CAT 2020 Slot 3 — DILR Question 13
Answer the next 4 questions based on the information given.
The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
- At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
- At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
- Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
- In exactly two out of the six rounds, Arun was the only player who bid Hi.
What were the bids by Arun, Bankim, Charu and Dipak, respectively in the first round?
Answer & solution
- A
Hi, Lo, Lo, Lo
- B
Lo, Lo, Lo, Hi
Hi, Lo, Lo, Hi
- D
Hi, Hi, Lo, Lo
Points scored in a round has the following possibilities:
H H H H: (-1, -1, -1, -1); Total -4
H H H L: (1, 1, 1, -3); Total 0
H H L L: (2, 2, -2, -2); Total 0
H L L L: (3, -1, -1, -1); Total 0
L L L L: (1, 1, 1, 1); Total 4
âââââââTotal points scored in a round can be -4, 0 or 4.
We can make the following table from the data given.
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Net score after first 3 rounds is 6 – 2 – 2 + 2 = 4.
This could have happened if the total score in first three rounds was {4, 4, -4} or {4, 0, 0} in any order.
∴ In one of the first 3 rounds the net score has to be 4. This is only possible when all of them bid Lo and score 1 point each.
Now, Arun scored total 6 points in first 3 rounds. Also, he scores 1 in one of the first 3 rounds. This is possible if he scores {3, 2, 1} in any order in the first 3 rounds.
For Arun to score 3 in a round he will have to bid Hi and other will bid Lo. Other 3 will score -1 each.
For Arun to score 2 in a round he will have to bid Hi along with one other and the remaining two will bid Lo. Scores of other 3 will be {2, -2, -2} in any order.
Dipak’s score in two of the rounds is 1 and -1. His net score in 3 rounds is 2. Hence, Dipak scores 2 in one of the first three rounds.
Also, Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
∴ We can make the following table for the first 3 rounds.
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Net score in last 3 rounds is 1 + 1 – 3 - 3 = -4.
This could have happened if the total score in last three rounds was {4, -4, -4} or {-4, 0, 0} in any order.
∴ In one of the last 3 rounds the net score has to be -4. This is only possible when all of them bid Hi and score -1 point each.
In exactly two out of the six rounds, Arun was the only player who bid Hi i.e., Arun scores 3 in exactly 2 of the six rounds.
∴ Arun scored 3 in one of the last 3 rounds. Also, his net score in last 3 rounds is 1. Hence, he scores -1 and -1 in 2 of the last 3 rounds.
∴ We can make the following table for the all 6 rounds.
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In first round Arun, Bankim, Charu and Dipak bid Hi, Lo, Lo and Hi.
Hence, option (c).