CAT 2023 Slot 3 DILR Set 3 Q11–Q15

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 3, with 5 questions (Venn & Set Puzzles). Answers are CAT's official key.

The set

An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:
1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

Question 11

How many Split Inverter ACs did D2 sell?

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

Answer: 14 Venn & Set Puzzles TITA

Solution

  1. Split Inverter = 80% of Inverter = 36, so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15 = 25% of total, so total = 60, Split = 45, Split Non-inverter = 9.
  2. Window: D3 = D4 = w, D2 = 3w, D1 = 15 - 5w, each at least 2, so w = 2: D1 5, D2 6, D3 2, D4 2. D1's Split = 10.
  3. Window Non-inverter: D2 4, D3 2 (others 0). So Window Inverter: D1 5, D2 2, D3 0, D4 2.
  4. D1 Inverter 13 = 5 + 8, so D1 Split Inverter = 8; then D2 = 2s, D3 = D4 = s with \(8+4s=36\), s = 7: D2 14, D3 7, D4 7.
  5. D2 sold 14 Split Inverter ACs.

Question 12

What percentage of ACs sold were of Non-inverter type?
  1. A
    33.33%
  2. B
    20.00%
  3. C
    25.00%
  4. D
    75.00%

Answer: (C) 25.00% Venn & Set Puzzles MCQ

Solution

  1. Split Inverter = 80% of Inverter = 36, so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15 = 25% of total, so total = 60, Split = 45, Split Non-inverter = 9.
  2. Non-inverter = 60 - 45 = 15, which is \(\frac{15}{60}=25\%\).

Question 13

What was the total number of ACs sold by D2 and D4?

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

Answer: 33 Venn & Set Puzzles TITA

Solution

  1. Split Inverter = 80% of Inverter = 36, so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15 = 25% of total, so total = 60, Split = 45, Split Non-inverter = 9.
  2. Window: D3 = D4 = w, D2 = 3w, D1 = 15 - 5w, each at least 2, so w = 2: D1 5, D2 6, D3 2, D4 2. D1's Split = 10.
  3. Window Non-inverter: D2 4, D3 2 (others 0). So Window Inverter: D1 5, D2 2, D3 0, D4 2.
  4. D1 Inverter 13 = 5 + 8, so D1 Split Inverter = 8; then D2 = 2s, D3 = D4 = s with \(8+4s=36\), s = 7: D2 14, D3 7, D4 7.
  5. D1 Split Non-inv = 2; D3 Non-inv 5 = 2 window + 3 split; D2 + D4 Split Non-inv = 9 - 5 = 4 (a + b). Totals: D1 15, D2 20 + a, D3 12, D4 9 + b.
  6. D2 + D4 = (20 + a) + (9 + b) = 29 + 4 = 33.

Question 14

Which of the following statements is necessarily false?
  1. A
    D2 sold the highest number of ACs.
  2. B
    D1 and D3 together sold more ACs as compared to D2 and D4 together.
  3. C
    D1 and D3 sold an equal number of Split ACs.
  4. D
    D4 sold more Split ACs as compared to D3.

Answer: (B) D1 and D3 together sold more ACs as compared to D2 and D4 together. Venn & Set Puzzles MCQ

Solution

  1. Split Inverter = 80% of Inverter = 36, so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15 = 25% of total, so total = 60, Split = 45, Split Non-inverter = 9.
  2. Window: D3 = D4 = w, D2 = 3w, D1 = 15 - 5w, each at least 2, so w = 2: D1 5, D2 6, D3 2, D4 2. D1's Split = 10.
  3. Window Non-inverter: D2 4, D3 2 (others 0). So Window Inverter: D1 5, D2 2, D3 0, D4 2.
  4. D1 Inverter 13 = 5 + 8, so D1 Split Inverter = 8; then D2 = 2s, D3 = D4 = s with \(8+4s=36\), s = 7: D2 14, D3 7, D4 7.
  5. D1 Split Non-inv = 2; D3 Non-inv 5 = 2 window + 3 split; D2 + D4 Split Non-inv = 9 - 5 = 4 (a + b). Totals: D1 15, D2 20 + a, D3 12, D4 9 + b.
  6. D1 + D3 = 27 while D2 + D4 = 33 always, so B is necessarily false. A is true (D2 at least 20), C is true (both sell 10 Split), D can hold (b = 4).

Question 15

If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
  1. A
    7
  2. B
    5
  3. C
    6
  4. D
    4

Answer: (B) 5 Venn & Set Puzzles MCQ

Solution

  1. Split Inverter = 80% of Inverter = 36, so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15 = 25% of total, so total = 60, Split = 45, Split Non-inverter = 9.
  2. Window: D3 = D4 = w, D2 = 3w, D1 = 15 - 5w, each at least 2, so w = 2: D1 5, D2 6, D3 2, D4 2. D1's Split = 10.
  3. Window Non-inverter: D2 4, D3 2 (others 0). So Window Inverter: D1 5, D2 2, D3 0, D4 2.
  4. D1 Inverter 13 = 5 + 8, so D1 Split Inverter = 8; then D2 = 2s, D3 = D4 = s with \(8+4s=36\), s = 7: D2 14, D3 7, D4 7.
  5. D1 Split Non-inv = 2; D3 Non-inv 5 = 2 window + 3 split; D2 + D4 Split Non-inv = 9 - 5 = 4 (a + b). Totals: D1 15, D2 20 + a, D3 12, D4 9 + b.
  6. D3 = D4 gives 12 = 9 + b, so b = 3 and a = 1. D2 Non-inverter = 4 (Window) + 1 (Split) = 5.

Same concept in other years

See every question on Cross-classification of a population by two or three attributes; fill the contingency table.

More Venn & Set Puzzles questions from CAT

All 60 Venn & Set Puzzles questions asked since 2017.