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Solve this DILR Question on Eight Friends from CAT 2017. You are expected to answer the questions that follow, based on the many constraints that are given. Given that there are much easier and less time time consuming sets in the same Question paper with the same number of Questions, Selection of the right set should is a skill that should be honed. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

CAT DILR : 2017 slot 2 questions

Eight Friends

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2-10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.

The following are known:
1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats and 1 Middle seat.
3. Seven of them had to pay extra amounts, totaling to Rs. 4600, for their choices of seat. One of them did not pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.

Question 4: Who among the following did not pay any extra amount for his/her choice of seat?

1. Kikira
2. Manik
3. Gargi
4. Tapesh

Video Explanation

Explanatory Answer

Method of solving this Question on CAT DILR

General Solution

Let us draw a simple diagram and visualize this.



4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.

Where should these three be? J, A and B should be in rows 10, 11 and 12 and should be window or aisle seats.
J = Row 10, A = Row 11, B = Row 12. All three aisle or all three window.

6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.

Where should these two be? They could be in rows 1 and 2, 13 & 14, or 20 & 21. They should be aisle seats if JAB take window . Window seats in JAB take aisle seats.

5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.

If seats are adjacent to each other, either they should both be aisle seats or we should have a middle seat involved.
So, JAB were aisle seats, then Manik also has to be an aisle seat, and GK have to be window and middle seat. In which case P&T would have window seats

If JAB have window seats, M would have to have a middle seat. GK would have to be two aisle seats and PT would have to take two aisle seats.
Possibility 1 = JABM Aisle in row number 10, 11, 12 and 10
GK = window and middle seats, PT = two window seats.
Possibility 2 = JABM seated in 3 window seats and a middle seat row number 10, 11, 12 and 10
GK = aisle seats, PT = two aisle seats.

3. Seven of them had to pay extra amounts, totaling to Rs. 4600, for their choices of seat. One of them did not pay any additional amount for his/her choice of seat.

4600 across 7 members. This is a lot of extra money. There has to be at least one Rs. 1000 extra. This leaves 3600 across 6 members. An average of Rs. 600 extra per person. This is also high. This tells us that there should have been two folks paying Rs. 1000 extra.So, we have Rs. 1000, Rs. 1000 and Rs. 2600 distributed across 5 people. This also averages out to more than Rs. 500. This tells us that we should have had 3 people paying Rs. 1000 extra. So, we have Rs. 1000, Rs. 1000, Rs, 1000 and Rs. 1600 across 4 people.So, we could have someone sitting in rows 1, 12 and 13. We also have folks in 10 and 11.

5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.

Possibility 1 = JABM Aisle in row number 10, 11, 12 and 10
GK = window and middle seats, PT = two window seats.
Extra charge for JABM = 500+400+1000+500 = 2400
3out of the other 4 should give 2200 – this should be 1000 + 1000 + 200. Or, GK could be Rs. 1000 seats in, row 13 or row 1. and PT could have window seats in rows 20 and 21.

Possibility 2 = JABM seated in 3 window seats and a middle seat row number 10, 11, 12 and 10
GK = aisle seats, PT = two aisle seats.
Extra charge for JABM = 300+200+1000+0 = 1500
The other 4 should add up to 3100. This should be as 1000 + 1000 + remaining. The remaining two cannot add up to 1100. So, this possibility can be eliminated.

Final State
JABM Aisle in row number 10, 11, 12 and 10
GK = window and middle seats in row 1 or row 13

PT = two window seats in rows 20 and 21.

Extra charge for JABM = 500+400+1000+500 = 2400
Extra charge for G and K = 1000 + 1000 = 2000
Extra charge for P and T = Rs. 200 + 0.
G and K sat in window and aisle seats of row 1 or 13. So, an additional amount of Rs. 1000 was paid.

The question is "Who among the following did not pay any extra amount for his/her choice of seat?"

Hence, the answer is "Tapesh".

Choice D is the correct answer.