Instructions
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.
How many Split Inverter ACs did D2 sell?
Question Explanation
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/4Now, 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=> A/4 - B/5 = 6 and 4B/5 = 36 => B = 46 and A = 60.
Now, from condition-6a) 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-2b) Let us assume, D1 sold "x" window inverter ACs => Number of split inverter ACs sold is 13-xFrom condition-4c) Number of split ACs sold by D1 will be "2x"From condition-5d) Let us assume 'y' is the number of window ACs sold by D3 & D4 => D2 sold 3y ACs of this type.From condition-7e) 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:
We 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:
Now, 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.
From the table, we see that 14 split inverter ACs are sold.
Master CAT Preparation with Previous Year Papers
Practicing CAT previous year papers is one of the most effective strategies for CAT exam preparation. By solving questions from CAT 2023 dilr-slot-3 and other previous years, you can understand the exam pattern, difficulty level, and types of questions asked in the Common Admission Test.
Why Practice CAT Previous Year Questions?
- Understand Exam Pattern: CAT previous papers help you familiarize yourself with the question format, marking scheme, and time management required for the actual exam.
- Identify Important Topics: By analyzing CAT solved questions from multiple years, you can identify frequently asked topics and focus your preparation accordingly.
- Improve Speed and Accuracy: Regular practice of CAT previous year papers enhances your problem-solving speed and accuracy, which are crucial for scoring well in the exam.
- Build Confidence: Solving CAT previous year questions builds confidence and reduces exam anxiety by making you comfortable with the exam format.
How to Use CAT Previous Papers Effectively
- Solve Under Exam Conditions: Attempt CAT previous year papers in a timed environment to simulate the actual exam experience.
- Analyze Your Performance: After solving each CAT previous paper, analyze your mistakes and identify areas that need improvement.
- Review Solutions Thoroughly: Study the detailed solutions and explanations provided for each question to understand the correct approach and methodology.
- Focus on Weak Areas: Use CAT solved questions to identify your weak areas and dedicate more time to improving them.
CAT Exam Sections Covered
Our comprehensive collection of CAT previous papers covers all three sections of the exam:
- VARC (Verbal Ability & Reading Comprehension): Practice reading comprehension passages, para jumbles, and other verbal ability questions from CAT previous years.
- DILR (Data Interpretation & Logical Reasoning): Master DI and LR questions with detailed solutions from CAT previous year papers.
- QA (Quantitative Ability): Solve arithmetic, algebra, geometry, and other quantitative ability questions from CAT solved papers.
Additional CAT Preparation Resources
Looking for more CAT preparation materials? Explore our comprehensive collection of:
- CAT Previous Papers Archive - Access questions from multiple years and slots
- CAT 2023 dilr-slot-3 Solved Solutions - Complete slot-wise solutions with explanations
- CAT Preparation Courses - Enroll in structured courses for comprehensive CAT preparation
Note: Regular practice of CAT previous year papers, combined with a structured study plan, is essential for achieving a high percentile in the CAT exam. Make sure to solve questions from all sections and review the solutions thoroughly to maximize your preparation effectiveness.
