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The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. A chain of departmental store collates the sales data, we have a partial filled table and some extra pieces of information to the puzzle. The questions are very straightforward and asks us comparisons between the data points, one needs to be careful to pick the right data point and zip through the set. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments – ‘Apparel’, ‘Electronics’, and ‘HomeDecor’. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table.



The following additional information is known.
1. The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018. 
2. The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in 2019.    
3. The sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018. 
4. The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.
5. The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
6. The sales amounts in the HomeDecor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
7. The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.
8. The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.

Question 9 : In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?

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Video Explanation

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Explanatory Answer

Before we begin solving, let's try to apply the easiest points to the table to see how much info we can get (Key is to apply the easiest looking rules first so that we can get as many missing numbers as possible, not a good idea to apply the rules in the order that they are given)
For now, let us apply points 1, 2, 3, 6 and see how the table looks:



Now let's apply point 5 so that we can get the missing value Z
(100+72+80+54) - (80 + Z + 60 + Z) = 70
306 - 140 - 2(Z) = 70
166 - 2(Z) = 70
2(Z) = 96
Z = 48

This is how the table looks as of now:


From the available info, we can get the answer to this question. Delhi had the highest sales in 2018 and 2019.

Let's continue to solve the table, let's apply point 7 now


Let's apply point 8.
Since Sales for Delhi, Kolkata and Bangalore in 2019 form an AP, the following must be true:

K (2019) - D (2019) = B (2019) - K (2019)
54 - Y = (2Y - X) - 54
108 = 3Y - X …........................(Equation 1)

Finally, let's apply point 4.

(98 + 102 + 70 + 100) - (78 + 82 + 90 + 80) = (Y + 54 + Y - X + 2Y - X + 54) - (X + Y + Y + X)
370 - 330 = (108 + 4Y - 2X) - (2Y + 2X)
40 = 108 + 2Y - 4X
4X - 2Y = 68…........................(Equation 2)

Solve equations 1 and 2

4X - 2Y= 68
12Y - 4X = 432
10Y = 500

Y = 50
X = 42

The finished table looks like this:

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The question is "In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?"

Hence, the answer is, "Delhi and Delhi"

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