 (1), 1st 4→6 (2), 2nd 6→13 (7), Std 13→21 (8)

5

20/5 = 4.00

Binders

Std 1→2 (1), 2nd 2→4 (2), 1st 4→5 (1), 2nd 5→16 (11)

4

15/4 = 3.75

Paper

2nd 2→4 (2), 1st 4→7 (3), 2nd 7→12 (5)

3

10/3 = 3.33

Phones

Std 2→4 (2), 1st 4→5 (1), Std 5→17 (12)

3

15/3 = 5.00

Appliances

2nd 2→4 (2), Std 4→12 (8)

2

5.0

Bookcases

2nd 3→4 (1), 1st 4→6 (2), 2nd 6→7 (1)

3

1.33

Fasteners

Std 2→4 (2), 2nd 4→6 (2), Std 6→8 (2)

3

2.0

Furnishings

2nd 1→5 (4), Std 5→12 (7)

2

5.5

Labels

2nd 2→4 (2), Std 4→12 (8)

2

5.0

Tables

Std 2→4 (2), 2nd 4→10 (6)

2

4.0

Chairs

Std 2→3 (1), 2nd 3→9 (6)

2

3.5

Accessories

Std 1→19 (18)

1

18

Envelopes

Std 3→7 (4)

1

4

Storage

2nd 2→7 (5), Std 7→22 (15)

2

10

Total

35

Booking days between Sep 1 and 14: 1, 2, 3, 4, 5, 6, 7 and 13. Days with no booking: 8, 9, 10, 11, 12, 14 – 6 days.

Hence, the answer is 6.

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