Answer the next 4 questions based on the information given below.
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.
The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.
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.
The sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018.
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.
The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
The sales amounts in the HomeDecor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
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.
The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic
1.
CAT 2020 LRDI Slot 2
| DI - Tables & Graphs
In HomeDecor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?
The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.
∴ Delhi (2018) = 100 – 20 = 80
Bengaluru (2018) = 80 – 20 = 60
The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.
Let Mumbai (2018) = Kolkata (2018) = a
∴ Data for Home Décor will be as follows
The total sales amounts of the four HomeDecor departments increased by Rs 70 Crores from 2018 to 2019.
∴ (80 + a + 60 + a) + 70 = (100 + 72 + 80 + 54)
⇒ 2a + 210 = 306
⇒ a = 48
Apparels:
The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.
Let Delhi (2018) = Kolkata (2018) = b
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.
Let Mumbai (2018) = Bengaluru (2018) = Delhi (2019) = c
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.
∴ Bengaluru (2019) = c + (c – b) = 2c – b
Also, Mumbai (2019) = c + (54 - b) = c – b + 54
The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.
∴ Delhi – Kolkata = Kolkata – Bengaluru
⇒ Delhi + Bengaluru = 2 × Kolkata
⇒ c + 2c – b = 2 × 54
3c – b = 108 …(1)
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.
From 2018 to 2019, total increase in apparels sales = Total increase in Electronics sales
∴ [c + (c – b + 54) + (2c - b) + 54] – [b + c + c + b] = [98 + 102 + 70 + 100] – [78 + 82 + 90 + 80]
⇒ [4c – 2b + 108] – [2b + 2c] = 370 – 330
⇒ c – 2b = -34 …(2)
Solving (1) and (2) we get,
b = 42 and c = 50 …(3)
∴ We can make the following table
For HomeDecor highest sales in 2018 as well as in 2019 was in Delhi.
Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in sales amount from 2018 to 2019?
A.
25
B.
50
C.
28
D.
75
Answer: Option
B
Explanation :
Consider the solution to the first question of this set.
Maximum percentage increase in sales amount from 2018 to 2019 was in Mumbai HomeDecor = (72 - 48)/48 × 100 = 50%
Answer the next 4 questions based on the information given below.
Twenty-five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
Two adjacent beads along the same row or column are always of different colors.
There is at least one Green bead between any two Blue beads along the same row or column.
There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty-five beads is called a configuration.
5.
CAT 2020 LRDI Slot 2
| LR - Board Games
The total number of possible configurations using beads of only two colors is:
Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximize the number of Red beads used in the configuration?
Answer the next 4 questions based on the information given below.
A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.
For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of each other.
9.
CAT 2020 LRDI Slot 2
| LR - Puzzles
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?
A.
6
B.
7
C.
5
D.
8
Answer: Option
B
Explanation :
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars.
∴ The configuration is
| 1 | 1 | 2 | 3 | 4 | 4 |
Here each cell represents a single parking slot.
Now, Car 1 leaves. The configuration will be:
| V | V | 2 | 3 | 4 | 4 |
Car 5 (a compact car) and car 6 (an SUV) arrive. The configuration will be:
| 5 | V | 2 | 3 | 4 | 4 | 6 | 6 |
Car 4 leaves. The configuration will be:
| 5 | V | 2 | 3 | V | V | 6 | 6 |
Car 7 (an SUV) and car 8 (a compact car) arrive. The configuration will be:
| 5 | 8 | 2 | 3 | 7 | 7 | 6 | 6 |
At this point cars that are parked next to car 3 are car 2 and car 7.
Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?
A.
8, 2, 3, V, 5, 7, 6
B.
8, 2, 3, V, 6, 5, 7
C.
V, 2, 3, 7, 5, 6, 8
D.
8, 2, 3, V, 5, 6, 7
Answer: Option
D
Explanation :
Let us consider each option.
Option (a): 8, 2, 3, V, 5, 7, 6
Here, 5, 7, 6 is not possible since car 7 cannot take position between cars 5 and 6.
Option (b): 8, 2, 3, V, 6, 5, 7
There cannot be two parking slots between 3 and 5.
Option (c): V, 2, 3, 7, 5, 6, 8
Since 7 is an SUV, it cannot come in place of 4 which is a compact car.
Option (d): 8, 2, 3, V, 5, 6, 7
This is possible in the following sequence of arrival of cars.
I. Cars 1 till 7 arrive one after the other. 1 2 3 4 (compact) 5 6 7(SUV)
II. Cars 1 and 4 leave. V 2 3 V 5 6 7(SUV)
III. Car 8 arrives. 8 2 3 V 5 6 7(SUV)
Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?
A.
Car 6 is a compact.
B.
Car 4 is an SUV.
C.
Car 7 is a compact.
D.
Car 2 is a compact.
Answer: Option
A
Explanation :
As cars 3 and 5 are still in their positions and car 6 is in between them, it means car 6 would have arrive after car 4 leaves.
Now 4 is not the first to leave, at least one of the cars 1 or 2 left before car 4.
Let us consider the following cases.
Case 1: Both cars 1 and 2 left before car 4.
This is not possible since car 6 (compact or SUV) would’ve occupied the first parking slot(s).
Case 2: Only car 1 left before car 4.
If car 1 is compact and cars 4 and 6 are SUVs, then car 6 would take place of car 4.
Now car 2 will leave and car 7 will arrive. In this case car 7 will take the first parking slot(s), which is not the case.
∴ This case is also not possible.
Case 3: Only car 2 left before car 4.
If car 2 is compact and cars 4 and 6 are SUVs, then car 6 would take place of car 4.
Now car 7 will arrive and take place of car 2.
Finally, car 1 leaves.
∴ This is the only case possible.
Answer the next 4 questions based on the information given below.
The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department.
Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.
Seminars by students from Economics are scheduled in each of the four slots.
A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
F is an Anthropology student whose seminar is scheduled at 10:30 am.
The seminar of a Sociology student is scheduled at 9:00 am.
B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
P, who is guiding both B and C, has students scheduled in the first two slots.
A and G are scheduled in two consecutive slots.
13.
CAT 2020 LRDI Slot 2
| LR - Selection & Distribution
Which one of the following statements is true?
A.
Only one seminar is scheduled in the second slot.
B.
Three seminars are scheduled in the first slot.
C.
Three seminars are scheduled in the last slot.
D.
Two seminars are scheduled in the first slot.
Answer: Option
D
Explanation :
Seminars by students from Economics are scheduled in each of the four slots.
A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
F is an Anthropology student whose seminar is scheduled at 10:30 am.
The seminar of a Sociology student is scheduled at 9:00 am.
Here, R is an Economics guide, and both his slots should be consecutive. Since there are 4 economics students there must be 2 economics guides.
∴ There must be one more economics guide.
One or R’s slot is at 10 am hence, his next slot will be at 10:30 so that the second economics guide will take the first two consecutive slots.
The seminar of an Economics student, who is guided by T, is also scheduled in the same slot. Therefore, T is the other economics guide who takes the first two slots.
P, who is guiding both B and C, has students scheduled in the first two slots. Also, B is a sociology student.
∴ P is a sociology guide and C is also a sociology student.
B and G are both Sociology students, whose seminars are scheduled in the same slot.
A and G are scheduled in two consecutive slots.
Answer the next 6 questions based on the information given below.
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election.
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.
The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.
The following additional facts are known:
The first runner up polled 10,000 more votes than the second runner up in constituency A.
None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
19.
CAT 2020 LRDI Slot 2
| DI - Tables & Graphs
What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?
The first runner up polled 10,000 more votes than the second runner up in constituency A.
⇒ Votes polled by the second runner-up = 95,000 – 10,000 = 85,000
∴ Total number of votes polled by the top three candidates in A = 2,75,000 + 95,000 + 85,000 = 4,55,000.
Votes polled by remaining 7 candidates = 5,00,000 – 4,55,000 = 45,000 (This is less than one-sixth of the total votes polled)
⇒ Each of the remaining gets polled less than one-sixth of the total polls in A.
∴ Last 7 candidates lose their security deposits and they polled a total of 45,000 votes.
⇒ Percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A = 45000/500000 × 100 = 9%
None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
Total votes polled in C is 6,00,030.
∴ The last candidate (C5) received more than one-sixth of 6,00,030.
The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
Votes polled by the first runner up = 37,500
Votes polled by the winner = 37,500 + 5x
Votes polled by the third runner up is 10% of valid votes which is less than one-sixth of valid votes. Hence third runner up will lose the security deposit.
Now for the second runner up to lose the security deposit total valid votes to be polled must be greater than 6 × 30,000 = 1,80,000.
Since all the options are less than 1,80,000, we can be sure than second runner up did not lose the security deposit.
Hence, number of candidates losing security deposit = 8 – 3 = 5. These 5 candidates get 35% of the total valid votes.
⇒ Winner, first runner-up and second runner-up polled 65% of the valid votes.
The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?
For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?
∴ Approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies = 3,62,500/16,00,030 × 100 = 23.91%
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