CAT 2022 Slot 2 DILR Set 1 Q1–Q5

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2022 Slot 2, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

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 100 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 30 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% of Lahur's on the second day.

Question 1

What was the total number of households met by Tohri, Hokli and Lahur on the first day?

TITA: type in the answer. There are no options and no negative marking.

Answer: 84 Quant-based Puzzles TITA

Solution

  1. Let each salesman meet \(N\) households in total. Lahur meets \(L\) per day and sells 50 per day, so \(N=2L\). Hokli meets 1 household on day 2 (sells 0), so on day 1 he meets \(N-1\) and sells 100. Tohri meets \(t\) and \(t+30\), so \(2t+30=2L\), i.e. \(L=t+15\).
  2. Tohri's day-1 sales \(a\): \(\frac{a}{t}=2\cdot\frac{50}{t+15}\Rightarrow a=\frac{100t}{t+15}\). Day 2: \(\frac{100-a}{t+30}=0.75\cdot\frac{50}{t+15}\). Since \(100-a=\frac{1500}{t+15}\), we get \(1500=37.5(t+30)\), so \(t=10\), \(L=25\), \(N=50\), \(a=40\).
  3. Day 1 households: Tohri 10 + Hokli \(N-1=49\) + Lahur 25 = 84.

Question 2

How many TRICCEK items were sold by Tohri on the first day?

TITA: type in the answer. There are no options and no negative marking.

Answer: 40 Quant-based Puzzles TITA

Solution

  1. Let each salesman meet \(N\) households in total. Lahur meets \(L\) per day and sells 50 per day, so \(N=2L\). Hokli meets 1 household on day 2 (sells 0), so on day 1 he meets \(N-1\) and sells 100. Tohri meets \(t\) and \(t+30\), so \(2t+30=2L\), i.e. \(L=t+15\).
  2. Tohri's day-1 sales \(a\): \(\frac{a}{t}=2\cdot\frac{50}{t+15}\Rightarrow a=\frac{100t}{t+15}\). Day 2: \(\frac{100-a}{t+30}=0.75\cdot\frac{50}{t+15}\). Since \(100-a=\frac{1500}{t+15}\), we get \(1500=37.5(t+30)\), so \(t=10\), \(L=25\), \(N=50\), \(a=40\).
  3. Tohri sold \(a=\frac{100\cdot 10}{25}=40\) items on day 1.

Question 3

How many households did Lahur meet on the second day?
  1. A
    20 or less
  2. B
    between 21 and 29
  3. C
    between 30 and 35
  4. D
    more than 35

Answer: (B) between 21 and 29 Quant-based Puzzles MCQ

Solution

  1. Let each salesman meet \(N\) households in total. Lahur meets \(L\) per day and sells 50 per day, so \(N=2L\). Hokli meets 1 household on day 2 (sells 0), so on day 1 he meets \(N-1\) and sells 100. Tohri meets \(t\) and \(t+30\), so \(2t+30=2L\), i.e. \(L=t+15\).
  2. Tohri's day-1 sales \(a\): \(\frac{a}{t}=2\cdot\frac{50}{t+15}\Rightarrow a=\frac{100t}{t+15}\). Day 2: \(\frac{100-a}{t+30}=0.75\cdot\frac{50}{t+15}\). Since \(100-a=\frac{1500}{t+15}\), we get \(1500=37.5(t+30)\), so \(t=10\), \(L=25\), \(N=50\), \(a=40\).
  3. Lahur meets \(L=25\) households each day, which is between 21 and 29.

Question 4

How many households did Tohri meet on the first day?
  1. A
    more than 40
  2. B
    10 or less
  3. C
    between 11 and 20
  4. D
    between 21 and 40

Answer: (B) 10 or less Quant-based Puzzles MCQ

Solution

  1. Let each salesman meet \(N\) households in total. Lahur meets \(L\) per day and sells 50 per day, so \(N=2L\). Hokli meets 1 household on day 2 (sells 0), so on day 1 he meets \(N-1\) and sells 100. Tohri meets \(t\) and \(t+30\), so \(2t+30=2L\), i.e. \(L=t+15\).
  2. Tohri's day-1 sales \(a\): \(\frac{a}{t}=2\cdot\frac{50}{t+15}\Rightarrow a=\frac{100t}{t+15}\). Day 2: \(\frac{100-a}{t+30}=0.75\cdot\frac{50}{t+15}\). Since \(100-a=\frac{1500}{t+15}\), we get \(1500=37.5(t+30)\), so \(t=10\), \(L=25\), \(N=50\), \(a=40\).
  3. Tohri met \(t=10\) households on day 1, i.e. 10 or less.

Question 5

Which of the following statements is FALSE?
  1. A
    Among the three, Tohri had the highest success rate on the first day.
  2. B
    Tohri had a higher success rate on the first day compared to the second day.
  3. C
    Among the three, Lahur had the lowest success rate on the first day.
  4. D
    Among the three, Tohri had the highest success rate on the second day.

Answer: (D) Among the three, Tohri had the highest success rate on the second day. Quant-based Puzzles MCQ

Solution

  1. Let each salesman meet \(N\) households in total. Lahur meets \(L\) per day and sells 50 per day, so \(N=2L\). Hokli meets 1 household on day 2 (sells 0), so on day 1 he meets \(N-1\) and sells 100. Tohri meets \(t\) and \(t+30\), so \(2t+30=2L\), i.e. \(L=t+15\).
  2. Tohri's day-1 sales \(a\): \(\frac{a}{t}=2\cdot\frac{50}{t+15}\Rightarrow a=\frac{100t}{t+15}\). Day 2: \(\frac{100-a}{t+30}=0.75\cdot\frac{50}{t+15}\). Since \(100-a=\frac{1500}{t+15}\), we get \(1500=37.5(t+30)\), so \(t=10\), \(L=25\), \(N=50\), \(a=40\).
  3. Day 1 rates: Tohri \(40/10=4\), Hokli \(100/49\approx2.04\), Lahur \(50/25=2\). Day 2 rates: Tohri \(60/40=1.5\), Hokli 0, Lahur 2.
  4. A, B and C are true. On day 2 Lahur (2) beat Tohri (1.5), so D is false.

More Quant-based Puzzles questions from CAT

All 127 Quant-based Puzzles questions asked since 2017.