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- Question
- If the top eight seeds make it to the quarterfinals, then who, among the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?
Options- A. Amelie Mauresmo
- B. Elena Dementieva
- C. Kim Clijsters
- D. Lindsay Davenport
- Correct Answer
- Kim Clijsters
ExplanationIf the top eight seeds make it to quarterfinals, then from the table we can find that Sharapova being top seed will meet seed 8 in the quarterfinals, and in the semifinals she will meet the winner of the match between seeds 4 and 5. So she will not meet seeds 4, 5 or 8 in the finals.
We can sum up the given information as below:
(ii) No team plays against the same team more than once
(iv) No ties permitted.
As per the information given for stage I, we can conclude and draw the table that
(a) As B lost at least one match, hence A won all the 3 matches.
(b) The two teams who lost all the matches cannot be A (as it won all 3 matches), cannot be B (since it is given that E lost to B), cannot be D (since D won against C & F). Hence, the two teams must be C and F.
(c) F did not play against the top team (i.e. A).
We can tabulate all the information as :
In the given below table a blank space means there was no match in this stage (i.e there was no match between A and E in this stage), Result of a match for a team is shown in its row,
(d) A lost both its matches against E and F.
(e) F won against A, hence is the bottom team (out of C and F) which won both the matches F won against C as well. This also means that C lost both its matches against B and F.
(f) Apart from A and C, one more team lost both the matches in Stage-II. That team can neither be E (since A lost to E), nor B (since C lost to B), nor F (as F won both its matches). Hence, the team must be D. - 1. 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 Deven port reaches quarter finals?
Options- A. Justine Henin
- B. Nadia Petrova
- C. Patty Schnyder
- D. Venus Williams Discuss
- 2. The football league of a certain country is played according to the following rules :
- Each team plays exactly one game against each of the other teams.
- The winning team of each game is awarded 1 point and the losing team gets 0 point.
- If a match ends in a draw, both the teams get ½ point. After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following :
- Exactly half of the points earned by each team were earned in games against the 10 teams which finished at the bottom of the table.
- Each of the bottom 10 teams earned half of their total points against the other 9 teams in the bottom 10 . How many teams participated in the league?
Options- A. 16
- B. 18
- C. 19
- D. 25 Discuss
- 3. What is the minimum number of matches won by the winner of the tournament?
Options- A. 8
- B. 6
- C. 5
- D. None of these Discuss
- 4. The minimum number of matches that a team who advanced to the next stage has won?
Options- A. 2
- B. 5
- C. 3
- D. None of these Discuss
- 5. The minimum number of matches that a team must win in order to qualify for the second round is
Options- A. 3
- B. 5
- C. 6
- D. None of these Discuss
- 6. 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?
Options- A. Anastasia Myskina
- B. Flavia Pennetta
- C. Nadia Petrova
- D. Svetlana Kuznetsova Discuss
- 7. If Elena Dementieva and Serena William 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?
Options- A. Dinara Safina
- B. Justine Henin
- C. Nadia Petrova
- D. Patty Schnyder Discuss
- 8. Diesel team won against which team?
Options- A. Edison
- B. Marconi
- C. Faraday
- D. None of these Discuss
- 9. If result of all the matches are interchanged i.e goals for will become goals conceded and vice versa then how many teams will have same number of goals scored as before?
Options- A. 1
- B. 2
- C. 3
- D. None of these Discuss
- 10. What % of total match end up with a result where winner won the match with a goal difference of 2.
Options- A. 66.67%
- B. 77.77%
- C. 55.55%
- D. None of these Discuss
Games and Tournament problems
Search Results
Correct Answer: Venus Williams
Explanation:
1st let us understand the concept of the tournament.
Try to understand the table, in the 1st round the sum of seed is always 33, the same for round 2 is 17 and so on considering there is no upset.
Lindsay Davenport (Seed 2) was scheduled to to meet seed 7, i.e., Justine Henin in the quarter finals. But in the second round since match 7 - involving seed 7 (Justine Henin) and seed 10 (Venus Williams) - resulted in an upset and Venus Williams won the game, hence Davenport will meet Venus Williams in the quarter finals.
Correct Answer: 25
Explanation:
Let total number of teams participated in tournament is n + 10
There are 10 teams in the bottom group then n teams in the top group. It is given that the bottom group gets 45 points since we have 1 point per match therefore 45 matches playing amongst themselves. Therefore they should get 45 points from their matches against the top group i.e., 45 out of the 10n points. The top group get nC2 points from the matches among themselves. They also get ( 10n ? 45 ) points against the bottom group, which is half their total points.
Hence nC2 = 10n ? 45 ? n(n + 1) = 20n ? 90 ? n2 ? 21n + 90 = 0 hence n = 6 or 15
If n = 6, the top group would get nC2 + 10n ? 45 = nC2 + 10(6) ? 45 = 30 points, or an average of 5 points per team, while the bottom group would get (45 + 45)/10 = 90/10 = 9. This is not possible. Hence n = 15. Then total number of teams is 10 + 15 = 25.
Correct Answer: 5
Explanation:
From the solution of previous question a team even with two wins can advanced to next stage where it has to play 3 matches so total number of matches is 5.
Correct Answer: 2
Explanation:
Consider top three team if they won maximum number of matches then points with them is 7 + 6 + 5 = 18, remaining 28 - 18 = 10 points can be distributed to bottom 5 teams, so even after getting 2 points or 2 wins a team can advanced to next stage by tie breaker rule.
Correct Answer: 6
Explanation:
From the solution of previous question even after winning 5 matches a team can get eliminated so to be sure a team must win 6 matches.
Correct Answer: Anastasia Myskina
Explanation:
All odd numbered seeds up to 15 reach the 2nd round while instead of seeds 2 to 16 the players who reach the second round are seeds 31, 29, 27, 25, 23, 21, 19 and 17.
The second round matches are between seeds 1-17, 31-15, 3-19, 29-13, 5-21, 27-11, 7-23 and 25-9. Since there are no upsets in that round the winners are seeds 1, 15, 3, 13, 5, 11, 7 and 9.
The quarter final line up would be
1-9, 15-7, 3-11 and 13-5.
If seed 13 wins her match in the quarters she will next meet seed 1, i.e. Maria Sharapova in semifinals.
Correct Answer: Nadia Petrova
Explanation:
Maria Sharapova, seed 1, would meet the winner of the match between seed 8 and seed 9, but it is given that Serena Williams, seed 8 lost against seed 9 Nadia Petrovain the second round. Hence Nadia Petrova (seed 9).
Correct Answer: Edison
Explanation:
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) ? (5 + 9 + 7 + 4 + 5) = 37 ? 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is casued only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 ? 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
From the table Diesel team won against Edison.
Correct Answer: 2
Explanation:
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) ? (5 + 9 + 7 + 4 + 5) = 37 ? 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is caused only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 ? 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
The new condition would be:
Initially total number of goals made by the teams are Bose (11), Diesel (9), Edison (= 5), Faraday (= 1), Marconi (= 7), and Rankin (= 4)
Now total number of goals made by the teams are Bose (5), Diesel (9), Edison (7), Faraday (4), Marconi (7), and Rankin (5)
So only Diesel and Marconi have the same number of goals.
Correct Answer: 77.77%
Explanation:
Since total number of goals scored and goals against is same hence we can find goals against Marconi which is (11 + 9 + 5 + 1 + 7 + 4) ? (5 + 9 + 7 + 4 + 5) = 37 ? 30 = 7. Since Bose sadan scored 11 goals while goals against is 5 it is possible when all the matches are won with (3-1) (4-2) and (4-2)
Since Marconi got 4 points which is possible with 1 win (3 points) 1 draw (1 point) and 1 loss (0 point) Similarly Rankin got 3 points and also Goals for is 4 and against is 5 so all three matches can not end with draw (It is when goals for is equal to goals against) so 3 points is possible with 1 win and 2 loss.
Faraday scored only 1 goal, goal against is 4 and won 1 match it is possible only when he won by (1-0) and lost two matches with (0-2) each[ as with the combination (0-1) and (0-3) is not possible since (0-3) goal difference is 3] Since Edison won on Wednesday with (2-0) and total goals for is 5 while against is 7, so in other two game it lost with (2-4) and (1-3)
Draw is casued only with Diesel and Marconi hence they must have played with each other and the match was tie.
On Monday Diesel played with Bose, on Tuesday Diesel played with Edison while on Wednesday Diesel played with Marconi.
On Wednesday Bose must have played with Marconi
Faraday played against Edison on Wednesday and lost with (0-2)
Marconi played against Faraday on Monday while against Bose on Tuesday.
Since Rankin scored 4 goals and conceded 5 goals result of Bose and Rankin (3-1) similarly result of Rankin and Edison (3 ? 1)
Now we can conclude that Bose sadan won against Diesel and Marconi with (4-2) and (4-2) Diesel won against Edison with (4-2)
So matches on Monday:
So final result :
Number of points are as follows: Bose (3 + 3 + 3 = 9), Diesel (0 + 3 + 1 = 4), Edison (0 + 0 + 3 = 3), Faraday (0 + 3 + 0 = 3), Marconi (3 + 0 + 1 = 4), and Rankin (3 + 0 + 0 = 3)
Total number of matches is 9, out these 9 matches, the matches that end with goal difference of 2 is Monday: all the three matches, Tuesday 2 matches and Wednesday 2 matches so required percentage is 7 × 100/9 = 77.77%
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