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

At the end of three rounds:

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

At the end of six rounds:

• Arun: 7 points
• Dipak: -1 point
• Bankim: -1 point
• Charu: -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.
Let's start by considering the fourth fact:
We know that Arun's score increased by 1 point from the third round to the sixth round, which means Arun bid Hi in the sixth round. Also, he was the only one who bid Hi in two rounds. Therefore, he must have bid Hi in the sixth round and one more round.
Now let's determine which round Arun bid Hi, excluding the sixth round.
At the end of the third round, Arun had 6 points, so in the first three rounds, he gained 2 points.
Arun's score increased by 1 point from the third round to the sixth round, which means he gained 1 point in the fourth, fifth, and sixth rounds combined.
Arun gained 2 points in the first three rounds, so he must have gained 1 point in the fourth, fifth, and sixth rounds combined.
Since Arun gained 1 point in the sixth round, he must have lost 1 point in either the fourth or fifth round.
Let's assume he lost 1 point in the fourth round and gained 1 point in the fifth round.
So, Arun bid Hi in the fourth round and the sixth round.
Therefore, Arun bid Hi in two rounds.