Air Conditioner Dealer Sales Analysis

CAT 2023 Slot 3 · DILR · Medium · Data Interpretation

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Passage / data 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 1 of 5

How many Split Inverter ACs did D2 sell?

Answer

12

Explanation

Given 36 Split Inverter ACs in total. Let xx be the number sold by D3 and D4 each, and 2x2x by D2. D1 sold 36−4x36 - 4x. Solving the total AC relationships gives x=6x = 6, so D2 sold 2(6)=122(6) = 12 Split Inverter ACs.

Question 2 of 5

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

Explanation

From the ratios of Window vs Split and Inverter vs Non-Inverter, 25.00% of all sold ACs were of Non-inverter type.

Question 3 of 5

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

Answer

32

Explanation

Calculating individual sales per dealer gives D2 = 20 ACs and D4 = 12 ACs. Total for D2 and D4 = 20+12=3220 + 12 = 32.

Question 4 of 5

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

Explanation

Total ACs sold by D1 + D3 = 18+10=2818 + 10 = 28. Total ACs sold by D2 + D4 = 20+12=3220 + 12 = 32. Hence, D1 and D3 together sold fewer ACs than D2 and D4 together, making option B necessarily false.

Question 5 of 5

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

C

Explanation

Under the condition that D3 and D4 sold equal numbers of ACs, solving the distribution gives 6 Non-inverter ACs sold by D2.

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