LRDI

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:

1. Two adjacent beads along the same row or column are always of different colours.

2. There is at least one Green bead between any two Blue beads along the same row or column.

3. 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.

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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.

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According to the question, cars 1, 4, 6 and 7 are
SUVs and cars 2, 3, 5 and 8 are compact cars.
Now, their arrival and departure are described in
the following steps.

I. 1, 2, 3, 4

II. V, V, 2, 3, 4

III. 5, V, 2, 3, 4

IV. 5, V, 2, 3, 4, 6

V. 5, V, 2, 3, V, V, 6

VI. 5, V, 2, 3, 7, 6

VII. 5, 8, 2, 3, 7, 6

Clearly, car 7 is parked next to car 3.

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Option 1 is not possible as car 7 cannot be parked
between car 3 and car 5 because car 7 is an SUV.

Option 2 is not possible as car 6 cannot be parked
just before car 5 because 4th slot is vacant and
car 4 is a compact car. Option 3 is also not possible
as car 7 which is an SUV cannot be parked
between car 5 and car 6.

Option 4 is the possible current configuration of
the parking lot (Car 1 and car 4 have left and in
place of car 1, car 8 then arrived in that slot)

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Seeing the sequence: 4, 5, 6, V, 3, we can conclude that car 1 and car 2 are definitely SUVs which occupied two slots each. After that car 4, car 5 and car 6 arrived and one slot is vacant which clearly means car 4 and car 5 are compact cars. We cannot say about the type of car 3 so option 4 is not necessarily true.

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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.

1. Seminars by students from Economics are scheduled in each of the four slots.

2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.

3. F is an Anthropology student whose seminar is scheduled at 10:30 am.

4. The seminar of a Sociology student is scheduled at 9:00 am.

5. 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.

6. P, who is guiding both B and C, has students scheduled in the first two slots.

7. A and G are scheduled in two consecutive slots.

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(i) E and H are guided by T.

(ii) G is guided by Q.

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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:

1. The first runner up polled 10,000 more votes than the second runner up in constituency A.

2. 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.

3. 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.

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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.

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