Question Bank (2) - Logical Reasoning - Hemant Malhotra
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As it is given that the row avg and column avg is an integer, the number should be divisible by both 3 (3 rows) and 4 (4 columns). So the required number is divisible by 12.
Sum of the numbers already placed in the grid = 1 + 9 + 14 + 5 = 29
Sum of the numbers in the list = 2 + 3 + 4 + 7 + 10 + 11 + 12 + 13 + 15 = 77
Total sum = 29 + 77 = 106
106 mod 12 = 10
So 10 should be removed from the list to make the total sum divisible by 12.
In case if your are interested in the final arrangement
1 13 3 15 11 9 7 5 12 2 14 4
Q11) Three cards, each with a positive integer written on it, are lying face-down on a table. Casey, Stacy, and Tracy are told that
(a) the numbers are all different,
(b) they sum to 13 , and
(c) they are in increasing order, left to right.
First, Casey looks at the number on the leftmost card and says, "I don't have enough information to determine the other two numbers." Then Tracy looks at the number on the rightmost card and says, "I don't have enough information to determine the other two numbers." Finally, Stacy looks at the number on the middle card and says, "I don't have enough information to determine the other two numbers." Assume that each person knows that the other two reason perfectly and hears their comments. What number is on the middle card?
Q12) A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.
Which of the following is one of the married couples?
a. A & B
b. B & E
c. D & E
d. A & D
What is E’s profession?
How many members of the group are males?
d. Cannot be determined
Q13) In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:
- Each candidates must visit each of the other cities exactly once.
- Each candidates must use only the direct roads between two cities for going from one
city to another.
- The candidates must return to his own city at the end of the campaign.
- No direct road between two cities would be used by more than one candidate.
The maximum possible number of candidates is ?
Q16) Four cities W, X, Y and Z together have 11 hotels.Five of which viz; P, Q, R, S and T, are five-star hotels and the rest viz; A, B, C, D, E and F are three-star hotels.
(i) P and Q are situated in different cities and they are the only five-star hotels in the cities in which they are situated.
(ii) E and F are the only hotels in city Y.
(iii)P is not situated in the city which has largest number of hotels.
(iv) Five-star hotels are situated in more number of cities than three-star hotels.
(v) City Z has more number of five-star hotels than W, which does not have any three-star hotels.
(vi) Each city has a different number of hotels.
How many hotels are there in city Z?
How many cities have three-star hotels?
Which of the following conditions are sufficient to determine the number of hotels in city W?
A.Only (i) and (v)
B. Only (ii), (v) and (vi)
C.Only (i),(ii) and (v)
D.Only (i), (v) and (vi)
Q17) There are three houses on each side of the road.
(ii) These six houses are labeled as P, Q, R, S, T and U.
(iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.
(iv) The houses are of different heights.
(v) T, the tallest house, is exactly opposite to the Red coloured house.
(vi) The shortest house is exactly opposite to the Green coloured house.
(vii) U, the Orange coloured house, is located between P and S.
(viii) R, the Yellow coloured house, is exactly opposite to P.
(ix) Q, the Green coloured house, is exactly opposite to U.
(x) P, the White coloured house, is taller than R, but shorter than S and Q.
What is the colour of the house diagonally opposite to the Yellow coloured house?
e) none of these
Which is the second tallest house?
e) cannot be determined
What is the colour of the tallest house?
e) none of these
Q18) Five people A, B, C, D and E stay in five different rooms of GMVN Hotel. Their rooms lie in a row and are numbered serially from ‘101’ to ‘105’. The number of C’s room is smaller than that of E’s room which in turn is smaller than that of A’s room. Moreover, the difference between the room numbers of E and C is the same as the difference between the room numbers of A and E. D is in room number 104 and his room is not next to E’s room.
What is E’s room number?
(d) Data Insufficient
Q19) P, Q, R, S and T were the five participants in a race. Before the race, there were five predictions
made for the final positions. The predictions were:
The leftmost means the first position and the rightmost means the fifth position in any sequence.
No prediction was completely correct. But two of them correctly predicted the position of exactly two of the runners. The remaining three predictions were incorrect for all the five participants.
What was the actual outcome of the race?
Q20) In a family of seven people A, B, C, D, E, F and G there is exactly one pair of twins. B is younger than F but older than E, G and D. C is younger than E but older than A and D. G is younger than F and E. Which of the following can be the pair of twins?
(a) B, C
(b) A, E
(c) C, G
(d) F, G
Q21) There are four persons Kurt, Cobain, Jim and Morrison out of whom two always lie and the other two always speak the truth. Each of the four persons makes a statement which is given below.
Kurt: Cobain lies.
Cobain: Jim lies.
Jim: Kurt speaks the truth.
Morrison: Exactly two out of Kurt, Cobain and Jim lie.
Who can be the liers?
(a) Kurt and Cobain
(b) Cobain and Morrison
(c) Kurt and Jim
(d) Either (b) or (c)
Q22) Three men A, B and C travel according to the following plan:
A, B and C start travelling and their journey has been carefully jotted out in the statements given below.
Following are the ten destinations P, Q, R, ..., W, X and Y with respect to point
e.g., ‘P’ is 6 km east and 4 km south of point ‘O’.
There are only three travelling speeds:
Speed ‘a’: 4 minutes for each km.
Speed ‘b’: 5 minutes for each km.
Speed ‘c’: 6 minutes for each km.
- ‘A’ starts from point ‘O’, moves north at speed ‘a’ for 12 minutes, turns right moves for 12 km at speed ‘b’, turns towards south and travels at certain constant speed for 14 km. Turns left again and travels at speed ‘c’ for 4 km before finally halting there.
- ‘B’ starting from ‘O’ travels east for 24 min at the fastest speed, moves south and travels for another 8 km at speed ‘a’, turns left travels for 13 km at speed ‘c’. Then turns south and travels for 3 km at speed 'a' and finally stops.
- ‘C’, however, does not start from point ‘O’. He starts from a certain point south of ‘O’, travels east for 1 hr. 28 min at speed ‘a’, turns south and travels for another 24 min at speed ‘c’, turns right, travels at speed ‘c’ for 5 km before turning left, then travels for 3 km at speed ‘a’ and finally stops there.
- ‘C’ starts at 11:58 hrs and ‘A’ and ‘B’ start simultaneously at 12:00 hrs.
If ‘A’ reaches intersection ‘Q’, 100 min after leaving ‘O’. What time shall he stop if he started from ‘O’ at 12:00 hrs?
d)None of these
If ‘C’ travels straight and passes intersection ‘P’ and ‘Q’ at 12:22 hrs and 12:46 hrs respectively, where does ‘C’ start from?
a) (6E, 2N)
b) Destination ‘Y’
c) (12E, 4S)
d) None of these
What is the maximum distance covered by any of the three men at 14:00 hrs?
a) 27 km
d) Cannot be determined
Q23) A, B, C and D were distributed with 12 shirts, each bearing a different no among 1 to 12. No two persons got the same number of shirts. All the prime numbered shirts are owned by B. Both the shirts owned by A bear even nos. THe sum of the numbers on two shirts of C is the same as the sum of numbers on all the shirts of A. Also the no on any of the shirts that C got is not the square of a prime no. Neither the shirt numbered 1 nor the shirt numbered 9 is with B. C received shirt no 12.
What is the maximum possible difference b/w the sum of numbers on all the shirts of any two persons ?
What is the minimum possible difference b/w the sum of nos on all the shirts of any two persons ?
If a shirt numbered 14 is given to anyone except the person having the maximum no of shirts without violating any of the earlier conditions. The sum of the nos all the shirts of C is more than that of B, then what is the sum of all the nos on the shirt of A ?
Which of the following conditions is required to get the unique solution for the distribution ?
a) The sum of all the nos on all the shirts of one of the person is a perfect cube
b) The sum of nos on all the shirts of C is 19
c) Twice the total of nos on all the shirts of A is equal to the total of numbers on all the shirt of B
d) Any of the above
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?