CAT Question Bank  Games & Tournaments

Number of Questions  30
Topic  Games & Tournaments
Answer key available?  Yes
Source  Curated Content

Q1) Two persons Alex and Mac played a game of coins. In the game, a player can pick 1, 2 or 3 coins in his turn. If a person is left with 3 coins, he can choose to pick either 1, 2 or 3 coins and if a person is left with 2 coins, he can choose to pick either 1 or 2 coins. But if a person is left with only one coin, he will have to pick that coin. Assume that both the players play intelligently. If Alex started the game and won the game, then which of the following statements is/are true?
(i) There were 49 coins and the person picking the last coin won the game
(ii) There were 36 coins and the person picking the last coin won the game
(iii) There were 42 coins and the person picking the last coin lost the game
(iv) There were 25 coins and the person picking the last coin lost the game
a Only (i) and (iv)
b Only (iv)
c Only (iii) and (i)
d Only (ii) and (iii)[OA: C]

Q2) There are 64 players in a knock out tournament and every player is ranked (seeded) from 1  64. The matches are played in such a manner that in round one the 1st seeded player plays with the 64th, 2nd with the 63rd and so on. The players who win move on to the next round whereas others are out of the competition. In second round, the winner of match 1 will play winner of the last match (which was between seed 32 and seed 33), and winner of match 2 will meet the winner of second last match in round 1 and so forth. Thus, after all rounds winner is declared. Which seeds will play Match no 7 and Match no 10 in Round 1 of a 32player tournament?
a. 26, 23
b. 27, 24
c. 28, 25
d. 29, 26[OA: 26, 23]

Q3) A mixed doubles tennis game is to be played between two teams ( each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played ?
a) 12
b) 48
c) 36
d) 42[OA: 42]

Q4) In a certain game of cards, each of four persons A, B, C and D draws a pair of cards, in turn, from a wellshuffled deck of 52 playing cards. The pair of cards are replaced in the deck after the turn of each person. In any draw, if both the cards drawn by a person are of the same suit, the person is considered to have won the game. Each round of the game begins with A drawing first, followed by B, C and D, in that order. If none of them wins in the first round of draws, they continue drawing cards in the same order. They decide to continue the game until one of them wins and then stop. However, there are several interruptions in the game before a player wins and whenever the game is resumed after an interruption, it resumes with the player whose turn it is. If immediately after the 11th interruption, A’s chances of winning the game are lower than those of exactly two others. Who was the person who drew cards immediately before the 11th interruption?

Q5) In a game played by two people there were initially N match sticks kept on the table. A move in the game consists of a player removing either one or two matchsticks from the table. The one who takes the last matchstick loses. Players make moves alternately. The player who will make the first move is A. The other player is B. The largest value of N (greater than 5) that ensures a win for B is?

Q6) There are 98 given points on a circle. Amar, Akbar and Anthony start playing a game by drawing a chord one by one between two of the points which have not yet been joined together. The game ends when all such points have been joined exhaustively. The winner is the one who draws the last chord. If Anthony starts the game, followed by Akbar, and then Amar, then who will win?
[OA: Anthony]

Q7) In a game, the winner awarded "W" points and the loser "L" points, where W and L are natural numbers such that W > L > 0. Bunty and Babli played a series of such games and it was found that the sum of their scores points is 60 in the end. Babli won exactly 2 games. If there was no tie in any game and Bunty had more points than Babli in the end, then find the maximum value of W.
[OA: 11]

Q8) Four people A, B, C and D are playing a game. Each of them starts with a different number of points. At the end of each round, one Winner is declared. Each of the other three players gives exactly half his points to the Winner. After three rounds. the scores for A, B, C and D respectively are 42, 12, 4 and 24.
 Who won the first round? ‘
 Who won the second round?
 How many points did B have at the start of the game?

Q9) Raju and Radhika are playing a game which involves picking up coins kept on a table. Each person in his/ her turn has to pick a minimum of 1 and a maximum of 7 coins, until all the coins are picked up by the players. Assume that both players are playing intelligently with the intention of winning the game. If there are 42 coins on the table and it is Raju’s turn to play, then how many coins should he pick up to ensure his win?
Assume that the player who picks the last coin win the game.[OA: 2]

Q10) Abhishek and Ajit are two friends playing a game where they throw a fair die alternately. The player who first throws a six wins the game. The total prize money is Rs. 110 which is split among the two friends in the ratio of number of games won. If Abhishek has the first throw, how much money does Ajit expect to win (in Rs.)?

Q11) A game involving a biased die is such that ₹ 5 is paid each time the die shows up a score of 3, while ₹ 8 is paid for every other score on the die. The die is such that the score of 3 occurs 4 times as frequently as any other score. How much would a person be willing to pay as entry fee each time , if in the long run , there has to be neither profit nor loss for taking part in this game?

Q12) A gaming company has created a computer based cricket game, in which a player can face different types of balls and hit different shots on them. Depending on the choice of shot and the timing, a player can score 2, 3, 4 or 6 runs. If the player misses the shot, a wicket is lost, which also causes a deduction of 5 runs in the score. No other result is possible on a ball. If a player faces 60 balls in a game, which of the following is not a possible score at the end of the game?
A) 280 runs with 7 wickets lost
B) 290 runs with 6 wickets lost
C) 271 runs with 8 wickets lost
D) 259 runs with 9 wickets lost[OA: C]

The maximum score possible in the game is 360 (60 balls × 6 runs) with no wickets lost.
For each wicket lost, this score decreases by 11 (6 runs not scored plus 5 runs lost due to the wicket). For example, if 3 wickets are lost, the maximum possible score is 327 [360 − (3 × 11)], which could be achieved by hitting sixes on all the remaining 57 balls.
For 7, 6, 9 and 8 wickets lost (as given in the options), the maximum possible scores are 283, 294, 261 and 272 respectively.
The scores in options 1 and 2 can be achieved if a player hits 3 or 2 runs instead of 6 on one ball. However, option 3 is not possible, as for that, a player would have to hit 5 runs instead of 6 on one ball, which is not possible in this game.
Hence, option C.
[Credits : Lokesh Agarwal]

Q13) A game is played between 2 players and one player is declared as winner. All the winners from first round, played in the second round. All the winners from second round played in third round and so on. If 8 rounds were played to declare only one player as winner, how many players played in first round?
(a) 256
(b) 128
(c) 255
(d) 127[OA: 256]

Q14) Six men engaged in a game. Whenever a player won a game he doubled the money of each of the players. That is, he gave each player as much money as he/she originally had in his/her pocket. They played six games and each player won one game. In the end all of them had Rs. 256 each. What was the difference between the money the person with the highest amount had and the person with the smallest amount had to start off with?

Q15) In the game of Dubblefud, red chips, blue chips and green chips are each worth 2,4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?
a) 1
b) 2
c) 3
d) 4
e) 5[OA: 1]

case 1: we are selecting no couple.
2 males can be selected in 4c2 = 6 ways.
We cannot select the wives of already selected males and should go for others.
so 2c2=1 way.
So in total 2 males and 2 females can be selected in 4c2 * 2c2 = 6 ways..
now the teams can be interchanged as well.
so 6 * 2 = 12 games possible.case 2: when exactly one couple is selected.
so u can select that couple in 4c1=4 ways.
Now after this u need to select 1 male and 1 female more but they should not be a couple.
so selecting 1 male from remaining 3 males in 3c1 way and now for a female u have 2 options left..
so 4c1 * 3c1 * 2 = 24 wayscase 3: when the 2 couples are selected. so 4c2 = 6 ways
Total = 42
Note : Assume A1 B1 and A2 B2 are the two couples selected. Now they cannot be in same team but can play in the same game. A1B2 in one team and A2B1 in other team
[Credits: Jasneet Dua]

Q16) Ashwin and Vijay are playing a game wherein each of them have to choose any no. between 2 and 5. For e.g. if Ashwin picks up 4 then Vijay can next pick from 6 and 9; following which Ashwin can again choose from 8 and 14 depending on what the former person has chosen. The person who chooses 60 first wins.
Given that Ashwin starts the game what no should he choose first ?
(a) 4
(b) 5
(c) 3
(d) he can never winAshwin starts first and chooses 10; what should Vijay choose next in order to win?
(a) 14
(b) 11
(c) 12
(e) None of the above

Q17) Four players – P, Q, R and S – played a game of bursting balloons by shooting at them. In this game the following terms are defined.
Aim = One attempt of shooting at a balloon.
Shot = One instance of shooting down a balloon.
Miss = One wasted aim.The rules of the game are as follows:
(i) Each person will be given a maximum of four rounds of aims, the first round comprising three aims. A person gets the second round of aims only if he scores at least one shot in the first (i.e. the previous) round and so on.
(ii) ( If in any round, the number of shots by a player is 50% or more but less than 100% of the number of aims he had in that round, then he gets one extra aim in each of the remaining rounds. If the number of shots by the player is 100% of the number of aims he had in that round, he gets two extra aims in each of the remaining rounds.)
(iii) For each shot, a player is awarded five points and for each miss, he earns two negative points.
If the number of shots in P’s first round = that in Q’s third round = that in S’s second round = that in R’s fourth round, and P scored eight points in the second round, then what is the maximum possible score by Q in the fourth round?