Question Bank (2) - Logical Reasoning - Hemant Malhotra
Q24) Ten players are participating in the Sunfeast Open Tennis tournament being held in India. Each of these ten players play exactly one match against each of the remaining 9 players in the tournament. At the end of every match an aggregate of 12 points are divided among the players playing that match such that each player gets atleast 2 points and at most 10 points in the match (points earned are always integers).
The following table provides partial information about the 10 players participating in the Sunfeast Open. The data in the table was updated just before the start of the tournament.
It is also known that the ‘World Ranking’ of these ten players lie between 5 and 16 (both inclusive) prior to the start of the tournament. Between any two players, a numerically lesser world ranking is given to a player who has earned more number of points. In case two players have earned same number of points, then they are given the same world ranking. World ranking of a player is 1 more than the number of players who have got more points than her. Hence in the following table if two players have a world ranking 10 then the next player will have world ranking 12. In the table given below no player has earned more points than the player just above him. The player with world ranking 1 has earned 53 points prior to the start of the tournament and during the time the Sunfeast Open is being played, there is no other tournament being held anywhere in the world that could possibly change the world ranking and the number of points earned by any player.
Which of the player/s among the 10 participating in the Sunfeast Open Tennis tournament had a World Ranking of 12 prior to the start of the tournament?
(a) Samantha Vickers
(b) Hannah James
(c) Both Samantha Vickers and Hannah James
(d) None of the 10 players
Given that Naomi Cavaday earns minimum possible number of points in exactly 4 matches and in each of the other 5 matches she earns a distinct number of points. Also, Hannah James earns maximum possible number of points in exactly 5 matches. What would be the maximum possible difference between the number of points earned by Naomi Cavaday and Hannah James at the end of the Sunfeast Open.
If Jade Curtis earns maximum possible number of points in all the matches played by her and gets World Ranking 3 at the end of Sunfeast Open, then which of the following players could possibly get the World Ranking 2 at the end of the Sunfeast Open?
(a) Naomi Broady
(b) Laura Slater
(c) Samantha Vickers
(d) None of these
Additional information for question 4: Each of the three players namely Naomi Cavaday, Jocelyn Rae and Laura Slater earns maximum possible number of points in ‘X’ matches. The value of ‘X’ is maximum possible.
4) Find the number of points earned by Laura Slater at the end of the Sunfeast Open.
(d) Cannot be determined
Q25) This week, Mr. & Mrs. Allman and four other couples are second-honeymooning at the Tie the Knot Lodge, with each couple staying in the same cottage in which they honeymooned when they first got married, including one couple in the garishly red-and-pink Valentine Cottage. Each of the couples, including Michelle and her husband, is also celebrating a wedding anniversary, with no two couples having been wed the same number of years. Given the clues below, can you find each second honeymoon couple's full names, the cottage in which they are celebrating, and the number of years they have been husband-and-wife?
- The couples have been married from a high of 50 years to a low of 15 years; the couple married the shortest time aren't Karen and her spouse.
- Mr. & Mrs. Epstein have been married twice as long as Will and his wife; neither is the couple second-honeymooning in the Bridal Veil Cottage.
- Steve and Mr. Bronson enjoy a daily round of golf together while their wives play tennis.
- For Leah Dixon and her husband, it is their first return to Tie the Knot Lodge since their original honeymoon.
- Rick and his wife have been wed 10 years longer than the Chandlers.
- Jasmine and her spouse have been husband-and-wife twice as long as the couple staying in the Rose Cottage.
- Nina and her mate have been married 10 years longer than Paul and his wife and 20 years longer than the couple second-honeymooning in Cupid's Cottage.
- Ted and his wife have been wed 10 fewer years than the couple who are staying in True Love Cottage; the latter are not Mr. & Mrs. Bronson.
- Will and his wife aren't lodging in Cupid's Cottage or in Rose Cottage.
- The couple staying in Bridal Veil Cottage is neither Jasmine and her husband nor Nina and her spouse.
Q1. For how long the Chandlers have been married?
Q2. Which couple is lodging in the Rose Cottage.
Q3. Which couple has been married for 15 years.
Q4. Name of ted's wife.
Q5. Jasmine's husband?
Q26) N girls and 2N boys played a chess tournament. Every player played every other player exactly once. The boys won 7/5 times as many matches as the girls (and there were no draws). Then which among the following is definitely false? (Assume 1 point for a win and 0 for a loss)
(a) Boys pocketed prime number of points against girls
(b) Girls always won twice or more matches than boys won against them
(c) The sum of the scores of top 3 individual players was not between 25 and 33
(d) The sum of the scores of top 3 individual players was 69
Total number of matches among boys were 2nC2, among girls were nC2 and between boys and girls were n * 2n.
so 2nC2 + nC2 + 2n^2 = 3nC2. Assume 1 point for a win and 0 for a loss.
Girls pocketed nC2 points amongst themselves and boys pocketed 2nC2 points among themselves. Let boys take k points from their matches against girls so girls take 2n^2 - k from their matches gainst boys.
so 2nC2 + k = 7/5 * (nC2 + 2n^2 - k), solving this 8k = n(5n+1). for n = 3, k = 6. For n = 8, k = 41, For n = 11, k = 77.
(a) can be true as for n = 8, k = 41. (b) can be true as can be seen for for n = 3, 8, 11, ... (c) is true as for n = 3, top 3 can score 8+7+6 = 21 points and for n = 11, when 33 matches are played top 3 will always score more than 16+15+14 = 45. (d) is true, For n = 11, we can have the top 3 score as 23+23+23 = 69.
Q27) Four students Khushi, Sonal, Darshan and Gourav are ranked 1 to 4, on the basis of their performance in a class test.
The following data is given about their ranks:
- If Khushi is ranked 1, then Sonal is not ranked 3.
- If Sonal is not ranked 1, then Gourav is ranked 4.
- If Darshan is not ranked 2, then Gourav is ranked 2.
- If Darshan is ranked 3, then Gourav is not ranked 2.
- If Gourav is ranked 3, then Khushi is not ranked 4.
Who is ranked 1 among the four students?
(d) Cannot be determined
Who is ranked 4 among the four students?
(d) Cannot be determined
The ranks of how many of the four students can be determined?
Q28) Seven Hockey teams A, B, C, D, E, F and G participated in a tournament. Each team played with every other team twice and D won all of its games and F lost all of its games. B and G scored equal points and are ahead of C. C, A and E also scored equal number of points. Each team gets 3 points, 1 point and no point for a win, draw and loss respectively. What is the highest possible number of points that can be scored by team A?
Q29) On a particular day, five persons — Pavan, Salman, Farhan, Lokesh and Manish — went to a multiplex to watch five movies each of a different duration among 100 minutes, 125 minutes, 160 minutes, I80 minutes and 205 minutes. The show of each of the five movies began at a different time among 11:00 AM, 11:25 AM, 11:45 AM, 11:50 AM and 12:15 PM. Further, each show ended exactly after the duration of that movie and the five persons came out of the multiplex immediately after the show ended.
It also known that
- No two persons came out of the multiplex at the same time
- Pavan, who watched 125-minute-long movie, did not come out of the multiplex before 1:20 PM.
- Among the five persons, the last person to come out of the multiplex was Farhan.
- Lokesh came out of the multiplex after 2:45 PM but he did not watch the 205 minute-long movie.
- Among the five persons, at least three persons came out of the multiplex before Manish did.
Who watched the 160-minute-long movie?
We know from the conditions that F will come out last. Manish will last second. & P/S/L will be 1st/2nd/3rd.
And in the questions too, there is no option of CBD so we get to know that our table will be complete. No multiple cases will be there so Now we can try filling our table with the given conditions.
Now L came out after 2:45 and It didn't stay for 205 minutes so he could have stayed for 180 minutes. Now he is also the third one to exit so we can say that he won't be the last one to enter. Because if he was the last one to enter and he stayed for 180 minutes(which is second largest time to stay) then he should have been the 4th one to come out which is not the possibility. The max position at which he can come out is 3rd. So now we can take the time to be 11:50 and he stayed for 180 minutes so he come out at 2:50(which is just greater than 2:45)
Now manish needs to be at 4th so set time of manish accordingly that F also comes out at last. And after a bit of checking you will see manish could have entered at 12:15 and stayed for 160 minutes and exit at 2:55. Similarly you have to proceed. Narrow down your cases and it will be done..
Q30) 38 fruits, apples, oranges, plums and guavas, are distributed among 4 people A, B, C and D. Each one gets a minimum of one fruits of each type and a maximum of four fruits of each type. There are 12 apples. There are two females, each of whom has the highest number of fruits. D, who has 3 plums, has 5 fruits less than the person who has the highest number of fruits. A has 4 apples and 4 plums and does not have the lowest number of fruits. B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. None of the friends has exactly the same composition of all fruits as any other friend.
- The females together had how many more fruits than the males had together? ﴾in numerical value﴿
- What is the total number of plums?
Manveer Sawhney last edited by
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