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CAT DI And LR Mock Test - 1 - CAT MCQ


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25 Questions MCQ Test - CAT DI And LR Mock Test - 1

CAT DI And LR Mock Test - 1 for CAT 2024 is part of CAT preparation. The CAT DI And LR Mock Test - 1 questions and answers have been prepared according to the CAT exam syllabus.The CAT DI And LR Mock Test - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT DI And LR Mock Test - 1 below.
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CAT DI And LR Mock Test - 1 - Question 1
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

On a particular day, six persons, A through F, got into and got down a bus at seven different bus stops - S1 through S7. The bus stopped at the seven stops in the same order as mentioned above. The first table below provides the persons who got into and got down the bus at each bus stop and the second table provides the duration (in minutes) for which each person was in the bus:

Assume that the duration for which the bus stops at any bus stop is negligible.

Q. How many minutes did the bus take to reach S7 from S6?

Detailed Solution for CAT DI And LR Mock Test - 1 - Question 1
The table below provides, for each person, the bus stop at which he got into the bus and the bus stop at which he got out of the bus.

From the table, we can see that A travelled from S1 to S4, for 41 minutes, and F travelled from S1 to S5, for 47 minutes. Hence, to travel from S4 to S5, the bus would have taken 6 minutes. B travelled from S4 to S6 for 16 minutes. To travel from S5 to S6, the bus would have taken 10 minutes. C travelled from S5 to S7, for 23 minutes. To travel from S6 to S7, the bus would have taken 13 minutes. D travelled from S3 to S5, for 17 minutes. To travel from S3 to S4, the bus would have taken 11 minutes. E travelled from S2 to S4, for 29 minutes. To travel from S2 to S3, the bus would have taken 18 minutes. A travelled from S1 to S4, for 41 minutes. To travel from S1 to S4, the bus would have taken 41 - 18 - 11 = 12 minutes. Hence, the bus took 12 minutes to travel from S1 to S2; 18 minutes for S2 to S3; 11 minutes for S3 to S4; 6 minutes for S4 to S5; 10 minutes for S5 to S6; 13 minutes for S6 to S7.

The bus took 13 minutes to reach S7 from S6.

CAT DI And LR Mock Test - 1 - Question 2
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

On a particular day, six persons, A through F, got into and got down a bus at seven different bus stops - S1 through S7. The bus stopped at the seven stops in the same order as mentioned above. The first table below provides the persons who got into and got down the bus at each bus stop and the second table provides the duration (in minutes) for which each person was in the bus:

Assume that the duration for which the bus stops at any bus stop is negligible.

Q. For how many minutes were both B and D in the bus?

Detailed Solution for CAT DI And LR Mock Test - 1 - Question 2
The table below provides, for each person, the bus stop at which he got into the bus and the bus stop at which he got out of the bus.

From the table, we can see that A travelled from S1 to S4, for 41 minutes, and F travelled from S1 to S5, for 47 minutes. Hence, to travel from S4 to S5, the bus would have taken 6 minutes. B travelled from S4 to S6 for 16 minutes. To travel from S5 to S6, the bus would have taken 10 minutes. C travelled from S5 to S7, for 23 minutes. To travel from S6 to S7, the bus would have taken 13 minutes. D travelled from S3 to S5, for 17 minutes. To travel from S3 to S4, the bus would have taken 11 minutes. E travelled from S2 to S4, for 29 minutes. To travel from S2 to S3, the bus would have taken 18 minutes. A travelled from S1 to S4, for 41 minutes. To travel from S1 to S4, the bus would have taken 41 - 18 - 11 = 12 minutes. Hence, the bus took 12 minutes to travel from S1 to S2; 18 minutes for S2 to S3; 11 minutes for S3 to S4; 6 minutes for S4 to S5; 10 minutes for S5 to S6; 13 minutes for S6 to S7.

Both B and D were in the bus from S4 to S5. Required duration = 6 minutes.

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CAT DI And LR Mock Test - 1 - Question 3
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

On a particular day, six persons, A through F, got into and got down a bus at seven different bus stops - S1 through S7. The bus stopped at the seven stops in the same order as mentioned above. The first table below provides the persons who got into and got down the bus at each bus stop and the second table provides the duration (in minutes) for which each person was in the bus:

Assume that the duration for which the bus stops at any bus stop is negligible.

Q. For how many minutes were there exactly two persons in the bus?

Detailed Solution for CAT DI And LR Mock Test - 1 - Question 3
The table below provides, for each person, the bus stop at which he got into the bus and the bus stop at which he got out of the bus.

From the table, we can see that A travelled from S1 to S4, for 41 minutes, and F travelled from S1 to S5, for 47 minutes. Hence, to travel from S4 to S5, the bus would have taken 6 minutes. B travelled from S4 to S6 for 16 minutes. To travel from S5 to S6, the bus would have taken 10 minutes. C travelled from S5 to S7, for 23 minutes. To travel from S6 to S7, the bus would have taken 13 minutes. D travelled from S3 to S5, for 17 minutes. To travel from S3 to S4, the bus would have taken 11 minutes. E travelled from S2 to S4, for 29 minutes. To travel from S2 to S3, the bus would have taken 18 minutes. A travelled from S1 to S4, for 41 minutes. To travel from S1 to S4, the bus would have taken 41 - 18 - 11 = 12 minutes. Hence, the bus took 12 minutes to travel from S1 to S2; 18 minutes for S2 to S3; 11 minutes for S3 to S4; 6 minutes for S4 to S5; 10 minutes for S5 to S6; 13 minutes for S6 to S7.

From S1 to S2, there were exactly two persons (A and F) in the bus.

From S5 to S6, there were exactly two persons (B and C) in the bus.

Hence, for 12 + 10 = 22 minutes, there were exactly two persons in the bus.

CAT DI And LR Mock Test - 1 - Question 4
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

On a particular day, six persons, A through F, got into and got down a bus at seven different bus stops - S1 through S7. The bus stopped at the seven stops in the same order as mentioned above. The first table below provides the persons who got into and got down the bus at each bus stop and the second table provides the duration (in minutes) for which each person was in the bus:

Assume that the duration for which the bus stops at any bus stop is negligible.

Q. For how many minutes were there at least three persons in the bus?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 4
The table below provides, for each person, the bus stop at which he got into the bus and the bus stop at which he got out of the bus.

From the table, we can see that A travelled from S1 to S4, for 41 minutes, and F travelled from S1 to S5, for 47 minutes. Hence, to travel from S4 to S5, the bus would have taken 6 minutes. B travelled from S4 to S6 for 16 minutes. To travel from S5 to S6, the bus would have taken 10 minutes. C travelled from S5 to S7, for 23 minutes. To travel from S6 to S7, the bus would have taken 13 minutes. D travelled from S3 to S5, for 17 minutes. To travel from S3 to S4, the bus would have taken 11 minutes. E travelled from S2 to S4, for 29 minutes. To travel from S2 to S3, the bus would have taken 18 minutes. A travelled from S1 to S4, for 41 minutes. To travel from S1 to S4, the bus would have taken 41 - 18 - 11 = 12 minutes. Hence, the bus took 12 minutes to travel from S1 to S2; 18 minutes for S2 to S3; 11 minutes for S3 to S4; 6 minutes for S4 to S5; 10 minutes for S5 to S6; 13 minutes for S6 to S7.

There were at least three persons in the bus from S2 to S3, S3 to S4 and S4 to S5, for a total of 18 + 11 + 6 = 35 minutes.

CAT DI And LR Mock Test - 1 - Question 5
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DIRECTIONS for question: Each question is followed by two statements, I and II. Answer each question based on the following instructions: Among the candidates who applied for CAT 2018, 40% are females. One third of these female candidates have anengineering background. What is the total number of candidates with a non-engineering background as a percentage of the total number of applicants for CAT 2018?

I. Two thirds of the male candidates who applied for CAT 2018 have a non-engineering background.

II. Among the applicants for CAT 2018, the number of male candidates with an engineering background was twice the number of female candidates with a non-engineering background.
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 5
As it is given that, 40% of the applicants are females

∴60% of them are males.

i.e., 2 / 3 x 60% = 40% of the total.

Given among females, one-third of them have an engineering background.

∴Two-thirds of the females have non-engineering background.

From statement A alone, two-thirds of the male applicants have a non-engineering background.

∴Total employees with a non-engineering background

= 2 / 3 x 100 = 66 x 2 / 3%

From statement B alone, the number of males with a non-engineering background was twice the number of females with a non-engineering background.

∴Total applicants with a non-engineering background

= 2 / 3 x 40 + 4 / 3 x 40 = 80% of the total.

The question can be answered using either statement alone.

CAT DI And LR Mock Test - 1 - Question 6
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

During a particular month, Tarak visited six cities, Delhi, Chennai, Mumbai, Kolkata, Hyderabad and Bangalore, not necessarily in the same order. After visiting the six cities, he ranked the cities, from 1 to 6, based on the order of his preference. The ranks of any two cities that he visited one immediately after the other differed by at least two, while for any two cities whose ranks differed by exactly two, he visited at least one city between them. It is also known that

i. he visited the city ranked three before he visited Chennai.

ii. he visited Kolkata after he visited the city ranked 1.

iii. Mumbai was not the third city that he visited.

iv. Delhi was the fourth city that he visited.

v. he visited the city ranked two before he visited Bangalore.

vi. he visited Hyderabad before he visited Mumbai.

Q. What is the rank of the second city that he visited?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 6
Given that the ranks of any two cities that he visited one immediately after the other differed by at least 2. But also, if these ranks differed by exactly 2, he visited at least one city between them. Hence, if the ranks differed by 2, he could not have visited the two cities one after the other. Hence, for any pair of cities that he visited one after the other, the rank must differ by at least 3. Consider the city ranked 4th. The only city which he could have visited immediately before or after will be the city ranked 1. Similarly, for the city ranked 3, the only which he could have visited immediately before or after will be the city ranked 6. Hence, the city ranked 4 and 3 must be the first and last cities that he visited in any order. Let the city ranked 4 be the first city. Then, the city ranked 1 must be the second city that he visited. The third city must differ from 1 by at least 3. Hence, the third city can be ranked 5 or 6. City ranked 3 will be the last city and the city ranked 6 must be the city that he visited fifth. Hence, the third city must be ranked 5 and the fourth city must be ranked 2. This is one possible case. Consider the case where the city ranked 3 is first and we get another case, which is the reverse order of the previous case. Hence, two possible order of ranks exist: 4, t, 5, 2, 6, 3 OR 3, 6,2, 5, 1, 4. From (i), he visited the city ranked three before he visited Chennai. Hence, only one possible case exists: 3, 6, 2, 5,1,4. From (iv), Delhi was the fourth city that he visited and must be ranked 2. From (ii), he visited Kolkata after visiting the city ranked 1. Since he visited only one city after visiting the city ranked 1, he must have visited Kolkata last and this must be ranked 4. From (v), he visited the city ranked 2 before he visited Bangalore Hence, he must have visited Bangalore S'*1 and this must have been ranked 1st. From (vi) and (iii), Mumbai has to be the second city that he visited and Hyderabad must be the first Hence, Chennai must be the third city that he visited. The following table provides the order in which he visited the six cities and the ranks of the six cities

The second city that he visited was ranked 6.

CAT DI And LR Mock Test - 1 - Question 7
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

During a particular month, Tarak visited six cities, Delhi, Chennai, Mumbai, Kolkata, Hyderabad and Bangalore, not necessarily in the same order. After visiting the six cities, he ranked the cities, from 1 to 6, based on the order of his preference. The ranks of any two cities that he visited one immediately after the other differed by at least two, while for any two cities whose ranks differed by exactly two, he visited at least one city between them. It is also known that

i. he visited the city ranked three before he visited Chennai.

ii. he visited Kolkata after he visited the city ranked 1.

iii. Mumbai was not the third city that he visited.

iv. Delhi was the fourth city that he visited.

v. he visited the city ranked two before he visited Bangalore.

vi. he visited Hyderabad before he visited Mumbai.

Q. What is the rank of Delhi?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 7
Given that the ranks of any two cities that he visited one immediately after the other differed by at least 2. But also, if these ranks differed by exactly 2, he visited at least one city between them. Hence, if the ranks differed by 2, he could not have visited the two cities one after the other. Hence, for any pair of cities that he visited one after the other, the rank must differ by at least 3. Consider the city ranked 4th. The only city which he could have visited immediately before or after will be the city ranked 1. Similarly, for the city ranked 3, the only which he could have visited immediately before or after will be the city ranked 6. Hence, the city ranked 4 and 3 must be the first and last cities that he visited in any order. Let the city ranked 4 be the first city. Then, the city ranked 1 must be the second city that he visited. The third city must differ from 1 by at least 3. Hence, the third city can be ranked 5 or 6. City ranked 3 will be the last city and the city ranked 6 must be the city that he visited fifth. Hence, the third city must be ranked 5 and the fourth city must be ranked 2. This is one possible case. Consider the case where the city ranked 3 is first and we get another case, which is the reverse order of the previous case. Hence, two possible order of ranks exist: 4, t, 5, 2, 6, 3 OR 3, 6,2, 5, 1, 4. From (i), he visited the city ranked three before he visited Chennai. Hence, only one possible case exists: 3, 6, 2, 5,1,4. From (iv), Delhi was the fourth city that he visited and must be ranked 2. From (ii), he visited Kolkata after visiting the city ranked 1. Since he visited only one city after visiting the city ranked 1, he must have visited Kolkata last and this must be ranked 4. From (v), he visited the city ranked 2 before he visited Bangalore Hence, he must have visited Bangalore S'*1 and this must have been ranked 1st. From (vi) and (iii), Mumbai has to be the second city that he visited and Hyderabad must be the first Hence, Chennai must be the third city that he visited. The following table provides the order in which he visited the six cities and the ranks of the six cities

Delhi was ranked 5.

CAT DI And LR Mock Test - 1 - Question 8
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

During a particular month, Tarak visited six cities, Delhi, Chennai, Mumbai, Kolkata, Hyderabad and Bangalore, not necessarily in the same order. After visiting the six cities, he ranked the cities, from 1 to 6, based on the order of his preference. The ranks of any two cities that he visited one immediately after the other differed by at least two, while for any two cities whose ranks differed by exactly two, he visited at least one city between them. It is also known that

i. he visited the city ranked three before he visited Chennai.

ii. he visited Kolkata after he visited the city ranked 1.

iii. Mumbai was not the third city that he visited.

iv. Delhi was the fourth city that he visited.

v. he visited the city ranked two before he visited Bangalore.

vi. he visited Hyderabad before he visited Mumbai.

Q. How many cities did he visit between Chennai and the city ranked three?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 8
Given that the ranks of any two cities that he visited one immediately after the other differed by at least 2. But also, if these ranks differed by exactly 2, he visited at least one city between them. Hence, if the ranks differed by 2, he could not have visited the two cities one after the other. Hence, for any pair of cities that he visited one after the other, the rank must differ by at least 3. Consider the city ranked 4th. The only city which he could have visited immediately before or after will be the city ranked 1. Similarly, for the city ranked 3, the only which he could have visited immediately before or after will be the city ranked 6. Hence, the city ranked 4 and 3 must be the first and last cities that he visited in any order. Let the city ranked 4 be the first city. Then, the city ranked 1 must be the second city that he visited. The third city must differ from 1 by at least 3. Hence, the third city can be ranked 5 or 6. City ranked 3 will be the last city and the city ranked 6 must be the city that he visited fifth. Hence, the third city must be ranked 5 and the fourth city must be ranked 2. This is one possible case. Consider the case where the city ranked 3 is first and we get another case, which is the reverse order of the previous case. Hence, two possible order of ranks exist: 4, t, 5, 2, 6, 3 OR 3, 6,2, 5, 1, 4. From (i), he visited the city ranked three before he visited Chennai. Hence, only one possible case exists: 3, 6, 2, 5,1,4. From (iv), Delhi was the fourth city that he visited and must be ranked 2. From (ii), he visited Kolkata after visiting the city ranked 1. Since he visited only one city after visiting the city ranked 1, he must have visited Kolkata last and this must be ranked 4. From (v), he visited the city ranked 2 before he visited Bangalore Hence, he must have visited Bangalore S'*1 and this must have been ranked 1st. From (vi) and (iii), Mumbai has to be the second city that he visited and Hyderabad must be the first Hence, Chennai must be the third city that he visited. The following table provides the order in which he visited the six cities and the ranks of the six cities

He visited one city between Chennai and the city ranked 3.

CAT DI And LR Mock Test - 1 - Question 9
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

During a particular month, Tarak visited six cities, Delhi, Chennai, Mumbai, Kolkata, Hyderabad and Bangalore, not necessarily in the same order. After visiting the six cities, he ranked the cities, from 1 to 6, based on the order of his preference. The ranks of any two cities that he visited one immediately after the other differed by at least two, while for any two cities whose ranks differed by exactly two, he visited at least one city between them. It is also known that

i. he visited the city ranked three before he visited Chennai.

ii. he visited Kolkata after he visited the city ranked 1.

iii. Mumbai was not the third city that he visited.

iv. Delhi was the fourth city that he visited.

v. he visited the city ranked two before he visited Bangalore.

vi. he visited Hyderabad before he visited Mumbai.

Q. Which city did Tarak visit between Chennai and the city ranked three?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 9

Given that the ranks of any two cities that he visited one immediately after the other differed by at least 2. But also, if these ranks differed by exactly 2, he visited at least one city between them. Hence, if the ranks differed by 2, he could not have visited the two cities one after the other. Hence, for any pair of cities that he visited one after the other, the rank must differ by at least 3. Consider the city ranked 4th. The only city which he could have visited immediately before or after will be the city ranked 1. Similarly, for the city ranked 3, the only which he could have visited immediately before or after will be the city ranked 6. Hence, the city ranked 4 and 3 must be the first and last cities that he visited in any order. Let the city ranked 4 be the first city. Then, the city ranked 1 must be the second city that he visited. The third city must differ from 1 by at least 3. Hence, the third city can be ranked 5 or 6. City ranked 3 will be the last city and the city ranked 6 must be the city that he visited fifth. Hence, the third city must be ranked 5 and the fourth city must be ranked 2. This is one possible case. Consider the case where the city ranked 3 is first and we get another case, which is the reverse order of the previous case. Hence, two possible order of ranks exist: 4, t, 5, 2, 6, 3 OR 3, 6,2, 5, 1, 4. From (i), he visited the city ranked three before he visited Chennai. Hence, only one possible case exists: 3, 6, 2, 5,1,4. From (iv), Delhi was the fourth city that he visited and must be ranked 2. From (ii), he visited Kolkata after visiting the city ranked 1. Since he visited only one city after visiting the city ranked 1, he must have visited Kolkata last and this must be ranked 4. From (v), he visited the city ranked 2 before he visited Bangalore Hence, he must have visited Bangalore S'*1 and this must have been ranked 1st. From (vi) and (iii), Mumbai has to be the second city that he visited and Hyderabad must be the first Hence, Chennai must be the third city that he visited. The following table provides the order in which he visited the six cities and the ranks of the six cities

Bangalore was ranked first.

CAT DI And LR Mock Test - 1 - Question 10
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a school, the students of two classes, Class VI and Class VII, wrote exams in two different subjects - Civics and Economics. Each class comprised exactly 50 students and all the students wrote each of the two exams. The table below provides, for each subject, the average marks of the students, the maximum marks scored by any student and the minimum marks scored by any student in each class.

Q. What is the maximum number of students from Class VII who scored at least 35 marks in each of the two subjects?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 10
To find the maximum number of students from any class who scored at least 35 marks in each of the two subjects, we can find the maximum number of students from each class who scored at least 35 marks in each subject.

For Class VII Civics, the total marks scored by 50 students = 50 x 30 = 1500 One student has to score 21 and one has to score 36.

Hence, the other 48 students must score 1500-21 - 36 = 1443.

To maximize the number of students who scored at least 35 marks, we can assume that some students scored 35 and the others scored 21.

If there are x students who scored 35 marks, there will be 48 - x students who scored 21 marks. Hence, 35x + 21(48 - x) = 1443 => x = 31.07

Hence, there can be 31 students who scored 35 marks, totalling 31 x 35 = 1085

The other 16 students must score a total of 1443 - 1085 = 358, which is possible. Hence, there can be a maximum of 32 (including the highest mark) students who scored at least 35 marks.

For Class VII Economics, the minimum score is 19, the average is 40.

Hence, we can take one student to have scored 19 and all the others can score at least 35.

In this case, there will be a maximum of 49 students who scored at least 35 marks.

All the students who scored at least 35 in Civics could also have scored at least 35 in Economics.

Hence, the maximum possible number of students = 32

CAT DI And LR Mock Test - 1 - Question 11
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a school, the students of two classes, Class VI and Class VII, wrote exams in two different subjects - Civics and Economics. Each class comprised exactly 50 students and all the students wrote each of the two exams. The table below provides, for each subject, the average marks of the students, the maximum marks scored by any student and the minimum marks scored by any student in each class.

Q. What is the maximum number of students from Class VI whose score in Civics was the same as that in Economics?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 11
Total marks scored by students of Class VI in Civics = 50 x 32 = 1600

Total marks scored by students of Class VI in Economics = 50 x 26 = 1300

If all the students scored the same mark in each of the two subjects, the two totals above must be equal.

To maximize the number of students who scored the same mark in each of the two subjects, we need to bring down the difference between these two numbers to zero (since the sum of the marks of each subject of all the students who scored the same mark in each of the two subjects will be the same).

The difference between the two totals = 1600 - 1300 = 300 If one student scored 46 in Civics and 20 in Economics, this difference will reduce by 26.

To reduce the difference to 0, we need 300 / 26 = 11.53, i.e., 12 students. 11 students could have scored 46 in Civics and 20 in Economics. The 12th student could have scored 46 and 32 in Civics and Economics.

The remaining 38 students must score 1048 in Civics and 1048 in Economics. Each student has to score around 28 marks on average, which falls within the range of marks for each of the two subjects (we can accommodate the highest in Economics and lowest in Civics among these 38 students).

Hence, the maximum number of students who could have scored the same mark in both Civics and Economics is 38.

CAT DI And LR Mock Test - 1 - Question 12
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a school, the students of two classes, Class VI and Class VII, wrote exams in two different subjects - Civics and Economics. Each class comprised exactly 50 students and all the students wrote each of the two exams. The table below provides, for each subject, the average marks of the students, the maximum marks scored by any student and the minimummarks scored by any student in each class.

Q. If the number of students from Class VI whose score in Civics was the same as that in Economics is the maximum possible, what is the maximum number of students who scored 46 marks in Civics?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 12
From the above solution, we can see that there are 12 students who scored 46 marks in Civics. Of the remaining 38 students, no one can score 46 marks in Civics because all these 38 students must score the same mark in both Civics and Economics. Hence, there can be a maximum of 12 students who scored 46 marks in Civics.

CAT DI And LR Mock Test - 1 - Question 13
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a school, the students of two classes, Class VI and Class VII, wrote exams in two different subjects - Civics and Economics. Each class comprised exactly 50 students and all the students wrote each of the two exams. The table below provides, for each subject, the average marks of the students, the maximum marks scored by any student and the minimummarks scored by any student in each class.

Q. For which class is it possible that the second highest mark scored by any student in one of the two subjects is lower than the second lowest mark scored by any student in the other subject?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 13
The second highest mark will be the lowest possible for the subject with the lower average.

Hence, for Class VI, we can calculate the lowest possible second highest mark for Economics and highest possible second lowest mark for Civics.

Total marks scored in Economics = 1300

Removing the maximum and minimum scores, we are left with 1300 - 39 -20 = 1241 For 48 students to score 1241, they must average around 25.85.

If we assume all the 48 students scored only 25 and 26 marks, the lowest possible second highest mark for Economics is 26.

Total marks scored in Civics = 1600

Removing the maximum and minimum scores, we are left with 1600 - 25 - 46 = 1529

For 48 students to score 1529, they must average around 31.85.

Hence, all the 48 students can score 31 or 32 marks. The highest possible second lowest mark for Civics is 31.

For Class VI, the given condition is satisfied.

For Class VII, we can calculate the lowest possible second highest mark for Civics and highest possible second lowest mark for Economics.

Lowest possible second highest mark for Civics will be1500 – 21 – 36 / 48 ≅ 30

Highest possible second lowest mark for Economics = 1600 – 45 – 19 / 48 = 32

Hence, for Class VII also, the given condition is satisfied.

Therefore, the condition is satisfied for both the classes.

CAT DI And LR Mock Test - 1 - Question 14
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DIRECTIONS for question: Select the correct alternative from the given choices.

Professor Theodore Bumblebee of IIM-A gave five assignments − I, II, III, IV and V − to five of his students − Super Subbu, Cunning Chetan, Lazy Laxman, Morose Mary and Reckless Rani, as part of a group assignment. The following table shows the times (in hours) taken by each of the students to complete the assignments:

In a group assignment, all the assignments given have to be completed and it is not necessary that every person does each and every assignment. Thus, this group arrives at a consensus and decides that each of them would do exactly one of the assignments.

Q. What is the cumulative time spent by all the students in completing the group assignment, if they finish it in the least possible time?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 14
Five assignments are to be completed by five students with each doing exactly are of the assignments.

By simple observation we can see that fastest that Reckless Rani can complete any assignment is 2 hrs (for assignment IV).

From this point let us try to minimize the time taken by the other four. This can be done when we assume that Super Subbu does assignment II, Lazy Laxman completes assignment V. Morose Mary completes assignment I and cunning Chetan does assignment II. Minimum time required is 2 hours.

Total time spent by all five is 2+15 + 15 + 15 + 2=85 hours.

Hence, total time spent by all students together is 8-5 hours.

CAT DI And LR Mock Test - 1 - Question 15
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a city, there are exactly five different malls - City Centre, Central, Central Square, City Square and Square Central. Each mall has a different restaurant among Eat Street, Eatery Bay, Bay Street, Streetfood and Food Bay. Further, each restaurant serves a different cuisine among Indian, Chinese, Italian, Mexican and French. On a particular day, each of five persons, A through E, visited a different restaurant among the ones mentioned above. It is also known that

i. Food Bay is in Central Square, while D visited City Square.

ii. the restaurant that serves Indian cuisine was visited by B, while the Bay Street does not serve French cuisine.

iii. E, who visited Eat Street, did not visit the restaurant that serves Mexican cuisine.

iv. Square Central has the restaurant which serves French cuisine and this was visited by C.

v. Streetfood, which is not in City Centre, serves Chinese cuisine and this was visited by A.

Q. Which mall did B visit?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 15
From (i), D visited City Square.

From (ii), B visited the restaurant that serves Indian cuisine.

From (iii), E visited Eat Street. From (iv), C visited Square Central mall and had French cuisine.

From (v), A visited Streetfood, which serves Chinese.

Since A, B and C visited the restaurants that served Chinese, Indian and French cuisines respectively, E must have visited the restaurant that serves Mexican or Italian. From (iii), E could not have visited the restaurant that serves Mexican.

French, E visited the restaurant that serves Italian, while D visited the restaurant that serves Mexican. Also, A, C, D and E could not have visited Food Bay, which is in Central Square. French, B must have visited Food Bay.

From (v), Streetfood is not in City Centre. French, Streetfood must be in Central and Eat Street must be in City Centre.

From (ii), Baystreet foes not serve French cuisine.

Hence, Bay Street must serve Mexican cuisine and Eatery Bay must serve French cuisine.

The following table provides the distribution:

Eat Street City Centre Italian B visited Central Square.

CAT DI And LR Mock Test - 1 - Question 16
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a city, there are exactly five different malls - City Centre, Central, Central Square, City Square and Square Central. Each mall has a different restaurant among Eat Street, Eatery Bay, Bay Street, Streetfood and Food Bay. Further, each restaurant serves a different cuisine among Indian, Chinese, Italian, Mexican and French. On a particular day, each of five persons, A through E, visited a different restaurant among the ones mentioned above. It is also known that

i. Food Bay is in Central Square, while D visited City Square.

ii. the restaurant that serves Indian cuisine was visited by B, while the Bay Street does not serve French cuisine.

iii. E, who visited Eat Street, did not visit the restaurant that serves Mexican cuisine.

iv. Square Central has the restaurant which serves French cuisine and this was visited by C.

v. Streetfood, which is not in City Centre, serves Chinese cuisine and this was visited by A.

Q. Which cuisine does the restaurant that D visited serve?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 16
From (i), D visited City Square.

From (ii), B visited the restaurant that serves Indian cuisine.

From (iii), E visited Eat Street. From (iv), C visited Square Central mall and had French cuisine.

From (v), A visited Streetfood, which serves Chinese.

Since A, B and C visited the restaurants that served Chinese, Indian and French cuisines respectively, E must have visited the restaurant that serves Mexican or Italian. From (iii), E could not have visited the restaurant that serves Mexican.

French, E visited the restaurant that serves Italian, while D visited the restaurant that serves Mexican. Also, A, C, D and E could not have visited Food Bay, which is in Central Square. French, B must have visited Food Bay.

From (v), Streetfood is not in City Centre. French, Streetfood must be in Central and Eat Street must be in City Centre.

From (ii), Baystreet foes not serve French cuisine.

Hence, Bay Street must serve Mexican cuisine and Eatery Bay must serve French cuisine.

The following table provides the distribution:

D visited Bay Street, which serves Mexican cuisine.

CAT DI And LR Mock Test - 1 - Question 17
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a city, there are exactly five different malls - City Centre, Central, Central Square, City Square and Square Central. Each mall has a different restaurant among Eat Street, Eatery Bay, Bay Street, Streetfood and Food Bay. Further, each restaurant serves a different cuisine among Indian, Chinese, Italian, Mexican and French. On a particular day, each of five persons, A through E, visited a different restaurant among the ones mentioned above. It is also known that

i. Food Bay is in Central Square, while D visited City Square.

ii. the restaurant that serves Indian cuisine was visited by B, while the Bay Street does not serve French cuisine.

iii. E, who visited Eat Street, did not visit the restaurant that serves Mexican cuisine.

iv. Square Central has the restaurant which serves French cuisine and this was visited by C.

v. Streetfood, which is not in City Centre, serves Chinese cuisine and this was visited by A.

Q. Which cuisine does the restaurant that D visited serve?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 17
From (i), D visited City Square.

From (ii), B visited the restaurant that serves Indian cuisine.

From (iii), E visited Eat Street. From (iv), C visited Square Central mall and had French cuisine.

From (v), A visited Streetfood, which serves Chinese.

Since A, B and C visited the restaurants that served Chinese, Indian and French cuisines respectively, E must have visited the restaurant that serves Mexican or Italian. From (iii), E could not have visited the restaurant that serves Mexican.

French, E visited the restaurant that serves Italian, while D visited the restaurant that serves Mexican. Also, A, C, D and E could not have visited Food Bay, which is in Central Square. French, B must have visited Food Bay.

From (v), Streetfood is not in City Centre. French, Streetfood must be in Central and Eat Street must be in City Centre.

From (ii), Baystreet foes not serve French cuisine.

Hence, Bay Street must serve Mexican cuisine and Eatery Bay must serve French cuisine.

The following table provides the distribution:

C visited Eatery Bay.

CAT DI And LR Mock Test - 1 - Question 18
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

In a city, there are exactly five different malls - City Centre, Central, Central Square, City Square and Square Central. Each mall has a different restaurant among Eat Street, Eatery Bay, Bay Street, Streetfood and Food Bay. Further, each restaurant serves a different cuisine among Indian, Chinese, Italian, Mexican and French. On a particular day, each of five persons, A through E, visited a different restaurant among the ones mentioned above. It is also known that

i. Food Bay is in Central Square, while D visited City Square.

ii. the restaurant that serves Indian cuisine was visited by B, while the Bay Street does not serve French cuisine.

iii. E, who visited Eat Street, did not visit the restaurant that serves Mexican cuisine.

iv. Square Central has the restaurant which serves French cuisine and this was visited by C.

v. Streetfood, which is not in City Centre, serves Chinese cuisine and this was visited by A.

Q. Which cuisine does the restaurant in Central serve?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 18
From (i), D visited City Square.

From (ii), B visited the restaurant that serves Indian cuisine.

From (iii), E visited Eat Street. From (iv), C visited Square Central mall and had French cuisine.

From (v), A visited Streetfood, which serves Chinese.

Since A, B and C visited the restaurants that served Chinese, Indian and French cuisines respectively, E must have visited the restaurant that serves Mexican or Italian. From (iii), E could not have visited the restaurant that serves Mexican.

French, E visited the restaurant that serves Italian, while D visited the restaurant that serves Mexican. Also, A, C, D and E could not have visited Food Bay, which is in Central Square. French, B must have visited Food Bay.

From (v), Streetfood is not in City Centre. French, Streetfood must be in Central and Eat Street must be in City Centre.

From (ii), Baystreet foes not serve French cuisine.

Hence, Bay Street must serve Mexican cuisine and Eatery Bay must serve French cuisine.

The following table provides the distribution:

The restaurant in Central serves Chinese cuisine.

CAT DI And LR Mock Test - 1 - Question 19
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Rahul and Kiran were playing a game in which Rahul distributes ten cards, numbered 1 through 10, equally between Kiran and him. Rahul initially forms a stack with these ten cards, shuffles them forn times, each time taking four cards which are exactly in the middle of the stack and placing them on top of the stack in the same order. He then distributes the stack of ten cards such that he first gives Kiran the top most card and then takes the next for himself; he gives the next card to Kiran and takes one for himself and so on until all the cards are distributed. After distributing all the cards, the person who has the card numbered 7 is declared the winner.

When Rahul initially formed a stack, the cards were present in the stack in the ascending order of their numbers, with card numbered 1 at the top and card numbered 10 at the bottom.

Q. For which of the following values of n will Rahul win?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 19
The cards are numbered 1 to 10. Depending on how many times Rahul shuffles the stack, the order of the cards will change. The table below provides the arrangements of cards in the stack for different values of n. For each arrangement, the cells shaded in grey represent the cards with Kiran

We can see that n = 7 is the same as n = 0 and the cycle will repeat from n = 7 onwards.

For n = 11, which is the same as n = 4, Rahul will win.

CAT DI And LR Mock Test - 1 - Question 20
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Rahul and Kiran were playing a game in which Rahul distributes ten cards, numbered 1 through 10, equally between Kiran and him. Rahul initially forms a stack with these ten cards, shuffles them forn times, each time taking four cards which are exactly in the middle of the stack and placing them on top of the stack in the same order. He then distributes the stack of ten cards such that he first gives Kiran the top most card and then takes the next for himself; he gives the next card to Kiran and takes one for himself and so on until all the cards are distributed. After distributing all the cards, the person who has the card numbered 7 is declared the winner.

When Rahul initially formed a stack, the cards were present in the stack in the ascending order of their numbers, with card numbered 1 at the top and card numbered 10 at the bottom.

Q. Which of the following pair of cards can Rahul never have simultaneously?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 20
The cards are numbered 1 to 10. Depending on how many times Rahul shuffles the stack, the order of the cards will change. The table below provides the arrangements of cards in the stack for different values of n. For each arrangement, the cells shaded in grey represent the cards with Kiran

We can see that n = 7 is the same as n = 0 and the cycle will repeat from n = 7 onwards.

Rahul cannot have card numbered 1 and card numbered 7 simultaneously.

CAT DI And LR Mock Test - 1 - Question 21
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Rahul and Kiran were playing a game in which Rahul distributes ten cards, numbered 1 through 10, equally between Kiran and him. Rahul initially forms a stack with these ten cards, shuffles them forn times, each time taking four cards which are exactly in the middle of the stack and placing them on top of the stack in the same order. He then distributes the stack of ten cards such that he first gives Kiran the top most card and then takes the next for himself; he gives the next card to Kiran and takes one for himself and so on until all the cards are distributed. After distributing all the cards, the person who has the card numbered 7 is declared the winner.

When Rahul initially formed a stack, the cards were present in the stack in the ascending order of their numbers, with card numbered 1 at the top and card numbered 10 at the bottom.

Q. If Kiran has two cards with consecutive numbers but was not the winner of the game, then which of the following will Rahul definitely not have?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 21
The cards are numbered 1 to 10. Depending on how many times Rahul shuffles the stack, the order of the cards will change. The table below provides the arrangements of cards in the stack for different values of n. For each arrangement, the cells shaded in grey represent the cards with Kiran

We can see that n = 7 is the same as n = 0 and the cycle will repeat from n = 7 onwards.

Kiran was not the winner of the game for n = 1, 4 and 5.

In each of these cases, Kiran has two cards with consecutive numbers and in each of these cases, Kiran has the card numbered 6. Hence, Rahul will not have the card numbered 6.

CAT DI And LR Mock Test - 1 - Question 22
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Rahul and Kiran were playing a game in which Rahul distributes ten cards, numbered 1 through 10, equally between Kiran and him. Rahul initially forms a stack with these ten cards, shuffles them forn times, each time taking four cards which are exactly in the middle of the stack and placing them on top of the stack in the same order. He then distributes the stack of ten cards such that he first gives Kiran the top most card and then takes the next for himself; he gives the next card to Kiran and takes one for himself and so on until all the cards are distributed. After distributing all the cards, the person who has the card numbered 7 is declared the winner.

When Rahul initially formed a stack, the cards were present in the stack in the ascending order of their numbers, with card numbered 1 at the top and card numbered 10 at the bottom.

Q. If the sum of the cards that Kiran has is the lowest possible, which of the following cards will Rahul have?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 22
The cards are numbered 1 to 10. Depending on how many times Rahul shuffles the stack, the order of the cards will change. The table below provides the arrangements of cards in the stack for different values of n. For each arrangement, the cells shaded in grey represent the cards with Kiran

We can see that n = 7 is the same as n = 0 and the cycle will repeat from n = 7 onwards.

The sum of the cards that Kiran has is the lowest possible for n = 5. Hence, Rahul will have cards numbered 3, 5, 7, 8, 10. From the given options, the answer is option A.

CAT DI And LR Mock Test - 1 - Question 23
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DIRECTIONS for question: Select the correct alternative from the given choices.

At a multiplex, the following six movies are scheduled as shown in the table given below:

You wish to see all the movies in a single day. If you need to have a break from 4:00 p.m. to 6:00 p.m., then which of the following is true?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 23
In order to see all the movies and to make sure you have a break between 4:00 p in. and 6:00 p.m. the schedules to be followed is

CAT DI And LR Mock Test - 1 - Question 24
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Five teams - A through E - participated in a hockey tournament in which each team played against each of the other teams exactly once. In any match, the winning team is awarded four points and the losing team no points. In case of a draw, the two teams are awarded one point each. At the end of the tournament, B had two points more than E, which, in turn, had two points more than A, which, in turn, had one point less than D, which, in turn, had three points more than C.

Q. What is the result of the match between C and D?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 24
Let the number of points that C was awarded be x.

The number of points that D was awarded will be x + 3.

The number of points that A was awarded will be x + 2.

The number of points that E was awarded will be x + 4.

The number of points that B was awarded will be x + 6.

Hence, the total number of points that the five teams were awarded = 5x + 15. In the tournament, 10 matches would have been played (since 5 teams played against each other exactly once).

Further, for every match that ended as a draw, two points will be given in total to the two teams that played the match.

For each match that did not end as a draw, 4 points will be given in total. If all the ten matches ended as draws, 20 points will be awarded to all the five teams combined.

If only 9 matches ended as draws, 22 points will be awarded to all the five teams combined. Hence, we can see that the points in the tournament can only be 20,22, 24, 26 and so on.

The maximum number of points in the tournament can be 40. Since the total number of points in the tournament is of the form 5x + 15, the total number of points in the tournament can only be 20 or 30 or 40.

However, if there were 20 points, then all the matches must have ended as draws and all the teams would have equal number of points. Since this is not the case, the total points cannot be 20. If there were 40 points, then all the matches must have had a result. In this case, the difference in points between any two teams must only be in multiples of 4 (since there were no draws). As this is not the case, the total points cannot be 40 as well. Hence, the total number of points must be 30 and x = 3.

The points scored by A, B, C, D and E must be 5,9, 3, 6 and 7 respectively.

A must have had 1 win, 1 draw and 2 losses.

B must have had 2 wins, 1 draw and 1 loss.

C must have had 3 draws and 1 loss.

D must have had 1 win, 2 draws and 1 loss.

E must have had 1 win and 3 draws. C has 3 draws.

If C did not draw against D, C must have drawn against A, B and E. In this case, E will be left with 2 draws and D will also be left with 2 draws and none of the other teams will have any draws left.

However, E and D could not have played against each other twice. Hence, C and D must have ended as a draw.

CAT DI And LR Mock Test - 1 - Question 25
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DIRECTIONS for questions: Answer the questions on the basis of the information given below.

Five teams - A through E - participated in a hockey tournament in which each team played against each of the other teams exactly once. In any match, the winning team is awarded four points and the losing team no points. In case of a draw, the two teams are awarded one point each. At the end of the tournament, B had two points more than E, which, in turn, had two points more than A, which, in turn, had one point less than D, which, in turn, had three points more than C.

Q. If E drew the match against A, which of the following teams won against D?
Detailed Solution for CAT DI And LR Mock Test - 1 - Question 25
Let the number of points that C was awarded be x.

The number of points that D was awarded will be x + 3.

The number of points that A was awarded will be x + 2.

The number of points that E was awarded will be x + 4.

The number of points that B was awarded will be x + 6.

Hence, the total number of points that the five teams were awarded = 5x + 15. In the tournament, 10 matches would have been played (since 5 teams played against each other exactly once).

Further, for every match that ended as a draw, two points will be given in total to the two teams that played the match.

For each match that did not end as a draw, 4 points will be given in total. If all the ten matches ended as draws, 20 points will be awarded to all the five teams combined.

If only 9 matches ended as draws, 22 points will be awarded to all the five teams combined. Hence, we can see that the points in the tournament can only be 20,22, 24, 26 and so on.

The maximum number of points in the tournament can be 40. Since the total number of points in the tournament is of the form 5x + 15, the total number of points in the tournament can only be 20 or 30 or 40.

However, if there were 20 points, then all the matches must have ended as draws and all the teams would have equal number of points. Since this is not the case, the total points cannot be 20. If there were 40 points, then all the matches must have had a result. In this case, the difference in points between any two teams must only be in multiples of 4 (since there were no draws). As this is not the case, the total points cannot be 40 as well. Hence, the total number of points must be 30 and x = 3.

The points scored by A, B, C, D and E must be 5,9, 3, 6 and 7 respectively.

A must have had 1 win, 1 draw and 2 losses.

B must have had 2 wins, 1 draw and 1 loss.

C must have had 3 draws and 1 loss.

D must have had 1 win, 2 draws and 1 loss.

E must have had 1 win and 3 draws. C has 3 draws.

Given that E drew the match against A. A has only one draw. Hence, all the other matches of A must have had a result. In the match between A and C, A must have won (since C did not win any match and could not have drawn against A). Since A won against C, C must have drawn against B, D and E. Since B has only one draw and this is against C, in the match between B and E, E must have won (since E did not lose any match). Since E won against B, it must have drawn against C and D. Further, since B lost against E, it must have won against A and D. Since D has 1 win, D must have won against A. Hence, B won against D.

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