# CAT Games and Tournaments Questions PDF [With Solutions]

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Games and Tournaments is one of the key topics in the CAT LRDI section. Over the past few years, CAT Games and Tournaments questions have made a recurrent appearance in the LRDI section. You can check out these Games and Tournaments CAT questions PDF from the CAT Previous Year Papers. In this article, we will look into some importantÂ  Games and Tournaments questions PDF(with solutions) for CAT.

If you’re weak in this concept, first learn the Games and Tournaments basics and watch the games and tournaments CAT concept video. Check out the below Games and Tournaments cat practice questions and sets.

Instructions

Answer the following questions based on the information given below:

In a sports event, six teams (A, B, C, D, E and F) are competing against each other Matches are scheduled in two stages. Each team plays three matches in Stage â€“ I and two matches in Stage â€“ II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage â€“ I and Stage â€“ II are as given below.

Stage-I:

â€¢ One team won all the three matches.

â€¢ Two teams lost all the matches.

â€¢ D lost to A but won against C and F.

â€¢ E lost to B but won against C and F.

â€¢ B lost at least one match.

â€¢ F did not play against the top team of Stage-I.

Stage-II:

â€¢ The leader of Stage-I lost the next two matches

â€¢ Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches.

â€¢ One more team lost both matches in Stage-II.

Question 1:Â The two teams that defeated the leader of Stage-I are:

a)Â B & F

b)Â E & F

c)Â B & D

d)Â E & D

e)Â F & D

Solution:

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the two teams that won against stage 1 leader A are E and F.

Question 2:Â The only team(s) that won both matches in Stage-II is (are):

a)Â B

b)Â E & F

c)Â A, E & F

d)Â B, E & F

e)Â B & F

Solution:

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the teams that won both of their stage 2 matches are B, E and F.

Question 3:Â The teams that won exactly two matches in the event are:

a)Â A, D & F

b)Â D & E

c)Â E & F

d)Â D, E & F

e)Â D & F

Solution:

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the wins by each team are A (3), B(4), C(0), D(2), E(4), F(2). Hence, D and F won exactly 2 matches.

Question 4:Â The team(s) with the most wins in the event is (are):

a)Â A

b)Â A & C

c)Â F

d)Â E

e)Â B & E

Solution:

There are a total of $^6 C_2$ matches => 15 matches. The first 9 matches are held in the first stage and remaining 6 in the second stage.

From the information given, we can conclude that the following matches were held in first stage:

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won)

One team won all matches. As B, C, D E and F have lost at least one match each, A won all three matches. As A, B, D, E have won at least one match, C and F lost both matches.

From the matches already deduced, we can see that A needs to play 2 more matches, B two more matches and C and F one match each. As C and F lose all matches in stage 1, they cannot play against each other. F did not play against the leader i.e. A. Hence, the remaining matches are A-B (A won), A-C (A won), B-F (B won).

Thus, the stage 1 matches are

Stage 1: D-A (A won), D-C (D won), D-F (D won), E-B (B won), E-C (E won), E-F (E won), A-B (A won), A-C (A won), B-F (B won)

Thus Stage 2 matches are D-B, D-E, E-A, F-A, B-C and C-F (all matches – stage 1 matches)

As A lost both matches, F and E must have won the match vs A. As F won against A, F won both its matches and C lost both its matches. One more team lost both its matches. As B, E and F have won at least one match and A and C have been discussed previously, D must have lost both matches. Hence, stage 2 results are:

Stage 2: D-B (B won), D-E (E won), E-A (E won), F-A (F won), B-C (B won) and C-F (F won)

Hence, the wins by each team are A(3), B(4), C(0), D(2), E(4), F(2). Hence, most wins are by B and E.

Instructions

In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.

<img “=”” alt=”” class=”img-responsive” src=”https://cracku.in/media/questionGroup/DI_4_5.png”/>

Question 5:Â If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?

a)Â Justine Henin

c)Â Patty Schnyder

d)Â Venus Williams

Solution:

There are no upsets in 1st round, so top 16 players go to the 2nd round.

In second round, nth player would play (17-n)th player. Now,Â match Nos. 6, 7, and 8 of the second round result in upsets.

So the people in the quarter finals would be 1,2,3,4,5,11,10,9.

So in quarterfinal 2nd seeeded player would play (9-2) = 7th position player.

Here no. 10 is in the 7th position and No. 10 player is venus williams.

Hence option D.

Question 6:Â If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?

a)Â Dinara Safina

b)Â Justine Henin

d)Â Patty Schnyder

Solution:

If Elena Dementieva and Serena Williams lose in the second round, Nadia petrova Â and patty schnyder will go through.

Hence ,in the quarter finals, following seed no. players will be in Â quarter finals: 1,2,3,4,5,11,7,9.

So, nowÂ Maria Sharapova is ranked is 1 so she’ll play 9th seed player whoÂ isÂ Nadia Petrova.

Hence option C.

Question 7:Â If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?

a)Â Anastasia Myskina

b)Â Flavia Pennetta

d)Â Svetlana Kuznetsova

Solution:

According to given condition, players of following ranking will go to the 2nd round 1,31,3,29,5,27,7,25,9,23,11,21,13,19,15,17.

Out of these players going to 3rd round / quarter finals are 1,15,3,13,5,11,7,9.

If maria (no.1) goes to semifinal she’ll face any on eout of the 13/5 th no. player in semis.

13th seed player is the lowest soÂ Anastasia Myskina.

Question 8:Â If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

a)Â Amelie Mauresmo

b)Â Elena Dementieva

c)Â Kim Clijsters

d)Â Lindsay Davenport

Solution:

If the top eight seeds make it to the quarterfinals then one out ofÂ Kim Clijsters or svetana kuznetsova will compete with maria sharapoava in semis.

So now if maria reaches semis, she’ll beat any one out of the two and both willÂ definitely not play against Maria Sharapova in the final, if she reaches .

Instructions

Directions for the next 5 questions:

Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated, The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.

The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.

Question 9:Â What is the total number of matches played in the tournament?

a)Â 28

b)Â 55

c)Â 63

d)Â 35

Solution:

In 1st stage there were 2 groups each group played 28 matches as $^8C_2$ = 28. So total 56 matches after 1st stage . IN 1st round of stage 2, 4 matches are played and in the next round we have 4 teams .The winner is one who defeats every team out of remaining 3Â matchesÂ . so 3 matches more needed. In total 56+4+3=63.

Question 10:Â The minimum number of wins needed for a team in the first stage to guarantee its advancement to the next stage is:

a)Â 5

b)Â 6

c)Â 7

d)Â 4

Solution:

Let us first try to find the maximum number of points with which a team cannot advance to the second stage.

For this to happen the top five teams should have highest possible equal number of points and one team does not advance after the tie breaker.

To maximize the points of top 5 teams all of the top 5 teams should win their matches with the bottom 3 teams. Now each team has 3 points.

The top 5 teams play 5C2 = 10 matches among themselves. There are 10 points to be won from these 10 matches.

Now as all the top 5 teams should have equal number of points each team gets 2 points from these games.

In all each top 5 team gets 3+2 = 5 points each.

In this case after getting 5 points also one of the top 5 teams will not advance to the second round.

Thus the maximum number of points with which a team cannot advance to the second stage is 5.

Therefore at least 6 wins are required for a team to guarantee its advancement to the next stage.

Question 11:Â What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?

a)Â 1

b)Â 2

c)Â 3

d)Â 5

Solution:

There are 28 matches in the 1st round of 8 player group so in total 28 wins.To find this, we need the top 5 teams to win nearly equal matches. So Let each of the top 5 teams win 5 matches each and the remaining 3 matches are won by the bottom 2 teams. The qualifiers will be decided based on the tie breaking rules. Hence, even with 5 wins a team may end up not qualifying for the next round. Thus, option D is the correct answer.

Question 12:Â What is the number of rounds in the second stage of the tournament?â€™

a)Â 1

b)Â 2

c)Â 3

d)Â 4

Solution:

2nd stage 1st round has 8 teams , 2nd round will have 4 teams and 3rd round 2 teams where the winner wins .

Instructions

The following questions relate to a game to be played by you and your friend. The game consists of a 4 x 4 board (see below) where each cell contains a positive integer. You and your friend make moves alternately. A move by any of the players consists of splitting the current board configuration into two equal halves and retaining one of them. In your moves you are allowed to split the board only vertically and to decide to retain either the left or the right half. Your friend, in his/her moves, can split the board only horizontally and can retain either the lower or the upper half. After two moves by each player a single cell will remain which can no longer be split and the number in that cell will be treated as the gain (in rupees) of the person who has started the game. A sample game is shown below. So your gain is Re.1. With the same initial board configuration as above and assuming that you have to make the first move, answer the following questions.
Initial Board

After your friends move (retain upper)

After your friends move (retain lower)

Question 13:Â If you choose (retain right) (retain left) in your turns, the best move sequence for your friend to reduce your gain to a minimum will be

a)Â (retain upper)(retain lower)

b)Â (retain lower) (retain upper)

c)Â (retain upper) (retain upper)

d)Â (retain lower) (retain lower)

Solution:

After my first move of retaining right board will be like

Now second person will force me to retain with the lowest value possible i.e. 2 or 3
So if he retains lower half and i retain with left one (as mentioned) then he can only force me to pick 3.
Or if he retains upper half and i retain with left one(as mentioned) then he can retain upper half so i will be having minimized profit of 2.
Hence second person will have moves as “Retain (upper half) and retain (upper half)”

Question 14:Â If both of you select your moves intelligently then at the end of the game your gain will be

a)Â Rs.4

b)Â Rs.3

c)Â Rs.2

d)Â None of these

Solution:

After second move i will be having from a quarter cell of board to make a move.

Since left quarters have cells with values 1, Hence i will choose to retain right in my first move so that second person can force my profit to be either 2 or 3 not 1.

So now after my first move of retaining right, we have two quarters

Now intelligently he will make a move to retain with lower half so that at fourth move i can retain with choices of 2 and 3 not 2 and 4.

Question 15:Â If your first move is (retain right), then whatever moves your friend may select you can always force a gain of no less than

a)Â Rs.3

b)Â Rs.6

c)Â Rs.4

d)Â None of these