CAT 2023 Slot 3 · DILR · Question 5
CAT 2023 Slot 3 previous year question on Caselet DI, with the answer and a step-by-step solution.
Set 1: AC Sales by Four Dealers — this question belongs to a set. Read the full set with all 5 questions →
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.
- A4
- B5
- C7
- D6
Answer & solution
Answer: Option B
Solving the set
Step 1 – City totals. Split Inverter = 36 and this is 80% of all Inverter ACs (20% are Window), so Inverter = 45 and Window Inverter = 9. Window = 9 + 6 = 15, which is 25% of the total, so the total is 60 and Split = 45, Split Non-inverter = 45 − 36 = 9.
Inverter | Non-inverter | Total | |
Window | 9 | 6 | 15 (25%) |
Split | 36 | 9 | 45 (75%) |
Total | 45 | 15 | 60 |
Step 2 – Window ACs by dealer. D3 = D4 = w and D2 = 3w (fact 5). D1 has the rest: 15 − 5w ≥ 2 (fact 1) ⇒ w = 2 (w = 1 is ruled out by fact 1, w = 3 leaves D1 nothing). So D1 = 5, D2 = 6, D3 = 2, D4 = 2. D1's Split = 2 × 5 = 10 (fact 4).
Step 3 – Window Non-inverter (6) is sold only by D2 and D3 with D2 = 2 × D3 ⇒ D2 4, D3 2. So D3's window ACs are both non-inverter, D2 has 2 window inverter, and D1 (5) and D4 (2) have only window inverter.
Step 4 – Split Inverter. D1 sold 13 inverter = 5 window + 8 split. D3 = D4 = s and D2 = 2s: 8 + 2s + s + s = 36 ⇒ s = 7. D2 = 14.
Step 5 – Split Non-inverter. D1 = 10 − 8 = 2. D3's non-inverter total is 5 = 2 window + 3 split. Remaining 9 − 2 − 3 = 4 split non-inverter go to D2 (a) and D4 (b), a + b = 4.
Dealer | Window Inv | Window Non-inv | Split Inv | Split Non-inv | Total |
D1 | 5 | 0 | 8 | 2 | 15 |
D2 | 2 | 4 | 14 | a | 20 + a |
D3 | 0 | 2 | 7 | 3 | 12 |
D4 | 2 | 0 | 7 | b (= 4 − a) | 9 + b |
Total | 9 | 6 | 36 | 9 | 60 |
This question
D3 = 12 and D4 = 9 + b. Equal totals ⇒ b = 3 ⇒ a = 1. D2's Non-inverter = 4 (Window) + 1 (Split) = 5.
Hence, the answer is option 2.
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