Logical Reasoning & DI (LRDI) Test

Result

Logical Reasoning & DI (LRDI) Test - 21

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
3 / -1

Directions For Questions

4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).

...view full instructions

Which of the following is the least number of wins that the winner of the world championship can have?

A
11

B
10

C
9

D
7

Solution

To win the world championship, a player must win all the five matches in that tournament.

In the four preceding tournaments there are 128 players.

So in an individual tournament.

64 will win 0 match.

32 will win 1 match.

16 will win 2 matches.

8 will win 3 matches.

4 will win 4 matches

2 will win 5 matches.

1 (finalist) will win 6 matches.

1 (champion) will win 7 matches.

There are 31 places which are already confirmed and 97 players are for the 32nd position.

We must maximize the number of matches won by the other 31 players

⇒ remaining 97 players must win least number of matches.

In the first tounament

Thus for 97 players, 64 will win 0 matches 32 will win 1 match and the remaining 1 player will win 2 matches.

n the first tournament total number of matches won by these 97 players= 64x0+32x1+1x2= 34 wins

In all the 4 tournaments total number of wins will be 4x34=136

There are 97 players, so they will distribute victories among themselves. As 136/97=1.402 some players can have 2 wins and others will have 1 win.

Suppose X players win 2 matches and Y win only 1 match.

So X+Y=97

2X+Y=136

X= 39

Y=58

So 39 players have 2 wins, and 58 players will have 1 win.

Among these players one will be selected for the world championship based on certain criteria.

Hence minimum number of wins required = 5 + 2 = 7
Question 2
3 / -1

Directions For Questions

4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).

...view full instructions

Which of the following is the maximum number of wins that a player could have had and still not be selected for the world championship tournament?

A
10

B
11

C
12

D
13

Solution

To get the maximum number, we need to take the case where 33 players won maximum number of matches, of which exactly 32 were selected for the World Championship based on certain criteria.

Consider these 33 players. Say each of them won at least n matches each.

In every tournament, 64 players win at least one match. Suppose the same set of 64 win the first round of each tournament. Our set of 33 goes on to win more than one match on average in the 4 tournaments.

Hence, 64 - 33 = 31 players win exactly one match.

Hence, players 1-33 win >= n matches, 34 - 64 win exactly one match and 65-128 win no matches.

Total number of wins in 4 tournaments = 4 * 127 = 508

Wins accounted for by players 34-64 = 31 * 4 = 124

Wins remaining = 508 - 124 = 384. These 384 wins need to be distributed over the remaining 33 players in the most equal way possible i.e difference in wins of player 1 and player 33 is the minimum possible.

The largest multiple of 33 <=384 is 33*11 i.e. 363. Suppose the first 33 players have 11 wins each. This accounts for 33*11 = 363 wins.

Hence, number of wins left = 384 - 363 = 21. Let these 21 wins go to the first 21 players.

Hence, players 1-21 win 12 matches, 22 - 33 win 11 matches, 34-64 win 1 match and 65 -128 win 0 matches.

Thus, the maximum number of wins a player can have and still not be selected is 11 wins.
Question 3
3 / -1

Directions For Questions

4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).

...view full instructions

Which of the following is the least number of wins one needs to enter the world championship?

A
1

B
2

C
3

D
4

Solution

To minimize the number of matches won by that player, we must maximize the number of matches won by the other 31 players => remaining 97 players must win least number of matches
In every round, 64 players win at least one match and 64 players win 0 matches.

Let the person who entered the world championship with least number of wins be X.

In the first tournament, of the 64 members who win at least one match, 32 players win exactly 1 match, 31 players win more than won match and X wins 2 matches.

From the second tournament to the fourth tournament, different 32 players win exactly 1 match and X won 0 matches.

From this we can say that after all the four tournaments, 31 players won maximum number of matches, and a few others, along with X, won exactly 2 matches.

Of these people who won exactly 2 matches, X was selected for the world championship based on certain criteria.
Question 4
3 / -1

Directions For Questions

4 Chess tournaments were held all over the world last year and in each tournament 128 chess players participated. Players who participated in the 1st tournament are same for other tournaments. At the end of these four tournaments, world championship is held that consists of 32 players. These 32 players are selected on the basis of total number of wins the 128 players got in the four tournaments. Each of the games in the tournaments (including the world championship) is a knockout game i.e. a person who loses a game will not play in that tournament again. The person who wins the last round in any tournament is called the winner of that tournament. If 31 slots of the 32 slots in the world championship tournament are filled and to fill the 32nd spot there is a tie between few players, exactly one of those players is selected based on certain criteria (like coin toss).

...view full instructions

After all the five tournaments, a table was made of the players in the descending order of their wins in all the five tournaments combined. What is the maximum number of wins the top four players could have got if no player among the 128 participants won more than one tournament?

A
92

B
104

C
107

D
112

Solution

Maximum number of wins is possible if these four players are the semifinalists in all the four tournaments and each of them won exactly one tournament.

Wins in each tournament = 5 + 5 + 6 + 7 = 23

Wins in all four tournaments = 23 * 4 = 92

So, none of these four players can win the World Championship.

⇒ All four are quarterfinalists, 3 are semifinalists and 1 is a finalist

⇒ Matches won in World

Championship = 2 + 3 + 3 + 4 = 12

Total wins = 92 + 12 = 104
Question 5
3 / -1

Directions For Questions

Alex, Cane and John are three drivers who drive a passenger bus, in shifts, from Paris to Luxembourg every day. Due to the heavy traffic at peak hours, the time it takes for them to travel between the two cities depends on their starting times at the originating city. If they start at 8:00 AM, 9:00 AM or 10:00 AM, it takes 18 hours to travel between the two cities. If they start at 7:00 PM, 8:00 PM or 9:00 PM, it takes them 20 hours to travel between the two cities. If they start at any other time, it takes them 15 hours to travel between the two cities. Each time they reach their destination city, they take rest for 1 hour before proceeding to the next city.

1 trip is defined as the journey from one city to another.

...view full instructions

If they start from Paris at 8:00 PM, what is the average time taken by them to travel from Paris to Luxembourg in their first 80 trips?

A
17.5 hours

B
16 hours

C
19 hours

D
18.5 hours

Solution

Let’s solve this set by converting the times into 24-hour format.

If they start at 8, 9, 10 hours, they will take 18 hours. If they start at 19, 20, 21 hours, they will take 20 hours. Else, they take 15 hours.

They start at 20:00 hours from Paris, they’ll reach Luxembourg at 16:00 hours.

Let’s continuously represent their journeys:

20:00 (P) - 16:00 (L) = 20 hours

17:00 (L) - 08:00 (P) = 15 hours

9:00 (P) - 3:00 (L) = 18 hours

4:00 (L) - 19:00 (P) = 15 hours

20:00 (P) -

Now, this cycle will continue.

In 80 trips, there will be 20 such cycles. 40 trips from Paris to Luxembourg.

2 trips each of 20 and 18 hours from Paris to Luxembourg.

Thus, average time from Paris to Luxembourg = 20*(20 + 18)/40 = 19 hours.
Question 6
3 / -1

Directions For Questions

Alex, Cane and John are three drivers who drive a passenger bus, in shifts, from Paris to Luxembourg every day. Due to the heavy traffic at peak hours, the time it takes for them to travel between the two cities depends on their starting times at the originating city. If they start at 8:00 AM, 9:00 AM or 10:00 AM, it takes 18 hours to travel between the two cities. If they start at 7:00 PM, 8:00 PM or 9:00 PM, it takes them 20 hours to travel between the two cities. If they start at any other time, it takes them 15 hours to travel between the two cities. Each time they reach their destination city, they take rest for 1 hour before proceeding to the next city.

1 trip is defined as the journey from one city to another.

...view full instructions

If they start at 6:00 AM from Luxembourg, what is the average time per trip for their first 25 trips?

A
15 hours

B
16.5 hours

C
17.5 hours

D
18.5 hours

Solution

Let’s solve this set by converting the times into 24-hour format.

If they start at 8, 9, 10 hours, they will take 18 hours. If they start at 19, 20, 21 hours, they will take 20 hours. Else, they take 15 hours.

They start at 6:00 hours from Luxembourg. They’ll reach Paris at 21:00 hours.

Let’s represent their trips -

6:00 (P) - 21:00 (L) = 15 hours

22:00 (L) - 13:00 (P) = 15 hours

14:00 (P) - 5:00 (L) = 15 hours

6:00 (L) - 21:00(P) = 15 hours

22:00 (P) - 13:00 (L) = 15 hours

14:00 (L) - 5:00 (P) = 15 hours

6:00(P) -

Now, this cycle will repeat. Since all the trips take 15 hours, the average trip time will also be 15 hours.
Question 7
3 / -1

Directions For Questions

Alex, Cane and John are three drivers who drive a passenger bus, in shifts, from Paris to Luxembourg every day. Due to the heavy traffic at peak hours, the time it takes for them to travel between the two cities depends on their starting times at the originating city. If they start at 8:00 AM, 9:00 AM or 10:00 AM, it takes 18 hours to travel between the two cities. If they start at 7:00 PM, 8:00 PM or 9:00 PM, it takes them 20 hours to travel between the two cities. If they start at any other time, it takes them 15 hours to travel between the two cities. Each time they reach their destination city, they take rest for 1 hour before proceeding to the next city.

1 trip is defined as the journey from one city to another.

...view full instructions

If they start at 4:00 AM from Paris, after a minimum of how many trips (including the first one) will they start from Luxembourg at 8:00 AM?

A
10

B
11

C
2

D
Never

Solution

Let’s solve this set by converting the times into 24-hour format.

If they start at 8, 9, 10 hours, they will take 18 hours. If they start at 19, 20, 21 hours, they will take 20 hours. Else, they take 15 hours.

They start at 4:00 hours from Paris. They’ll reach at 19:00 hours in Luxembourg.

Let’s represent the bus journey:

4:00 (P) - 19:00 (L)

20:00 (L) - 16:00 (P)

17:00(P) - 8:00 (L)

9:00(L) - 3:00 (P)

4:00(P) - 19:00 (L)

This cycle will repeat.

They’ll never start at 8:00 AM from Luxembourg.
Question 8
3 / -1

Alex, Cane and John are three drivers who drive a passenger bus, in shifts, from Paris to Luxembourg every day. Due to the heavy traffic at peak hours, the time it takes for them to travel between the two cities depends on their starting times at the originating city. If they start at 8:00 AM, 9:00 AM or 10:00 AM, it takes 18 hours to travel between the two cities. If they start at 7:00 PM, 8:00 PM or 9:00 PM, it takes them 20 hours to travel between the two cities. If they start at any other time, it takes them 15 hours to travel between the two cities. Each time they reach their destination city, they take rest for 1 hour before proceeding to the next city.

1 trip is defined as the journey from one city to another.

If they start at 2: 00 PM from Luxembourg, how many times will they start between 1:00 PM and 11:00 PM from Paris in their first 100 trips?

A
48

B
33

C
50

D
32

Solution

Let’s solve this set by converting the times into 24-hour format.

If they start at 8, 9, 10 hours, they will take 18 hours. If they start at 19, 20, 21 hours, they will take 20 hours. Else, they take 15 hours.

Let’s compute their trip times.

14:00 (L) - 5: 00 (P)

6: 00 (P) - 21: 00 (L)

22:00 (L) - 13:00 (P)

14:00 (P) - 5:00 (L)

6:00 (L) - 21:00 (P)

22:00(P) - 13:00 (L)

This cycle will repeat itself.

In each cycle they will start twice between 1:00 PM and 11:00 PM from Paris.

The cycle will repeat 16 times. Thus, 32 times they will start between the given times.

Further, in the next 4 trips, they’ll start once. Thus, they’ll start 33 times.
Question 9
3 / -1

Directions For Questions

A B-school has 4 clubs - Sports, Dramatics, Literary, and Quiz. 60 students joined these clubs in the first year. A person can join only one of these 4 clubs. After the first year was over, some students did not like the club they joined and hence, moved from one club to another.

Further the following information is known:

No student moved from the quiz club to the sports club.

The number of students who moved from dramatics club to the sports club is the same as the number of students who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well.

The number of students who moved out from the sports and quiz clubs are equal.

The number of students who moved to the literary club is one more than the number of persons who moved to the sports club.

At least one student moved from the sports club to literary club.

The number of students who left the quiz club for the dramatics club and the literary club is the same.

A total of 21 students shifted from one club to another.

4 students moved out of dramatics club and 5 students moved out of literary club.

The number of students who joined sports club is exactly half the number of students who left it.

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

...view full instructions

From which club did maximum number of people leave for the dramatics club?

A
Literary club

B
Sports club

C
Quiz club

D
More than one of the above

Solution

Let us start by tabulating the data available.

We have no information about the number of persons in each club.

The sports-sports cell in the table represents the number of persons from sports club who stayed in sports club. Since we do not have this information (we have information only regarding the movement from one club to another), let us mark all such cells with X.

The cell sports-dramatics (row-column) represents the number of students from sports club who left for dramatics club. Therefore, the cell sports-total will provide the number of students who left the sports club and the cell total-sports will provide the number of students who left other clubs for the sports club.

The number of persons who moved from dramatics club to the sports club is the same as the number of persons who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well. Let us use ‘a’ to denote the number of persons who moved from the dramatics club to the sports club and ‘b’ to denote the number of persons who moved from sports club to literary club. The number of persons who moved out of sports and quiz clubs is the same. Let us denote it by ‘c’.

A total of 21 students left one club for another. No person moved from the quiz club to sports club (quiz-sports = 0).

The number of persons who moved to the literary club is one more than the number of persons who moved to the sports club. Let the number of persons who moved to the literary club be ‘d+1’ and the number of persons who moved to the sports club be ‘d’.
The number of persons who left the quiz club for the dramatics club and the literary club is the same. Let us denote the number of persons who left the quiz club for dramatics club by ‘e’. 4 students moved out of dramatics club and 5 students moved out of literary club.

As we can see from the table, c+c+4+5 =21

⇒ c = 6

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

Let the number of students who left other clubs for quiz club be ‘f’.

⇒ Number of students who left other clubs for dramatics club = f + 4.

The number of students who joined sports club is exactly half the number of students who left it. We know that 6 students left the sports club. Therefore, 3 students should have joined the sports club. ⇒ d = 3

We can see from the table that e + e = 6

⇒ e = 3

Let us fill the vacant cells with variables from g to k. We get the following table.

f + f + 4 + 3 + 4 = 21

⇒ 2f = 10

f = 5

a+b = 3

a+b+i = 6

⇒ i = 3

a+h+j = 4 --------------(1)

b+h = 1 ----------------(2)

a+b = 3 ----------------(3)

b+g+k = 5 -------------(4)

j + k = 2 --------------(5)

a+g = 6 ---------------(6)

Let us rewrite every variable in terms of 'a'.

b = 3-a

g =6-a

Substituting these values in (4), we get,

3-a+6-a+k = 5

9-2a+k = 5

k = 2a-4

Substituting the value of 'k' in (5), we get,

j+2a-4 = 2

j = 6-2a

(1)⇒ a+h+j = 4

a + h + 6 - 2a = 4

⇒ h = a - 2

It has been given that at least one student moved from Sports to Literary club. Therefore, the value of 'a' cannot be 3.

We know that k=2a-4. Therefore, the value of 'a' should be at least 2.

2 is the only value that falls within the range.

Solving the equations using a=2, we get the following table:

Maximum number of people left literary club for dramatics club. Therefore, option A is the right answer.
Question 10
3 / -1

Directions For Questions

A B-school has 4 clubs - Sports, Dramatics, Literary, and Quiz. 60 students joined these clubs in the first year. A person can join only one of these 4 clubs. After the first year was over, some students did not like the club they joined and hence, moved from one club to another.

Further the following information is known:

No student moved from the quiz club to the sports club.

The number of students who moved from dramatics club to the sports club is the same as the number of students who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well.

The number of students who moved out from the sports and quiz clubs are equal.

The number of students who moved to the literary club is one more than the number of persons who moved to the sports club.

At least one student moved from the sports club to literary club.

The number of students who left the quiz club for the dramatics club and the literary club is the same.

A total of 21 students shifted from one club to another.

4 students moved out of dramatics club and 5 students moved out of literary club.

The number of students who joined sports club is exactly half the number of students who left it.

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

...view full instructions

How many persons moved from the sports club to quiz club?

A
0

B
1

C
2

D
3

Solution

Let us start by tabulating the data available.

We have no information about the number of persons in each club.

The sports-sports cell in the table represents the number of persons from sports club who stayed in sports club. Since we do not have this information (we have information only regarding the movement from one club to another), let us mark all such cells with X.

The cell sports-dramatics (row-column) represents the number of students from sports club who left for dramatics club. Therefore, the cell sports-total will provide the number of students who left the sports club and the cell total-sports will provide the number of students who left other clubs for the sports club.

The number of persons who moved from dramatics club to the sports club is the same as the number of persons who moved from the sports club to the dramatics club. The same is the case with sports club and literary club as well. Let us use ‘a’ to denote the number of persons who moved from the dramatics club to the sports club and ‘b’ to denote the number of persons who moved from sports club to literary club. The number of persons who moved out of sports and quiz clubs is the same. Let us denote it by ‘c’.

A total of 21 students left one club for another. No person moved from the quiz club to sports club (quiz-sports = 0).

The number of persons who moved to the literary club is one more than the number of persons who moved to the sports club. Let the number of persons who moved to the literary club be ‘d+1’ and the number of persons who moved to the sports club be ‘d’.
The number of persons who left the quiz club for the dramatics club and the literary club is the same. Let us denote the number of persons who left the quiz club for dramatics club by ‘e’. 4 students moved out of dramatics club and 5 students moved out of literary club.

As we can see from the table, c+c+4+5 =21

⇒ c = 6

The number of students who left other clubs for dramatics club is 4 more than the number of students who left other clubs for the quiz club.

Let the number of students who left other clubs for quiz club be ‘f’.

⇒ Number of students who left other clubs for dramatics club = f + 4.

The number of students who joined sports club is exactly half the number of students who left it. We know that 6 students left the sports club. Therefore, 3 students should have joined the sports club. ⇒ d = 3

We can see from the table that e + e = 6

⇒ e = 3

Let us fill the vacant cells with variables from g to k. We get the following table.

f + f + 4 + 3 + 4 = 21

⇒ 2f = 10

f = 5

a+b = 3

a+b+i = 6

⇒ i = 3

a+h+j = 4 --------------(1)

b+h = 1 ----------------(2)

a+b = 3 ----------------(3)

b+g+k = 5 -------------(4)

j + k = 2 --------------(5)

a+g = 6 ---------------(6)

Let us rewrite every variable in terms of 'a'.

b = 3-a

g =6-a

Substituting these values in (4), we get,

3-a+6-a+k = 5

9-2a+k = 5

k = 2a-4

Substituting the value of 'k' in (5), we get,

j+2a-4 = 2

j = 6-2a

(1)⇒ a+h+j = 4

a + h + 6 - 2a = 4

⇒ h = a - 2

It has been given that at least one student moved from Sports to Literary club. Therefore, the value of 'a' cannot be 3.

We know that k=2a-4. Therefore, the value of 'a' should be at least 2.

2 is the only value that falls within the range.

Solving the equations using a=2, we get the following table:

3 persons have moved from sports club to quiz club. Therefore, option D is the right answer.