Question

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 lose 1 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:
1.At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
2.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.
3.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.
4.In exactly two out of the six rounds, Arun was the only player who bid Hi.
In how many rounds did Arun bid Hi? [This Question was asked as TITA]

• A. 4 rounds
• B. 2 rounds
• C. 3 rounds
• D. 5 rounds

Answer 1

The Correct Option is B

After three rounds:

• Arun: 6 points
• Dipak: 2 points
• Bankim: -2 points
• Charu: -2 points

After six rounds:

• Arun: 7 points
• Dipak: -1 point
• Bankim: -1 point
• Charu: -5 points

Dipak scored less in the third round than in the first, but more than in the second.
Arun was the sole player to bid Hi in exactly two of the six rounds.
Focusing on the fourth fact: Arun's score increased by 1 point from round three to round six, indicating he bid Hi in round six. As he was the only one to bid Hi in two rounds, he must have bid Hi in round six and one other round.
Now, let's identify the other round Arun bid Hi. At the end of round three, Arun had 6 points, meaning he gained 2 points in the first three rounds.
Arun's score increased by 1 point from round three to round six. This implies a combined gain of 1 point across rounds four, five, and six.
Given he gained 1 point in round six, he must have lost 1 point in either round four or round five.
Assuming a loss of 1 point in round four and a gain of 1 point in round five.
This implies Arun bid Hi in round four and round six.
Therefore, Arun bid Hi in two rounds.