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Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation PDF Download

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.

Q1: How many Split Inverter ACs did D2 sell?

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: 14
Let us assume, A is the total number of AC's sold
⇒ From the information that the total number of ACs sold in the city, 25% were of Window variant => Window AC's = A/4 and Split AC's = 3A/4
Now, let us assume B is the total number of inverter ACs
⇒ From the information that among the Inverter ACs sold, 20% were of Window variant.=> Window Inverter AC's = B/5 and Window Non
Inverter AC's = 4B/5
From - Condition-3:

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

⇒ A / 4 - B / 5 = 6 and 4B / 5 = 36 ⇒ B = 46 and A = 60.

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, from condition-6:
a) D1 & D4 sold "0" window Non-inverter ACs ⇒ D2 & D3 sold 6 window non-inverter ACs, it is given that D2 sold twice as many as D3 ⇒ D2 sold 4 and D3 sold 2 ACs of this type.
From condition-2:
b) Let us assume, D1 sold "x" window inverter ACs ⇒ Number of split inverter ACs sold is 13-x
From condition-4:
c) Number of split ACs sold by D1 will be "2x"
From condition-5:
d) Let us assume 'y' is the number of window ACs sold by D3 & D4 ⇒ D2 sold 3y ACs of this type.
From condition-7:
e) Let us assume 'z' is the number of split inverter ACs sold by D3 and D4 ⇒ D2 sold 2z ACs of this type.
Let us use a, b, c, d, and e make a table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationWe know that the total number of window ACs is 15
⇒ x + 3y + y + y = 15 ⇒ x + 5y = 15, also x and y should be greater than or equal to 2 from condition-1
⇒ x = 5 and y = 2 is the only solution.
Filling this in the table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, Number of split inverter ACs is 36
⇒ 8 + 2z + z + z = 36 ⇒ 4z = 28 ⇒ z = 7.
Filling this and using (5), the number of split AC's sold by D1 is 2*5 = 10.
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

From the table, we see that 14 split inverter ACs are sold.

Q2: Which of the following statements is necessarily false?
(a) D2 sold the highest number of ACs.
(b) D4 sold more Split ACs as compared to D3.
(c) D1 and D3 sold an equal number of Split ACs.
(d) D1 and D3 together sold more ACs as compared to D2 and D4 together.

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: (d)
Let us assume, A is the total number of AC's sold
⇒ From the information that the total number of ACs sold in the city, 25% were of Window variant => Window AC's = A/4 and Split AC's = 3A/4
Now, let us assume B is the total number of inverter ACs
⇒ From the information that among the Inverter ACs sold, 20% were of Window variant.=> Window Inverter AC's = B/5 and Window Non
Inverter AC's = 4B/5
From - Condition-3

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

⇒ A / 4 - B / 5 = 6 and 4B / 5 = 36 ⇒ B = 46 and A = 60.

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, from condition-6
a) D1 & D4 sold "0" window Non-inverter ACs ⇒ D2 & D3 sold 6 window non-inverter ACs, it is given that D2 sold twice as many as D3 ⇒ D2 sold 4 and D3 sold 2 ACs of this type.
From condition-2
b) Let us assume, D1 sold "x" window inverter ACs ⇒ Number of split inverter ACs sold is 13-x
From condition-4
c) Number of split ACs sold by D1 will be "2x"
From condition-5
d) Let us assume 'y' is the number of window ACs sold by D3 & D4 ⇒ D2 sold 3y ACs of this type.
From condition-7
e) Let us assume 'z' is the number of split inverter ACs sold by D3 and D4 ⇒ D2 sold 2z ACs of this type.
Let us use a, b, c, d, and e make a table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationWe know that the total number of window ACs is 15
⇒ x + 3y + y + y = 15 ⇒ x + 5y = 15, also x and y should be greater than or equal to 2 from condition-1
⇒ x = 5 and y = 2 is the only solution.
Filling this in the table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, Number of split inverter ACs is 36
⇒ 8 + 2z + z + z = 36 ⇒ 4z = 28 ⇒ z = 7.
Filling this and using (5), the number of split AC's sold by D1 is 2*5 = 10.
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

We see that D1 & D3 sold 27 ACs together which is less than 60 - 27 = 33 sold by D2 & D4.
⇒ Option-D is definitely false.

Q3:  If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
(a) 4
(b) 5
(c) 7
(d) 6

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: (b)
Let us assume, A is the total number of AC's sold
⇒ From the information that the total number of ACs sold in the city, 25% were of Window variant => Window AC's = A/4 and Split AC's = 3A/4
Now, let us assume B is the total number of inverter ACs
⇒ From the information that among the Inverter ACs sold, 20% were of Window variant.=> Window Inverter AC's = B/5 and Window Non
Inverter AC's = 4B/5
From - Condition-3

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

⇒ A / 4 - B / 5 = 6 and 4B / 5 = 36 ⇒ B = 46 and A = 60.

Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, from condition-6
a) D1 & D4 sold "0" window Non-inverter ACs ⇒ D2 & D3 sold 6 window non-inverter ACs, it is given that D2 sold twice as many as D3 ⇒ D2 sold 4 and D3 sold 2 ACs of this type.
From condition-2
b) Let us assume, D1 sold "x" window inverter ACs ⇒ Number of split inverter ACs sold is 13-x
From condition-4
c) Number of split ACs sold by D1 will be "2x"
From condition-5
d) Let us assume 'y' is the number of window ACs sold by D3 & D4 ⇒ D2 sold 3y ACs of this type.
From condition-7
e) Let us assume 'z' is the number of split inverter ACs sold by D3 and D4 ⇒ D2 sold 2z ACs of this type.
Let us use a, b, c, d, and e make a table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationWe know that the total number of window ACs is 15
⇒ x + 3y + y + y = 15 ⇒ x + 5y = 15, also x and y should be greater than or equal to 2 from condition-1
⇒ x = 5 and y = 2 is the only solution.
Filling this in the table:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT PreparationNow, Number of split inverter ACs is 36
⇒ 8 + 2z + z + z = 36 ⇒ 4z = 28 ⇒ z = 7.
Filling this and using (5), the number of split AC's sold by D1 is 2 * 5 = 10.
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

If D3 and D4 sold equal number of AC's, the table will look as follows:
Practice Question - 73 (Quant Based) | 100 DILR Questions for CAT Preparation

Number of non-inverter ACs sold is 1 + 4 = 5.

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FAQs on Practice Question - 73 (Quant Based) - 100 DILR Questions for CAT Preparation

1. What is the format of the Quantitative Aptitude section in the CAT exam?
Ans. The Quantitative Aptitude section of the CAT exam typically consists of multiple-choice questions (MCQs) and non-MCQs. The questions cover a range of topics including arithmetic, algebra, geometry, and data interpretation. The total number of questions can vary, but candidates usually have a set amount of time to attempt them, requiring effective time management skills.
2. What types of topics should one focus on while preparing for the Quant section of the CAT exam?
Ans. Candidates should focus on key topics such as number systems, percentages, profit and loss, ratios and proportions, algebra, geometry, and data interpretation. Practicing a variety of problem types from these areas is essential, as they frequently appear in the exam.
3. How important is time management during the Quantitative Aptitude section of the CAT exam?
Ans. Time management is crucial during the Quantitative Aptitude section, as candidates often have limited time to solve a significant number of questions. Developing strategies to quickly identify solvable questions and effectively manage the time spent on each problem can greatly enhance a candidate's performance.
4. Are there any recommended resources for preparing for the Quantitative Aptitude section of the CAT exam?
Ans. Yes, there are several recommended resources for preparation, including CAT preparation books, online courses, and practice tests. Books by authors like Arun Sharma and R.S. Aggarwal are popular. Additionally, joining coaching institutes or online platforms can provide structured learning and access to mock tests.
5. What strategies can help improve performance in the Quantitative Aptitude section of the CAT exam?
Ans. To improve performance, candidates should regularly practice solving problems, review and understand their errors, and take timed practice tests to simulate exam conditions. Focusing on weak areas, learning shortcuts for calculations, and developing a clear understanding of concepts can also be beneficial.
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