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CAT 2022 Slot 2 DILR · Set 4 of 4Data InterpretationModerate DifficultyQ16–Q20 · 3 MCQ + 2 TITA

CAT 2022 Slot 2 DILR Set 4: Tables (5 Questions) with Solutions

The Tables set from the official CAT 2022 Slot 2 DILR paper: the caselet, all 5 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 2022 Slot 2 DILR · Questions 16–20
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below.
1
Over the two days, all three of them met the same total number of households, and each of them sold a total of 100100 items.
2
On both days, Lahur met the same number of households and sold the same number of items.
3
Hokli could not sell any item on the second day because the first household he met on that day complained against him.
4
Tohri met 3030 more households on the second day than on the first day.
5
Tohri's success rate was twice that of Lahur's on the first day, and it was 75%75 \% of Lahur's on the second day.

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

Q16. Tables

TITA · +3 / 0
What was the total number of households met by Tohri, Hokli and Lahur on the first day?
Correct Answer
84
Step-by-step solution
📌 Core Concept
Set up household and item equations for each salesman, using the fact that Lahur's two days are identical and that Hokli met exactly one household on day 2.
🔢 Step-by-Step Solution
1
Clue 2: Lahur sold the same number of items on both days and 100 in total, so he sold 50 each day. Let him meet LL households each day. His success rate is 50L\frac{50}{L} on both days.
2
Clue 5: Tohri's rate is 100L\frac{100}{L} on day 1 and 0.75×50L=37.5L0.75\times\frac{50}{L}=\frac{37.5}{L} on day 2.
3
Let Tohri meet TT households on day 1. Clue 4 gives T+30T+30 on day 2. Clue 1 says each salesman met the same total, which is 2L2L for Lahur, so 2T+30=2L2T+30=2L and L=T+15L=T+15.
4
Tohri's items total 100: 100TL+37.5(T+30)L=100\frac{100T}{L}+\frac{37.5(T+30)}{L}=100. This gives 137.5T+1125=100(T+15)137.5T+1125=100(T+15), so 37.5T=37537.5T=375 and T=10T=10. Then L=25L=25.
5
Hokli's total is 2L=502L=50 households. Clue 3: he left after the first household on day 2, so he met 1 household that day and 4949 on day 1.
6
Day 1 total: 10+49+25=8410+49+25=84.
Quick Check
Tohri's items are 100×1025=40\frac{100\times10}{25}=40 on day 1 and 37.5×4025=60\frac{37.5\times40}{25}=60 on day 2, which total 100.
Correct Answer: 84

Q17. Tables

TITA · +3 / 0
How many TRICCEK items were sold by Tohri on the first day?
Correct Answer
40
Step-by-step solution
📌 Core Concept
Find Lahur's household count from the equal-totals condition, then use the success-rate relations to get Tohri's items.
🔢 Step-by-Step Solution
1
Clue 2: Lahur sold 50 items on each day (100 in total) and met LL households each day. His success rate is 50L\frac{50}{L}.
2
Clue 5: Tohri's rate is 100L\frac{100}{L} on day 1 and 37.5L\frac{37.5}{L} on day 2.
3
Let Tohri meet TT households on day 1 and T+30T+30 on day 2 (clue 4). Clue 1 gives 2T+30=2L2T+30=2L, so L=T+15L=T+15.
4
Tohri's 100 items: 100TL+37.5(T+30)L=100\frac{100T}{L}+\frac{37.5(T+30)}{L}=100. This gives 137.5T+1125=100T+1500137.5T+1125=100T+1500, so T=10T=10 and L=25L=25.
5
Tohri's day 1 items are 10×10025=4010\times\frac{100}{25}=40.
Quick Check
Day 2 items are 40×1.5=6040\times1.5=60, and 40+60=10040+60=100, which matches clue 1.
Correct Answer: 40

Q18. Tables

MCQ · +3 / −1
How many households did Lahur meet on the second day?
  1. A) 20 or less
  2. B) Between 21 and 29
  3. C) More than 35
  4. D) Between 30 and 35
Correct Answer
B) Between 21 and 29
Step-by-step solution
📌 Core Concept
Lahur's two days are identical (clue 2), so his household count follows from the equal-totals condition that links him to Tohri.
🔢 Step-by-Step Solution
1
Clue 2: Lahur sold 50 items each day and met LL households each day. His rate is 50L\frac{50}{L} both days.
2
Clue 5: Tohri's rates are 100L\frac{100}{L} on day 1 and 37.5L\frac{37.5}{L} on day 2.
3
Let Tohri meet TT households on day 1 and T+30T+30 on day 2 (clue 4). Clue 1 gives 2T+30=2L2T+30=2L, so L=T+15L=T+15.
4
Tohri's items total 100: 100TL+37.5(T+30)L=100\frac{100T}{L}+\frac{37.5(T+30)}{L}=100, so 137.5T+1125=100T+1500137.5T+1125=100T+1500. Then T=10T=10 and L=25L=25.
5
Lahur met 25 households on day 2, which lies between 21 and 29.
Why Not the Others
A: 25 is more than 20.
C: 25 is not more than 35.
D: 25 is below 30.
Correct Answer: B

Q19. Tables

MCQ · +3 / −1
How many households did Tohri meet on the first day?
  1. A) more than 40
  2. B) 10 or less
  3. C) Between 21 and 40
  4. D) Between 11 and 20
Correct Answer
B) 10 or less
Step-by-step solution
📌 Core Concept
Express Tohri's items through the success-rate relations, then use the equal household totals to solve for his day 1 count.
🔢 Step-by-Step Solution
1
Clue 2: Lahur sold 50 items each day and met LL households each day, so his rate is 50L\frac{50}{L}.
2
Clue 5: Tohri's rate is 100L\frac{100}{L} on day 1 and 37.5L\frac{37.5}{L} on day 2.
3
Let Tohri meet TT households on day 1 and T+30T+30 on day 2 (clue 4). Clue 1 gives 2T+30=2L2T+30=2L, so L=T+15L=T+15.
4
His 100 items give 100T+37.5(T+30)T+15=100\frac{100T+37.5(T+30)}{T+15}=100. This simplifies to 137.5T+1125=100T+1500137.5T+1125=100T+1500, so 37.5T=37537.5T=375 and T=10T=10.
5
Tohri met 10 households on day 1, so he met 10 or fewer.
Why Not the Others
A, C, D: each requires more than 10 households, but T=10T=10 exactly.
Correct Answer: B

Q20. Tables

MCQ · +3 / −1
Which of the following statements is FALSE?
  1. A) Among the three, Tohri had the highest success rate on the second day.
  2. B) Tohri had a higher success rate on the first day compared to the second day.
  3. C) Among the three, Tohri had the highest success rate on the first day.
  4. D) Among the three, Lahur had the lowest success rate on the first day.
Correct Answer
A) Among the three, Tohri had the highest success rate on the second day.
Step-by-step solution
📌 Core Concept
Compute each salesman's success rate on both days and test each statement against the rates.
🔢 Step-by-Step Solution
1
Solving the clues gives Tohri 10 and 40 households (day 1 and day 2), and Lahur 25 households on each day with 50 items each day. Tohri sold 40 and 60 items.
2
Hokli met 50 households in total (clue 1). Clue 3 says he met only 1 household on day 2, so he met 49 on day 1 and sold all 100 items that day.
3
Day 1 rates: Tohri 4010=4\frac{40}{10}=4, Lahur 5025=2\frac{50}{25}=2, Hokli 10049≈2.04\frac{100}{49}\approx2.04.
4
Day 2 rates: Tohri 6040=1.5\frac{60}{40}=1.5, Lahur 5025=2\frac{50}{25}=2, Hokli 00.
5
Statement A claims Tohri had the highest rate on day 2, but Lahur's 2 exceeds Tohri's 1.5, so A is false.
Why Not the Others
B: 4>1.54>1.5, true.
C: Tohri's 4 is above 2.04 and 2, true.
D: Lahur's 2 is below 2.04 and 4, true.
Correct Answer: A
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CAT 2022 Slot 2 DILR at a Glance

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

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