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CAT 2021 Slot 2 DILR · Set 1 of 4Data InterpretationEasy DifficultyQ1–Q4 · 2 MCQ + 2 TITA

CAT 2021 Slot 2 DILR Set 1: Bar Graphs (4 Questions) with Solutions

The Bar Graphs set from the official CAT 2021 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 2 DILR · Questions 1–4
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.
Official Reference Chart - CAT 2021 Slot 2 Official Reference Chart - CAT 2021 Slot 2

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q1. Bar Graphs

TITA · +3 / 0
How many days between Sep 1 and Sep 14 (both inclusive) had no booking from this client considering all the above categories?
Correct Answer
6
Step-by-step solution
📌 Core Concept
Each bar segment is one order, and its left end is a booking day. Collect all booking days in Sep 1 to 14, then count the days left over.
🔢 Step-by-Step Solution
1
Read the start of every segment. Sep 1: Art, Binders, Furnishings and Accessories all start.
2
Sep 2: Paper, Phones, Appliances, Fasteners, Labels, Tables, Chairs and Storage start. Sep 3: Art (Second Class), Bookcases and Envelopes start.
3
Sep 4: Art (First Class), Binders, Paper, Phones, Appliances, Fasteners, Labels and Tables start. Sep 5: Furnishings (Standard), Binders and Phones start.
4
Sep 6: Art, Bookcases and Fasteners start. Sep 7: Paper and Storage start.
5
Sep 8 to 12 have no segment starting. Appliances, Labels, Paper and Furnishings only end on Sep 12, and Phones, Binders and Accessories are still running.
6
Sep 13: Art (Standard) starts. Sep 14 has no start.
7
Days with a booking are Sep 1, 2, 3, 4, 5, 6, 7 and 13, which is 8 days.
8
Days with no booking: 14−8=614 - 8 = 6 (Sep 8, 9, 10, 11, 12 and 14).
Quick Check
The days without bookings are Sep 8, 9, 10, 11, 12 and 14, which is 6 days.
Correct Answer: 6

Q2. Bar Graphs

TITA · +3 / 0
What was the average processing time of all orders in the categories which had only one type of ship mode?
Correct Answer
11
Step-by-step solution
📌 Core Concept
First find the categories whose orders all share one ship mode. Then average the processing times of their orders, where processing time is dispatch day minus booking day.
🔢 Step-by-Step Solution
1
Every category except two shows at least two colours. Accessories and Envelopes are the only single-colour bars, both Standard Class.
2
Accessories has one order, booked Sep 1 and dispatched Sep 19. Its processing time is 19−1=1819 - 1 = 18 days.
3
Envelopes has one order, booked Sep 3 and dispatched Sep 7. Its processing time is 7−3=47 - 3 = 4 days.
4
Average processing time =18+42=11= \frac{18 + 4}{2} = 11 days.
Correct Answer: 11

Q3. Bar Graphs

MCQ · +3 / −1
The sequence of categories Art, Binders, Paper and Phones in decreasing order of average processing time of their orders in this period is:
  1. A) Paper, Binders, Art, Phones
  2. B) Phones, Art, Binders, Paper
  3. C) Art, Binders, Paper, Phones
  4. D) Phones, Binders, Art, Paper
Correct Answer
B) Phones, Art, Binders, Paper
Step-by-step solution
📌 Core Concept
For each category, average processing time is the total bar length divided by the number of orders. Segment lengths come from the booking and dispatch days.
🔢 Step-by-Step Solution
1
Art has 5 orders: Sep 1 to 3, 3 to 4, 4 to 6, 6 to 13 and 13 to 21. The times are 2,1,2,7,82, 1, 2, 7, 8, so the total is 20 and the average is 20/5=420/5 = 4.
2
Binders has 4 orders: Sep 1 to 2, 2 to 4, 4 to 5 and 5 to 16. The times are 1,2,1,111, 2, 1, 11, so the total is 15 and the average is 15/4=3.7515/4 = 3.75.
3
Paper has 3 orders: Sep 2 to 4, 4 to 7 and 7 to 12. The times are 2,3,52, 3, 5, so the total is 10 and the average is 10/3≈3.3310/3 \approx 3.33.
4
Phones has 3 orders: Sep 2 to 4, 4 to 5 and 5 to 17. The times are 2,1,122, 1, 12, so the total is 15 and the average is 15/3=515/3 = 5.
5
In decreasing order: Phones (5), Art (4), Binders (3.75), Paper (3.33).
Why Not the Others
A puts Paper first, but Paper has the lowest average.
C starts with Art, but Phones (5) is higher than Art (4).
D puts Binders above Art, but Art (4) is higher than Binders (3.75).
Correct Answer: B

Q4. Bar Graphs

MCQ · +3 / −1
Approximately what percentage of orders had a processing time of one day during the period Sep 1 to Sep 22 (both dates inclusive)?
  1. A) 16%
  2. B) 22%
  3. C) 20%
  4. D) 25%
Correct Answer
C) 20%
Step-by-step solution
📌 Core Concept
Count all orders (segments) in the chart, then count those whose booking and dispatch days are one day apart.
🔢 Step-by-Step Solution
1
Orders per category: Art 5, Binders 4, Paper 3, Phones 3, Appliances 2, Bookcases 3, Fasteners 3, Furnishings 2, Labels 2, Tables 2, Chairs 2, Accessories 1, Envelopes 1, Storage 2. The total is 35.
2
One-day orders in Art: Sep 3 to 4 (1 order).
3
One-day orders in Binders: Sep 1 to 2 and Sep 4 to 5 (2 orders).
4
One-day orders in Phones: Sep 4 to 5 (1 order).
5
One-day orders in Bookcases: Sep 3 to 4 and Sep 6 to 7 (2 orders).
6
One-day orders in Chairs: Sep 2 to 3 (1 order).
7
Every other segment is 2 days or longer, so there are 7 one-day orders.
8
Percentage =735×100=20%= \frac{7}{35} \times 100 = 20\%.
Why Not the Others
16%, 22% and 25% do not match 7/357/35. For example, 25% would need about 9 orders.
Correct Answer: C
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CAT 2021 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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