The below article is brought to you by SDA Bocconi Asia Center and written by Dr Shashank Prabhu to help aspirants in their test prep. He is a CAT 100 percentiler, CET Rank 1, IIFT 100 percentile. He had a scaled score of 249/360 in NMAT BY GMAC 2016 and 99 percentile in each of the sections and overall score. SDA Bocconi Asia Center accepts CAT, NMAT, GMAT, GRE for its International Master in Business.
This was arguably the most difficult set in the second slot of CAT 2017. Although it was almost impossible to solve this set during the test, I would strongly suggest that you give it a try once and see for yourself the thought process that separates an easy set from a difficult set. As I have already mentioned elsewhere, the difficult sets in CAT are not un-attemptable because of conceptual depth, but because of the reluctance of average aspirants to write down cases and muscle through the cluttered information. Here we go:
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
The key to cracking this set does not lie so much in the drawing the entire layout and writing down numbers on your sheet than it does in understanding the significance of the extra charges.
Consider this: there are 8 people out of whom, 7 paid extra charge for the seat of their choice. These 7 people together paid Rs. 4600. Which means that the per head spend was slightly more than Rs. 650.
If we look at the extra charges, we can see that the various numbers are Rs. 1000, Rs. 300, Rs. 500, Rs. 200 and Rs. 400. A basic understanding of averages (the average lies between the highest and the lowest quantity) will tell us that the per head cost of approximately Rs. 650 is not possible if none of the passengers paid Rs. 1000. So, there exists at least one person who paid Rs. 1000. If we remove this person from the overall charge, we have to account for Rs. 3600 among 6 people. The per head average still comes out to be Rs. 600 which needs another person to pay Rs. 1000 to be viable. If we remove another 1000 from the Rs. 3600 that we had earlier, we have to distribute Rs. 2600 among 5 people. Again the per head average comes out to be Rs. 520 which indicates that at least one more person would have paid Rs. 1000. If we remove this person from the tally as well, we get Rs. 1600 to be distributed among 4 people. This is possible in multiple ways and so, we can leave it at that. We have inferred till now the fact that there exist at least 3 people who would have paid Rs. 1000 each.
Now coming to the paid seats, we can see that the ones that don’t need any extra payment are the middle seats in rows 2 to 11 and from 14 to 20. The seats beyond row 20 had no extra charge.
The most prominent point is the seating of Jayanta, Ajit and Byomkesh. As can be understood, we need 3 consecutive rows where there is a disparity in the prices. This can be seen only in case of rows 10, 11 and 12. So, Jayanta, Ajit and Byomkesh are sitting in rows 10, 11 and 12 respectively.
From point number 5, we can see that Jayanta and Manik are sitting together and hence Manik will also be sitting in row 10.
There are two cases from here onwards (given that there are 3 Window seats, 4 Aisle seats and 1 Middle seat):
- Jayanta, Ajit and Byomkesh are all occupying window seats. So, Manik will be occupying a middle seat in row 10. It can be inferred that Manik is the only person who would not be paying any extra charge. Jayanta, Ajit and Byomkesh will end up spending a total amount of Rs. 1500. We have taken care of one instance of Rs. 1000 out of the three that we had figured out earlier. So, at least two of the remaining four people should occupy seats worth Rs. 1000 (total amount still left to distribute is Rs. 4600 – Rs. 1500 = Rs. 3100) and all of them should be occupying the aisle seats. As row 12 is already accounted for, the only options for Rs. 1000 seats are row 1 and row 13. Prodosh and Tapesh can occupy either rows 1-2 or 13-14 (we don’t consider 20-21 as we have already figured out that Manik is the only person who has not paid anything extra). If they occupy aisle seats in rows 1-2, we get the cost to be Rs. 1500 and if they occupy aisle seats in rows 13-14, we get the cost to be Rs. 1400. In the first case, we have to account for Rs. 3100 – Rs. 1500 = Rs. 1600 which translates into 2 aisle seats of Rs. 800 each which is not possible. In the second case, we have to account for Rs. 3100 – Rs. 1400 = Rs. 1700 which translates into 2 aisle seats of Rs. 850 each which is again not possible. So, the cases don’t lead us to possible conclusions and so, out hypothesis is incorrect
- Jayanta, Ajit and Byomkesh are all occupying aisle seats. So, Manik will occupy an aisle seat or a middle seat on row 10. The cost comes out to be Rs. 2400 and Rs. 1500 respectively. If Manik occupies the lone middle seat, three out of the remaining four should occupy window seats and the last one, an aisle seat which is not possible because two out of the four are neighbours. So, Manik should occupy an aisle seat. The cost till now is Rs. 2400 and so, we have to account for Rs. 2200 to be distributed among three window seats and one middle seat, out of which, one is a zero-cost seat. Also, if we recollect, there are still at least two Rs. 1000 charge seats that we need to account for and so, Rs. 200 has to be the cost of the third seat (so, 1000 + 1000 + 200 is the split). As this is possible, we can go ahead with this case. Prodosh and Tapesh should be sitting in window seats in rows 1-2 (cost Rs. 1300, so out), 13-14 (cost Rs. 1200) or 20-21 (cost Rs. 200). Also, Gargi and Kikira should occupy a middle seat and a window seat in some order in the same row. If Prodosh and Tapesh occupy window seats in Rows 13 and 14, Gargi and Kikira will have to account for Rs. 1000 such that exactly one of them does not pay anything extra, which is not possible. So, Prodosh and Tapesh occupy window seats in rows 20 and 21 respectively. Also, Gargi and Kikira will be seating in row 1 or 13 occupying window and middle seats in some order
To sum it up, we have got:
Gargi and Kikira: 1 window and 1 middle seats in Row 1 or Row 13
Jayanta and Manik: Both aisle seats in row 10
Ajit: Aisle seat in row 11
Byomkesh: Aisle seat in row 12
Prodosh: Window seat in row 20
Tapesh: Window seat in row 21
Q1. In which row was Manik sitting?
It is obvious that Manik sits in Row 10. Option A is correct.
Q2. How much extra did Jayanta pay for his choice of seat?
A. Rs. 300
B. Rs. 400
C. Rs. 500
D. Rs. 1000
We can see that Jayanta occupied an aisle seat in Row 10 and so, paid Rs. 500 extra. Option C is correct.
Q3. How much extra did Gargi pay for her choice of seat?
B. Rs. 300
C. Rs. 500
D. Rs. 1000
Gargi sat in either Row 1 or Row 13 and so, should have paid Rs. 1000 extra. Option D is correct.
Q4. Who among the following did not pay any extra amount for his/her choice of seat?
We can see that Tapesh did not pay anything for the seat of his choice. Option D is correct.
This was a scorcher of a set and it was not because of too much calculation or too deep a concept. It was a beautiful example of retention. If you were able to build the thought process that I have written above in your head, you would have been able to eliminate cases much quicker. This is precisely what CAT looks for in a good candidate and if you focus intently on this aspect, you should be able to do very well in the section.
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