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CAT 2020 Slot 3 DILR · Set 4 of 5Data InterpretationModerate DifficultyQ15–Q18 · 4 MCQ

CAT 2020 Slot 3 DILR Set 4: Tables (4 Questions) with Solutions

The Tables set from the official CAT 2020 Slot 3 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 2020 Slot 3 DILR · Questions 15–18
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.
The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.
It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively.
DayCumulative orders bookedOrders delivered on dayCumulative orders lost
13th2191191
14th2492792
15th2772394
16th30211106
17th32721118
18th33213120
19th33714129

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q15. Tables

MCQ · +3 / −1
Among the following days, the largest fraction of orders booked on which day was lost?
  1. A) 13th
  2. B) 16th
  3. C) 15th
  4. D) 14th
Correct Answer
C) 15th
Step-by-step solution
📌 Core Concept
Rebuild the daily booking, delivery and loss figures from the cumulative columns. An order booked on day dd is lost at the end of day d+2d+2, so the loss on day d+2d+2 belongs to day dd's bookings.
🔢 Step-by-Step Solution
1
Daily bookings come from differences of the cumulative column: 14th = 30, 15th = 28, 16th = 25, 17th = 25.
2
Daily losses come from differences of the cumulative-lost column: 14th = 1, 15th = 2, 16th = 12, 17th = 12, 18th = 2.
3
Let ada_d be the orders booked on day dd and delivered the next day. Let bdb_d be those delivered after two days. Orders delivered on day dd equal ad−1+bd−2a_{d-1}+b_{d-2}.
4
The 13th delivered 11 and b11=4b_{11}=4, so a12=7a_{12}=7. The 14th delivered 27 and b12=6b_{12}=6, so a13=21a_{13}=21. The 15th delivered 23 and b13=8b_{13}=8, so a14=15a_{14}=15.
5
Orders booked on the 12th: 7+6+17+6+1 lost on the 14th =14=14. Orders booked on the 13th: 21+8+221+8+2 lost on the 15th =31=31.
6
Orders booked on the 14th number 30. Of these, 12 were lost on the 16th, so the fraction lost is 12/30=0.4012/30=0.40.
7
Orders booked on the 15th number 28. Of these, 12 were lost on the 17th, so the fraction lost is 12/28≈0.4312/28\approx0.43.
8
Orders booked on the 16th number 25. Of these, 2 were lost on the 18th, so the fraction lost is 2/25=0.082/25=0.08.
9
Orders booked on the 13th number 31. Of these, 2 were lost on the 15th, so the fraction lost is 2/31≈0.062/31\approx0.06.
Quick Check
The 15th has the largest fraction lost, 12/2812/28, which is above the 14th's 12/3012/30.
Correct Answer: C

Q16. Tables

MCQ · +3 / −1
On which of the following days was the number of orders booked the highest?
  1. A) 15th15^{th}
  2. B) 13th13^{th}
  3. C) 14th14^{th}
  4. D) 12th12^{th}
Correct Answer
B) 13th13^{th}
Step-by-step solution
📌 Core Concept
Orders booked on a day equal those delivered next day, those delivered after two days, and those lost. The lost orders appear in the cumulative-lost column two days later.
🔢 Step-by-Step Solution
1
Let ada_d be the orders booked on day dd and delivered the next day. Orders delivered on day dd equal ad−1+bd−2a_{d-1}+b_{d-2}, where bdb_d is the number of day-dd bookings that took two days.
2
The 13th delivered 11 and b11=4b_{11}=4, so a12=7a_{12}=7. The 14th delivered 27 and b12=6b_{12}=6, so a13=21a_{13}=21.
3
Losses on the 14th: 92−91=192-91=1. These come from the 12th's bookings. Booked on the 12th: 7+6+1=147+6+1=14.
4
Losses on the 15th: 94−92=294-92=2. These come from the 13th's bookings. Booked on the 13th: 21+8+2=3121+8+2=31, using b13=8b_{13}=8.
5
The cumulative column gives the 14th as 249−219=30249-219=30 and the 15th as 277−249=28277-249=28.
6
Compare the four days: 12th = 14, 13th = 31, 14th = 30, 15th = 28.
Quick Check
The 13th has 31 bookings, only just above the 14th's 30. This is why the two-day figures matter.
Correct Answer: B

Q17. Tables

MCQ · +3 / −1
The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on the second day after booking. On which of the following days, was the delivery ratio the highest?
  1. A) 13th13^{th}
  2. B) 15th15^{th}
  3. C) 14th14^{th}
  4. D) 16th16^{th}
Correct Answer
C) 14th14^{th}
Step-by-step solution
📌 Core Concept
Split each day's bookings into next-day deliveries (aa) and two-day deliveries (bb). Use the delivered column, the lost column and the given two-day counts. The delivery ratio is a/ba/b.
🔢 Step-by-Step Solution
1
Orders delivered on day dd equal ad−1+bd−2a_{d-1}+b_{d-2}. The given values are b11=4b_{11}=4, b12=6b_{12}=6, b13=8b_{13}=8.
2
The 14th delivered 27, so a13=27−6=21a_{13}=27-6=21. The 15th delivered 23, so a14=23−8=15a_{14}=23-8=15.
3
The cumulative column gives 30 bookings on the 14th. The cumulative-lost column gives 12 lost on the 16th (106−94106-94). So b14=30−15−12=3b_{14}=30-15-12=3.
4
The 16th delivered 11, so a15=11−3=8a_{15}=11-3=8.
5
The 15th had 28 bookings and 12 were lost on the 17th (118−106118-106). So b15=28−8−12=8b_{15}=28-8-12=8.
6
The 16th had 25 bookings and 2 were lost on the 18th (120−118120-118), so a16+b16=23a_{16}+b_{16}=23. The 17th delivered 21, so a16=21−8=13a_{16}=21-8=13 and b16=10b_{16}=10.
7
Ratios a/ba/b: 13th = 21/8=2.6321/8=2.63, 14th = 15/3=515/3=5, 15th = 8/8=18/8=1, 16th = 13/10=1.313/10=1.3.
Quick Check
The 14th has a ratio of 5, far above the other three.
Correct Answer: C

Q18. Tables

MCQ · +3 / −1
The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be xx and the number of orders delivered the day after be yy. Then the average time to deliver order is (x+2y)/(x+y)(x+2y)/(x+y). On which of the following days was the average time taken to deliver orders booked the least?
  1. A) 16th16th
  2. B) 15th15th
  3. C) 13th13th
  4. D) 14th14th
Correct Answer
D) 14th14th
Step-by-step solution
📌 Core Concept
The average time is x+2yx+y=1+yx+y\frac{x+2y}{x+y}=1+\frac{y}{x+y}. It is smallest where the share of two-day deliveries among delivered orders is smallest.
🔢 Step-by-Step Solution
1
Let xx be the number of day-dd bookings delivered next day and yy the number delivered after two days. Orders delivered on day dd equal xd−1+yd−2x_{d-1}+y_{d-2}. Given: y13=8y_{13}=8.
2
The 14th delivered 27 and y12=6y_{12}=6, so x13=21x_{13}=21. The 15th delivered 23 and y13=8y_{13}=8, so x14=15x_{14}=15.
3
The 14th had 30 bookings and 12 were lost on the 16th. So y14=30−15−12=3y_{14}=30-15-12=3.
4
The 16th delivered 11, so x15=11−3=8x_{15}=11-3=8. The 15th had 28 bookings and 12 were lost on the 17th, so y15=28−8−12=8y_{15}=28-8-12=8.
5
The 16th had 25 bookings and 2 were lost on the 18th, so x16+y16=23x_{16}+y_{16}=23. The 17th delivered 21, so x16=21−8=13x_{16}=21-8=13 and y16=10y_{16}=10.
6
Values of yx+y\frac{y}{x+y}: 13th = 8/29≈0.288/29\approx0.28, 14th = 3/18≈0.173/18\approx0.17, 15th = 8/16=0.58/16=0.5, 16th = 10/23≈0.4310/23\approx0.43.
7
The smallest share is on the 14th, so its average time is lowest, about 1.17 days.
Quick Check
The 14th has x=15x=15 against y=3y=3, so almost all delivered orders arrived the next day.
Correct Answer: D
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CAT 2020 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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