Description

This mock test of Sample CAT LRDI MCQ for CAT helps you for every CAT entrance exam.
This contains 32 Multiple Choice Questions for CAT Sample CAT LRDI MCQ (mcq) to study with solutions a complete question bank.
The solved questions answers in this Sample CAT LRDI MCQ quiz give you a good mix of easy questions and tough questions. CAT
students definitely take this Sample CAT LRDI MCQ exercise for a better result in the exam. You can find other Sample CAT LRDI MCQ extra questions,
long questions & short questions for CAT on EduRev as well by searching above.

QUESTION: 1

Group Question

Answer the following question based on the information given below.

In order to promote entrepreneurship, a state government started facilitating the innovative entrepreneurs with the ‘Entrepreneur of the Year’ award.

The initiative was started in 2009, when there were 4 recipients whose ages then were 37, 32, 30 and 41 years. Every year hence, a new recipient joined the league, except in 2014 where two persons were facilitated with the award.

The below graph shows the average age of all the recipients over the years.

(i) In 2012, a person then aged 33 died. Hence the average was calculated for the living recipients only.

(ii) The difference in the ages of the two recipients in the year 2014 was 5 years.

*Q. What are the ages of the oldest and the youngest recipients award respectively? (In the year they receive the award) *

Solution:

Sum of the ages of recipients in 2009 = 140 Therefore, The sum becomes 144 in 2010.

But one more recipient is added in 2010 and the sum of the five in 2010 = 38 x 5 = 190 Hence, age of the recipient of 2010 = 190 - 144 = 46 years Similarly, age of the recipient added in 2011 = 38 x 6 - 39 x 5 = 33 In 2012, the person whose age was 33, died.

Hence, the age of the recipiet, who was added in 2012 = 41 x 6 - (39 x 6 - 33) = 45 New recipient’s age in 2013 = 44 x 7 - 42 x 6 = 56 In 2014, 2 persons joined the group. So, sum of their ages = 42 x 9 - 45 x 7 = 63 Since the difference in their ages is 5, their ages are 29 and 34.

Recipient’s age in 2015 = 41 x 10 - 43 x 9 = 23

Oldest recipient was 56 (2013) while the youngest was 23 (2015).

Hence, option 3.

QUESTION: 2

In order to promote entrepreneurship, a state government started facilitating the innovative entrepreneurs with the ‘Entrepreneur of the Year’ award.

The initiative was started in 2009, when there were 4 recipients whose ages then were 37, 32, 30 and 41 years. Every year hence, a new recipient joined the league, except in 2014 where two persons were facilitated with the award.

The below graph shows the average age of all the recipients over the years.

(i) In 2012, a person then aged 33 died. Hence the average was calculated for the living recipients only.

(ii) The difference in the ages of the two recipients in the year 2014 was 5 years.

*Q. Of the two recipients who were awarded in 2014, what was the age of the elder person?*

Solution:

Solution: Age of the elder recipient of 2014 was 34 years. Hence, option 1.

QUESTION: 3

In order to promote entrepreneurship, a state government started facilitating the innovative entrepreneurs with the ‘Entrepreneur of the Year’ award.

The initiative was started in 2009, when there were 4 recipients whose ages then were 37, 32, 30 and 41 years. Every year hence, a new recipient joined the league, except in 2014 where two persons were facilitated with the award.

The below graph shows the average age of all the recipients over the years.

(i) In 2012, a person then aged 33 died. Hence the average was calculated for the living recipients only.

(ii) The difference in the ages of the two recipients in the year 2014 was 5 years.

*Q. What was age of the recipient in the year 2012?*

Solution:

Solution: The recipient in 2012 was 45 years old. Hence, option 4.

QUESTION: 4

In order to promote entrepreneurship, a state government started facilitating the innovative entrepreneurs with the ‘Entrepreneur of the Year’ award.

The initiative was started in 2009, when there were 4 recipients whose ages then were 37, 32, 30 and 41 years. Every year hence, a new recipient joined the league, except in 2014 where two persons were facilitated with the award.

The below graph shows the average age of all the recipients over the years.

(i) In 2012, a person then aged 33 died. Hence the average was calculated for the living recipients only.

(ii) The difference in the ages of the two recipients in the year 2014 was 5 years.

*Q. In 2015, how many of the recipients are aged more than 40? *

Solution:

Solution: In 2015, the ages of the recipients were 43, 38, 47, 51,37, 48, 58, 30, 35, 23 years.So, 5 of them are aged more than 40. Hence, option 2.

*Answer can only contain numeric values

QUESTION: 5

Group Question

Answer the following question based on the information given below.

2000 athletes participated in 2015 Summer Olympics Games. Of 2000 athletes, 800 athletes did not participate in any of the four most popular sports viz., Bowling, Cycling, Tennis and Football. The diagram below represents the athletes who participated in the four most popular sport.

(i) 500 athletes participated in Bowling. Rectangle represents Bowling.

(ii) 500 athletes participated in Cycling. Triangle represents Cycling.

(iii)600 athletes participated in Tennis. Hexagon represents Tennis.

(iv)400 athletes participated in Football. Circle represents Football.

300 athletes participated in only Bowling and Cycling while 100 athletes participated in all the most popular games except Cycling.

*Q. How many athletes participated in exactly two most popular sports?*

Solution:

Considering the diagram we get, U = Total number of athletes who participated in all sports i.e. including Bowling, Cycling, Tennis and Football = 2000 j = Number of athletes who didn't participate in these four sports = 800.

Cycling = a + b = 500, Bowling = b + c + d + e + f = 500, Football = f + e + g + h = 400, Tennis = d + e + h + i = 600, a + c + g + i + 2 ( b + d + f + h ) + 3e = 500 + 500 + 600 + 400 = 2000.

a + c + g + i + b + d + f + h + e = 2000 - 800 = 1200 and e = 100

Number of athletes who participated in exactly two sport = b + d + f + h = 800 - 2(100) = 600

Answer: 600

*Answer can only contain numeric values

QUESTION: 6

2000 athletes participated in 2015 Summer Olympics Games. Of 2000 athletes, 800 athletes did not participate in any if the four most popular sports viz., Bowling, Cycling, Tennis and Football. The diagram below represents the athletes who participated in the four most popular sport.

(i) 500 athletes participated in Bowling. Rectangle represents Bowling.

(ii) 500 athletes participated in Cycling. Triangle represents Cycling.

(iii)600 athletes participated in Tennis. Hexagon represents Tennis.

(iv)400 athletes participated in Football. Circle represents Football.

300 athletes participated in only Bowling and Cycling while 100 athletes participated in all the most popular games except Cycling.

*Q. How many athletes participated in exactly one most popular sports? *

Solution:

Solution: From the solution to the first question of the set, a + c + g + i + b + d + f + h + e = 1200 ... (i) b + d + f + h = 600 ... (ii) e = 100 ...(iii) Substituting (ii) and (iii) in (i) we get, a + c + g + i = 1200 - 600 - 100 = 500 Number of athletes who participated in exactly one most popular sport = 500 Answer: 500

*Answer can only contain numeric values

QUESTION: 7

2000 athletes participated in 2015 Summer Olympics Games. Of 2000 athletes, 800 athletes did not participate in any if the four most popular sports viz., Bowling, Cycling, Tennis and Football. The diagram below represents the athletes who participated in the four most popular sport.

(i) 500 athletes participated in Bowling. Rectangle represents Bowling.

(ii) 500 athletes participated in Cycling. Triangle represents Cycling.

(iii)600 athletes participated in Tennis. Hexagon represents Tennis.

(iv)400 athletes participated in Football. Circle represents Football.

300 athletes participated in only Bowling and Cycling while 100 athletes participated in all the most popular games except Cycling.

*Q. How many athletes participated only in Bowling and Tennis if 25 athletes participated only in Football?*

Solution:

Solution: Considering solution to the first question of the set, Number of athletes participated only in Football = g = 25 Number of athletes who participated in exactly two sport = b + d + f + h = 600 As there were 300 athletes participated in only Bowling and Cycling, b = 300 : . d + f + h = 300 ... (i) Also,

Football = f + e + g + h = 400 and e = 100, f + g + h = 300 .. (ii) From (i) and (ii) we get, d = g

Number of athletes participated only in Bowling and Tennis = 25 Answer: 25

*Answer can only contain numeric values

QUESTION: 8

2000 athletes participated in 2015 Summer Olympics Games. Of 2000 athletes, 800 athletes did not participate in any if the four most popular sports viz., Bowling, Cycling, Tennis and Football. The diagram below represents the athletes who participated in the four most popular sport.

(i) 500 athletes participated in Bowling. Rectangle represents Bowling.

(ii) 500 athletes participated in Cycling. Triangle represents Cycling.

(iii)600 athletes participated in Tennis. Hexagon represents Tennis.

(iv)400 athletes participated in Football. Circle represents Football.

*Q. How many athletes participated only in tennis if 50 and 25 athletes participated only in bowling and football respectively?*

Solution:

Solution: Considering solution to the first question of the set, c = 50 and g = 25 ... (i) Now, Cycling = a + b = 500 Also, there were 300 athletes participated in only Bowling and Cycling. b = 300 a = 200 ... (ii) Number of athletes who participated in exactly one sport = a + c + g + i = 500 ... (iii) Substituting (i) and (ii) in (iii) we get, / = 500 - 200 - 50 - 25 = 225

Number of athletes participated only in tennis = 225 Answer: 225

QUESTION: 9

Group Question

Answer the following question based on the information given below.

12 candidates appeared in front of a panel for interviews for ISB Hyderabad admissions. It was a tough decision for the panelists to select among those as all candidates were equally good. After evaluation they selected 6 of the candidates.

Below table lists the profile of the 12 candidates:

Below statements give the information about the 6 candidates who were offered admission to the institute:

i. Only one out of the candidates with the age equal to the average age of the 12 was selected and his/her marks are above the average marks of the 12.

ii. One candidate each was selected from the Arts and Medicine streams.

iii. Only one candidate below the average marks was selected.

iv. Two of the selected candidates have their ages above the average age of the 12.

v. One of the candidates with the highest marks was selected and one of the youngest was selected.

vi. Maximum candidate selected from any stream was 2.

vii. The 6 candidates who were selected were from 4 streams.

*Q. Who among these were selected? *

Solution:

Average Age = (Sum of individual ages)/12 = 26 Average Marks = (Sum of individual marks)/12 = 90 Pradeep and Leela have age equal to average age but only Pradeep has marks more than average marks. So Pradeep is selected and Leela is not.

From (ii), it can be concluded that Irfan is selected.

Irfan has score below the average. So from (iii), Balwant and Steve cannot be selected.

Consider (v). Risha and Balwant are the youngest. Balwant is already rejected, hence Risha is selected. She is also one of the highest scorers. Hence, Triveni won’t be selected. Therefore Ojaswi is selected (one from Arts). Risha and Pradeep are from Engineering, so from (vi), Charan shall not be selected.

Candidates from 4 streams are selected. 4 are already selected from 3 streams. So the rest two are either both from law or both from commerce. But Balwant and Steve, who are from law are rejected. So the two candidates from commerce are selected.

Selected candidates: Pradeep, Risha, Ojaswi, Ekta, Maninder and Irfan.

Hence, option 2.

QUESTION: 10

12 candidates appeared in front of a panel for interviews for ISB Hyderabad admissions. It was a tough decision for the panelists to select among those as all candidates were equally good. After evaluation they selected 6 of the candidates.

Below table lists the profile of the 12 candidates:

Below statements give the information about the 6 candidates who were offered admission to the institute:

i. Only one out of the candidates with the age equal to the average age of the 12 was selected and his/her marks are above the average marks of the 12.

ii. One candidate each was selected from the Arts and Medicine streams.

iii. Only one candidate below the average marks was selected.

iv. Two of the selected candidates have their ages above the average age of the 12.

v. One of the candidates with the highest marks was selected and one of the youngest was selected.

vi. Maximum candidate selected from any stream was 2.

vii. The 6 candidates who were selected were from 4 streams.

*Q. How many females were selected? *

Solution:

From the solution to the previous question we can see that there are 3 females (Ojaswi, Ekta & Risha).

Hence, option 3.

QUESTION: 11

12 candidates appeared in front of a panel for interviews for ISB Hyderabad admissions. It was a tough decision for the panelists to select among those as all candidates were equally good. After evaluation they selected 6 of the candidates.

Below table lists the profile of the 12 candidates:

Below statements give the information about the 6 candidates who were offered admission to the institute:

i. Only one out of the candidates with the age equal to the average age of the 12 was selected and his/her marks are above the average marks of the 12.

ii. One candidate each was selected from the Arts and Medicine streams.

iii. Only one candidate below the average marks was selected.

iv. Two of the selected candidates have their ages above the average age of the 12.

v. One of the candidates with the highest marks was selected and one of the youngest was selected.

vi. Maximum candidate selected from any stream was 2.

vii. The 6 candidates who were selected were from 4 streams.

*Q. What is the average marks and average age respectively of the selected candidates?*

Solution:

From the solution to the first question of the set, Average marks = (91+92+90+90+90+88)/6 = 90.17 Average age = (26+23+25+28+25+31 )/6 = 26.33 Hence, option 4.

QUESTION: 12

Below table lists the profile of the 12 candidates:

Below statements give the information about the 6 candidates who were offered admission to the institute:

ii. One candidate each was selected from the Arts and Medicine streams.

iii. Only one candidate below the average marks was selected.

iv. Two of the selected candidates have their ages above the average age of the 12.

v. One of the candidates with the highest marks was selected and one of the youngest was selected.

vi. Maximum candidate selected from any stream was 2.

vii. The 6 candidates who were selected were from 4 streams.

*Q. From which of the streams, none of the candidates were “ selected?*

Solution:

From the solution to the first question of the set, no candidate is selected from Law. Hence, option 1.

QUESTION: 13

Group Question

Answer the following question based on the information given below.

A game of basketball was played between two teams: DET Pistons and DAL Mavericks. Below is the score of the teams in the 4 quarters of the game:

The scoring shots of the game are either a 2-pointer or a 3-pointer. Each team scored at least two 2 pointers in each quarter.

Note: A 2-pointer means the team scores 2 points in that shot and likewise for a 3-pointer.

*Q. What can be the maximum number of 3-pointers scored by DET pistons? *

Solution:

Each team scored at least two 2-pointers in each quarter. Hence, the maximum score by a team in 3-pointers could be (n - 4), where n is the score in the quarter.

Max 3-pointers by DET Pistons in 1st quarter = 5 Similarly, they can score 5, 7, 4 3-pointers in the 2nd, 3rd and 4th quarter respectively.

Total = 21 Hence, option 4

QUESTION: 14

A game of basketball was played between two teams: DET Pistons and DAL Mavericks. Below is the score of the teams in the 4 quarters of the game:

The scoring shots of the game are either a 2-pointer or a 3-pointer. Each team scored at least two 2-pointers in each quarter.

Note: A 2-pointer means the team scores 2 points in that shot and likewise for a 3-pointer.

*Q. What can be the maximum number of 3-pointers scored by DAL Mavericks?*

Solution:

DAL Mavericks will score 4, 6, 6 and 9 3-pointers in the 1st, 2nd, 3rd and 4th quarter respectively. Total = 25 Hence, option 3.

QUESTION: 15

A game of basketball was played between two teams: DET Pistons and DAL Mavericks. Below is the score of the teams in the 4 quarters of the game:

The scoring shots of the game are either a 2-pointer or a 3-pointer. Each team scored at least two 2-pointers in each quarter.

Note: A 2-pointer means the team scores 2 points in that shot and likewise for a 3-pointer.

*Q. If DET Pistons had the maximum number of scoring shots in the first half while DAL Mavericks had the minimum scoring shots during the same, what is the difference in the number of their scoring shots?*

Solution:

For the scoring shots to be maximum, there should be maximum 2-pointers and for the scoring shots to be minimum, there should be maximum 3-pointers.

DET Pistons had the maximum number of scoring shots in the first half. (10,1) in Q1 and (9,1) in Q2 i.e., total 21 shots.

DAL Mavericks had the minimum scoring shots in the first half. (2.4) in Q1 and (1,8) in Q2 i.e., total 15 shots Difference = 6 Hence, option 2.

QUESTION: 16

A game of basketball was played between two teams: DET Pistons and DAL Mavericks. Below is the score of the teams in the 4 quarters of the game:

The scoring shots of the game are either a 2-pointer or a 3-pointer. Each team scored at least two 2-pointers in each quarter.

Note: A 2-pointer means the team scores 2 points in that shot and likewise for a 3-pointer.

*Q. If DAL Mavericks had the same number of scoring shots in Q3 and Q4 and the total shots by them in second half was the same as the total shots by DET Pistons in the second half, how many 3 pointers did DET Pistons score in Q3?*

Solution:

Let the number of 3-pointers and 2-pointers scored by DAL Mavericks in Q3 and Q4 be (x, y) and (a, b) respectively.

Now, x + y = a + b ... (i) Also, 3x + 2y = 26 ... (ii); 3a + 2b = 31 ... (iii) From equations (i), (ii) and (iii) x - a = 5 It means they must have scored five more 3-pointers in Q4 than in Q3.

So their scores could be (7,4), (2,9) or (10,2), (5,7) or (13,0), (8.5) in Q3 & Q4 respectively. (2-pointer, 3-pointer) So 11, 12 or 13 shots in each quarter or a total of 22, 24 or 26 shots.

Now DET Pistons could have scores of (4,7), (7,5), (10,3) or (13,1) in Q3 and (3,4), (6,2) or (9,0) in Q4. So 11, 12, 13 or 14 shots in Q3 and 7, 8 or 9 shots in Q4.

Here two cases are possible for (Q3, Q4) viz. (13, 9) or (14, 8)

Hence, DET Pistons scores either one or three 3-pointers in Q3.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 17

Group Question

Answer the following question based on the information given below.

Five friends Adam, Sukhbir, Hitesh, Navneet and Mushtaq went to a gym on a morning. They spent 24, 25, 28, 32 and 45 minutes in the gym not necessarily in the same order. Not more than two people were present inside the gym at the same time. The below information is known about their visits:

• Adam entered at 6:50 am.

• The person who entered 64 minutes after Hitesh, spent 32 minutes in the gym.

• Sukhbir entered 13 minutes after Mushtaq did and left 30 minutes after Mushtaq had left.

• Adam and Sukhbir spent 10 minutes together in the gym.

• The last person left at 7:30 am.

*Q. Since morning, how many people left the gym before Sukhbir did?*

Solution:

Sukhbir entered 13 minutes after Mushtaq did and left 30 minutes after Mushtaq had left. Hence, Sukhbir spent 17 minutes more than Mushtaq did. So Mushtaq and Sukhbir spent 28 and 45 minutes respectively in the gym as this is the only combination possible.

Adam and Sukhbir spent 10 minutes together in the gym and Adam entered at 6:50 am. The case that Sukhbir entres 10 minutes before Adam left is not possible as Sukhbir spent 45 minutes and the last person left at 7:30 am. So, Sukhbir must have left the gym at 7:00 am.

Thus, Sukhbir entred at 6:15 am and left at 7:00 am while Mushtaq entred at 6:02 am and left at 6:30 am.

The person who entered 64 minutes after Hitesh, spent 32 minutes. So clearly Hitesh was not the last person to leave, nor was Mushtaq and Sukhbir. The last person cannot be Adam as no person spent 40 minutes in the gym. So Navneet was the last person to leave the gym at 7:30 am. If Navneet spent 32 minutes in the gym, he would have entered at 6:58 am. But in that case, there were three people in the gym together, Navneet, Adam, and Sukhbir. Hence, Navneet spends 24 or 25 minutes in the gym. Only Adam can spend 32 minutes in gym. Hence, Hitesh enters at 5:46 am.

We get the following table :

Thus, two people left before Sukhbir did. Answer: 2

*Answer can only contain numeric values

QUESTION: 18

Five friends Adam, Sukhbir, Hitesh, Navneet and Mushtaq went to a gym on a morning. They spent 24, 25, 28, 32 and 45 minutes in the gym not necessarily in the same order. Not more than two people were present inside the gym at the same time. The below information is known about their visits:

• Adam entered at 6:50 am.

• The person who entered 64 minutes after Hitesh, spent 32 minutes in the gym.

• Sukhbir entered 13 minutes after Mushtaq did and left 30 minutes after Mushtaq had left.

• Adam and Sukhbir spent 10 minutes together in the gym.

• The last person left at 7:30 am.

*Q. Adam spent how many minutes in the gym? *

Solution:

Solution: From the solution to previous question, Adam spent 32 minutes in the gym.

Answer: 32

*Answer can only contain numeric values

QUESTION: 19

Five friends Adam, Sukhbir, Hitesh, Navneet and Mushtaq went to a gym on a morning. They spent 24, 25, 28, 32 and 45 minutes in the gym not necessarily in the same order. Not more than two people were present inside the gym at the same time. The below information is known about their visits:

• Adam entered at 6:50 am.

• The person who entered 64 minutes after Hitesh, spent 32 minutes in the gym.

• Sukhbir entered 13 minutes after Mushtaq did and left 30 minutes after Mushtaq had left.

• Adam and Sukhbir spent 10 minutes together in the gym.

• The last person left at 7:30 am.

*Q. What is the difference between the entering times of Hitesh and Mushtaq in minutes?*

Solution:

Solution: From the solution to the first question of the set, required difference = 16 minutes.

Answer: 16

*Answer can only contain numeric values

QUESTION: 20

Five friends Adam, Sukhbir, Hitesh, Navneet and Mushtaq went to a gym on a morning. They spent 24, 25, 28, 32 and 45 minutes in the gym not necessarily in the same order. Not more than two people were present inside the gym at the same time. The below information is known about their visits:

• Adam entered at 6:50 am.

• The person who entered 64 minutes after Hitesh, spent 32 minutes in the gym.

• Sukhbir entered 13 minutes after Mushtaq did and left 30 minutes after Mushtaq had left.

• Adam and Sukhbir spent 10 minutes together in the gym.

• The last person left at 7:30 am.

*Q. For how many minutes was Navneet alone in the gym? *

Solution:

Solution: From the solution to the first question of the set, Adam left the gym at 7:22 am and Navneet left at 7:30 am. Navneet was alone in the gym for 8 minutes. Answer: 8

QUESTION: 21

Group Question

Answer the following question based on the information given below.

Ten R&AW agents, who have finished their training, are to be sent to ten different locations. They will depart to Beijing, Cairo, Cape Town, Dubai, London, Moscow, New York, Paris, Sydney and Toronto in a week starting from Monday to Sunday. The departure timings of the flights are 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm and 10 pm not necessarily in the same order. There are three days when two flights will depart and neither Saturday nor Sunday is one of them.

Furthermore, the below information is known about the departure of flights:

• The first flight will depart at 6 pm while the last will depart at 7 pm.

• The flights to the two cities whose names start with the same alphabet will depart on the same day with a difference of 5 hours between them.

• The flight to Moscow will depart at 9 pm on Friday.

• The days on which two flights depart are not consecutive.

• The flight to Paris will depart at 4 pm and that to New York at 5 pm.

• The flight to London will not depart on Monday and the flight to Sydney is not the first flight to depart.

• The flight to Dubai will depart just before the flight to Cairo.

• The flight to Toronto will depart before the flight to New York but not before the flight to Paris.

• The flight departing at 1 pm will not be departing on Friday or Saturday.

*Q. How many flights are scheduled between the departures of the flights to Sydney and Paris? *

Solution:

There are three days when two flights will depart and are not consecutive. Also, neither Saturday nor Sunday is one such day. Hence, the three days on which 2 flights will depart are Monday, Wednesday and Friday. From the given statements, we have:

Of the given 10 cities, names of only two of them, Cairo and Cape Town, start with the same letter. Hence, the flights to these cities will depart on Wednesday. Now the times of departure of these flights cannot be 1,6 (6 pm flight on Monday), 2,7 (7 pm flight on Sunday), 4,9 (Flight to Moscow at 9) and 5,10 (Flight to New York at 5). Hence, the timings of the flights on Wednesday are 3 pm and 8 pm.

Now, the flight to Dubai will depart just before the flight to Cairo. Hence, the flight to Dubai will be on Tuesday, Cairo, Cape Town in the order on Wednesday. Hence, the second flight of Monday must be at 10 pm.

The flights to Paris and New York will depart at 4 pm and 5 pm respectively. Hence, they can only be on Thursday, Friday or Saturday. The flight to Toronto will depart before the flight to New York but not before the flight to Paris. Hence, we have: Paris, Thursday, 4pm; Toronto, Friday and New York, Saturday, 5 pm. From the condition for the 1 pm flight, we get Dubai -1 pm and Toronto - 2 pm.

The flight to London will not depart on Monday hence, it has to depart on Sunday. Also, the flight to Sydney is not the first flight to depart. Hence, the flight to Beijing is the first flight to depart.

Three flights to cities namely Dubai, Cairo and Cape Town are scheduled between the departures of the flights to Sydney and Paris Hence, option 2.

QUESTION: 22

Ten R&AW agents, who have finished their training, are to be sent to ten different locations. They will depart to Beijing, Cairo, Cape Town, Dubai, London, Moscow, New York, Paris, Sydney and Toronto in a week starting from Monday to Sunday. The departure timings of the flights are 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm and 10 pm not necessarily in the same order. There are three days when two flights will depart and neither Saturday nor Sunday is one of them.

Furthermore, the below information is known about the departure of flights:

• The first flight will depart at 6 pm while the last will depart at 7 pm.

• The flights to the two cities whose names start with the same alphabet will depart on the same day with a difference of 5 hours between them.

• The flight to Moscow will depart at 9 pm on Friday.

• The days on which two flights depart are not consecutive.

• The flight to Paris will depart at 4 pm and that to New York at 5 pm.

• The flight to London will not depart on Monday and the flight to Sydney is not the first flight to depart.

• The flight to Dubai will depart just before the flight to Cairo.

• The flight to Toronto will depart before the flight to New York but not before the flight to Paris.

• The flight departing at 1 pm will not be departing on Friday or Saturday.

*Q. Which flight is scheduled to depart at 1 pm? *

Solution:

Solution: From the solution to the previous question, the flight to Dubai is scheduled to depart at 1 pm on Tuesday.

Hence, option 4.

QUESTION: 23

Ten RA&W agents, who have finished their training, are to be sent to ten different locations. They will depart to Beijing, Cairo, Cape Town, Dubai, London, Moscow, New York, Paris, Sydney and Toronto in a week starting from Monday to Sunday. The departure timings of the flights are 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm and 10 pm not necessarily in the same order. There are three days when two flights will depart and neither Saturday nor Sunday is one of them.

Furthermore, the below information is known about the departure of flights:

• The first flight will depart at 6 pm while the last will depart at 7 pm.

• The flights to the two cities whose names start with the same alphabet will depart on the same day with a difference of 5 hours between them.

• The flight to Moscow will depart at 9 pm on Friday.

• The days on which two flights depart are not consecutive.

• The flight to Paris will depart at 4 pm and that to New York at 5 pm.

• The flight to London will not depart on Monday and the flight to Sydney is not the first flight to depart.

• The flight to Dubai will depart just before the flight to Cairo.

• The flight to Toronto will depart before the flight to New York but not before the flight to Paris.

• The flight departing at 1 pm will not be departing on Friday or Saturday.

*Q. What is the difference in the time of the departures of the two flights on Friday?*

Solution:

Solution: From the solution to the first question of the set, we can see that the flights scheduled on Friday are Toronto (2 pm) and Moscow (9 pm).

Difference = 7 hours Hence, option 1.

QUESTION: 24

Ten R&AW agents, who have finished their training, are to be sent to ten different locations. They will depart to Beijing, Cairo, Cape Town, Dubai, London, Moscow, New York, Paris, Sydney and Toronto in a week starting from Monday to Sunday. The departure timings of the flights are 1 pm, 2 pm, 3 pm, 4 pm, 5 pm, 6 pm, 7 pm, 8 pm, 9 pm and 10 pm not necessarily in the same order. There are three days when two flights will depart and neither Saturday nor Sunday is one of them.

Furthermore, the below information is known about the departure of flights:

• The first flight will depart at 6 pm while the last will depart at 7 pm.

• The flight to Moscow will depart at 9 pm on Friday.

• The days on which two flights depart are not consecutive.

• The flight to Paris will depart at 4 pm and that to New York at 5 pm.

• The flight to Dubai will depart just before the flight to Cairo.

• The flight departing at 1 pm will not be departing on Friday or Saturday.

Q. The flights to which two cities are the first and the last to depart respectively?

Solution:

Solution: From the solution to the first question of the set, the first flight will depart for Beijing on Monday at 6 pm while the last flight will depart for New York on Sunday at 7 pm.

Hence, option 2.

QUESTION: 25

Group Question

Answer the following question based on the information given below.

An office has three office assistants: Sudip, Pankaj and Yash. Everyday, at least one of the three has to come to the office. No employee should come for more than 2 days consecutively. Each employee has to come 4 days in a week from Sunday to Saturday.

Q. If Sudip and Pankaj both come to the duty together for exactly 3 days, for how many days does Yash has to do his duty alone?

Solution:

Solution: Both Pankaj and Sudip came together for 3 days out of 7 days in the week. They have to attend their duties for one more day (but not together). So, Pankaj will come on one day and Sudip will come on another day. There are 5 days in which either Pankaj or Sudip or both will come. So, on the other 2 days, Yash has to come alone.

Hence, option 3.

QUESTION: 26

An office has three office assistants: Sudip, Pankaj and Yash. Everyday, at least one of the three has to come to the office. No employee should come for more than 2 days consecutively. Each employee has to come 4 days in a week from Sunday to Saturday.

Q. In a particular week, if Yash and Sudip come together for 2 days, and Yash and pankaj come together for 2 days and Sudip comes alone on Monday and with Pankaj on Tuesday, when will Pankaj come alone? (All 3 persons cannot come on a day)

Solution:

Solution: If Pankaj comes alone on Sunday or Wednesday, Yash will come on 3 consecutive days, which is not possible.

Also, Sudip cannot come on either Sunday or Wednesday. Hence, Yash and Pankaj come on both Sunday and Wednesday.

Now, Pankaj cannot come on Thursday, hence Yash and Sudip come on Thursday.

Yash cannot come on Friday.

Hence, Pankaj alone comes on Friday.

Hence, option 4.

QUESTION: 27

An office has three office assistants: Sudip, Pankaj and Yash. Everyday, at least one of the three has to come to the office. No employee should come for more than 2 days consecutively. Each employee has to come 4 days in a week from Sunday to Saturday.

Q. If Yash and Sudip come to duty together for only one day, for what minimum number of days will both Yash and Pankaj, but not Sudip come together?

Solution:

Solution: Since Yash and Sudip come together on one day, Sudip has to come to duty on his other 3 days without Yash So, out of the 7 days: 1 day - both Yash and Sudip come 3 days - Yash comes, but not Sudip 3 days - Sudip comes, but not Yash Even if Pankaj comes to his duty along with Sudip, but not Yash for all the possible 3 days, for at least 1 day he has to come along with Yash.

Hence, option 2.

QUESTION: 28

An office has three office assistants: Sudip, Pankaj and Yash. Everyday, at least one of the three has to come to the office. No employee should come for more than 2 days consecutively. Each employee has to come 4 days in a week from Sunday to Saturday.

Q. What will be the minimum number of days per week when Only one among the three comes to duty?

Solution:

Solution: Each person comes 4 times per week. So, 3 persons come 12 times.

If they don’t want to come alone, at least 2 have to come daily that means they have to come 7 x 2 = 14 times a week.

But, it is only 12. So, for at least 2 days, only one person comes to duty.

Hence, option 3.

QUESTION: 29

Group Question

Answer the following question based on the information given below.

Manjit had deodorant and talc of 4 brands each in his house. One day, when he was in his office, his son painted all the bottles and arranged them according to their heights on the table.

i. Manjit had Park Avenue, Nivea, Axe and Yardley.

ii. The bottles were painted blue, black, green and silver colours not necessarily in that order. The colour of the deodorant bottle and talc bottle of the same brand was different.

iii. The height of the talc bottle was smaller than the height of the deodorant bottle for the same brand.

iv. Park Avenue deodorant was figured out to be black in colour and placed at the third position (ascending). Its height was more than Yardley talc.

v. Axe deodorant was placed exactly in between blue and silver colored bottles.

vi. The bottle at the 5th position (ascending) was silver in colour.

vii. Axe talc was taller than Nivea deodorant.

viii. The 1st and the last bottles were blue in colour.

ix. Deodorant of neither Nivea nor Yardley was green in colour.

*Q. What are the brands of the shortest and the tallest bottles? *

Solution:

Let us assume that the bottles are kept in the ascending order of their heights from position 1 to position 8, position 1 being the shortest.

From (iv), Park Avenue (Deo) is Black and is kept at Position 3.

From (iii), Park Avenue (Talc) and Yardley (Talc) are kept at positions 1 & 2 in any order.

From (iv), (ix) & (viii), Axe (Deo) is Green in colour and is kept at position 7. Also, bottles at Position 6 and Position 8 are Silver & Blue respectively.

From (iii) & (vii), Axe (Deo) is taller than Axe (Talc), which is taller than Nivea (Deo) which is taller than Nivea (Talc).

Since Axe (Deo) is at position 7, these four bottles are kept from positions 4 through 7. Since Deodorant bottle is always taller than the Talc bottle for the same brand, Yardley (Deo) has to come at position 8. From (ii), Yardley (Talc) cannot be Blue in colour and hence has to be placed at position 2. Thus, Park Avenue (Talc) is placed at postion 1.

These inferences can be summarised in a table as shown below.

Thus, Yardley has the tallest bottle while Park Avenue has the shortest bottle.

Hence, option 4.

QUESTION: 30

Manjit had deodorant and talc of 4 brands each in his house. One day, when he was in his office, his son painted all the bottles and arranged them according to their heights on the table.

i. Manjit had Park Avenue, Nivea, Axe and Yardley.

ii. The bottles were painted blue, black, green and silver colours not necessarily in that order. The colour of the deodorant bottle and talc bottle of the same brand was different.

iii. The height of the talc bottle was smaller than the height of the deodorant bottle for the same brand.

iv. Park Avenue deodorant was figured out to be black in colour and placed at the third position (ascending). Its height was more than Yardley talc.

v. Axe deodorant was placed exactly in between blue and silver colored bottles.

vi. The bottle at the 5th position (ascending) was silver in colour.

vii. Axe talc was taller than Nivea deodorant.

viii. The 1st and the last bottles were blue in colour.

ix. Deodorant of neither Nivea nor Yardley was green in colour.

Q. How many bottles are there between deodorant and talc of Yardley?

Solution:

Solution: From the solution to the previous question, we can see that, Yardley (Deo) is at position 8 while Yardley (Talc) is at 2nd position. Hence, 5 bottles are between them.

Hence, option 3.

QUESTION: 31

Manjit had deodorant and talc of 4 brands each in his house. One day, when he was in his office, his son painted all the bottles and arranged them according to their heights on the table.

i. Manjit had Park Avenue, Nivea, Axe and Yardley.

ii. The bottles were painted blue, black, green and silver colours not necessarily in that order. The colour of the deodorant bottle and talc bottle of the same brand was different.

iii. The height of the talc bottle was smaller than the height of the deodorant bottle for the same brand.

iv. Park Avenue deodorant was figured out to be black in colour and placed at the third position (ascending). Its height was more than Yardley talc.

v. Axe deodorant was placed exactly in between blue and silver colored bottles.

vi. The bottle at the 5th position (ascending) was silver in colour.

vii. Axe talc was taller than Nivea deodorant.

viii. The 1st and the last bottles were blue in colour.

ix. Deodorant of neither Nivea nor Yardley was green in colour.

*Q. Which of the following is definitely correct? *

Solution:

Solution: From the solution to the first question of the set, we can see that Nivea (Deo) is Silver while the colour of Nivea (Talc) can be Black or Green and thus cannot be determined.

Hence, option 4.

QUESTION: 32

Manjit had deodorant and talc of 4 brands each in his house. One day, when he was in his office, his son painted all the bottles and arranged them according to their heights on the table.

i. Manjit had Park Avenue, Nivea, Axe and Yardley.

v. Axe deodorant was placed exactly in between blue and silver colored bottles.

vi. The bottle at the 5th position (ascending) was silver in colour.

vii. Axe talc was taller than Nivea deodorant.

viii. The 1st and the last bottles were blue in colour.

ix. Deodorant of neither Nivea nor Yardley was green in colour.

*Q. If Manjit picks bottles of the same brand and picks the second shortest bottle, then which other bottle he picks?*

Solution:

Solution: From the solution to the previous question, we can see that The second shortest bottle is Yardley talc. Hence, he picks the Yardley deodorant along with it.

Hence, option 1.

### Drop Year / Gap Year | CAT 2019 | CAT Preparation strategy

Video | 08:11 min

### Mixture & Alligation - CAT

Video | 52:24 min

- Sample CAT LRDI MCQ
Test | 32 questions | 40 min

- CAT LRDI MCQ
Test | 32 questions | 40 min

- CAT LRDI MCQ - 1
Test | 32 questions | 40 min

- CAT LRDI MCQ - 2
Test | 32 questions | 40 min

- CAT LRDI MCQ - 3
Test | 32 questions | 40 min