Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for 2 minutes at each of the junction stations on the way and for 1 minute at each of the other stations. It takes 2 minutes to reach the next station for trains going in east-west direction and 3 minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every 15 minutes in the north-south lines and every 10 minutes in the east west lines. A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)
1.
CAT 2022 LRDI Slot 1
| DI - Routes & Networks
If Hari is ready to board a train at 8:05 am from station M, then when is the earliest that he can reach station N?
Case 1: T – R – S
The first train to depart T will be at (6 am + 9 + 2 + 2 =) 6:13 am.
∴ Now a train will depart T every 15 minutes, hence the train which Priya can catch for T → R is at 10:28.
Time taken to reach R = 12 + 3 = 15 mins.
∴ Priya reaches R at 10:43 am.
The first train to depart R will be at (6 am + 8 + 3 + 2 =) 6:13 am.
∴ Now a train will depart R every 10 minutes, hence the train which Priya can catch for R → S is at 10:43 itself.
Time taken to reach S = 20 + 9 = 29 mins.
∴ Priya reaches S at 11:12 am.
Case 2: T – S – R
The first train to depart T will be at (6 am + 8 + 3 + 2 =) 6:13 am.
∴ Now a train will depart T every 10 minutes, hence the train which Priya can catch for T → V is at 10:33 itself.
Now time taken from T → V is 29 mins and time taken from V → S is 15 mins.
Even if Priya does not have to wait at V she can S latest by 10:33 am + 29 + 15 = 11:17 am.
Haripriya is expected to reach station S late. What is the latest time by which she must be ready to board at station S if she must reach station B before 1 am via station R?
Time taken from S → R:
Travel time = 10 × 2 = 20 mins
Stoppage time = 9 × 1 = 9 mins
Total time = 20 + 9 = 29 mins
Similarly, Time taken from R → B: 7 × 3 + 7 = 28 mins
In the north-south direction, the first train from A arrives at R at time = 6 am + (3 × 3) + (2 × 1) mins = 6:11 am.
Since R is a junction so this train will halt for 2 minutes at R and leave at 6:13.
Every 15 minutes, a train starts from A in the north-south direction.
The last train that leaves A will be at 12:00 am and it will leave R at 12:13 am, so Haripriya must reach R till 12:13 am.
If she catches this train from R at 12:13, she will reach B by 12:13 + 28 = 12:41 am.
Travelling time between S and R = (10 × 2) + (9 × 1) = 29
So Haripriya must board the train at S by (12:13 - 29 =) 11:44 pm
In the east-west direction, the first train from N arrives at S at time = 6 am + (6 × 2) + (5 × 1) = 6:17 am.
Since S is a junction so this train will halt for 2 minutes at S and leave at 6:19.
Every 10 minutes, a train starts from N in the east-west direction.
Therefore, Haripriya should board the train which leaves S at 11:39.
A train leaves A for B and B to A every 15 minutes starting from 6 am.
Total time taken by a north-south train:
There are total 10 stations from M till N, hence total travelling time = 10 * 3 = 30 minutes.
There are 2 junctions, hence stoppage time = 2 * 2 = 4 mins
There are 7 other stations, hence stoppage time = 7 * 1 = 7 mins
∴ Total time taken = 30 + 4 + 7 = 41 mins.
The train which starts from A to B at 6 am reaches B at 6:41 am. It needs to rest for 15 minutes before it can start the journey back to A i.e., it can start it’s journey at 6:56 or after that.
As per schedule north-south trains leave every 15 minutes starting from 6 am. Hence, the train that starts from A to B at 6 am, can start its backward journey at 7 am.
∴ There have to be trains starting at 6 am, 6:15 am, 6:30 am and 6:45 am before trains coming from A can start their journey back.
Hence, we need at least 4 trains from B to A and similarly from A to B.
We need at least 8 trains on AB route as well as 8 trains on CD route.
∴ 16 trains on north-south routes.
Total time taken by a east-west train = 61 mins (calculated in first question of this set)
A train going from M to N at 6 am will reach N at 7:01 and will be ready for journey back at 7:16 am. A train starts from N every 10 mins. Hence, this train can start its journey at 7:20 am.
∴ There have to be trains starting at 6 am, 6:10 am, 6:20 am, 6:30 am, 6:40 am, 6:50 am, 7 am and 7:10 am before trains coming from M can start their journey back.
Hence, we need at least 8 trains from N to M and similarly from M to N.
∴ We need at least 16 trains on the route MN and 16 trains on PQ route
∴ 32 trains on east-west routes.
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.
Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.
The following facts are also known:
1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.
There are boys and girls in the class. Each of the boy or girl is either a dance or singer or none of these but not both.
There are 6 singers in the class, 4 of them are boys.
⇒ There are 4 male singers and 2 female singers
There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer
⇒ There are 6 male dances and 4 female dancers
From (4): No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
Since all 4 male singers are interested in a 3-day event, they all must also be interested in a 2-day and a 1-day event.
Since 2 male dancers are interested in a 3-day event, male dancers interested in a 2-day event must be greater than or equal to 2.
From (1): All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
From (3): 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. Hence, 30% of those who are interested in a 2-day event are dancers or singers.
Now, (2 + b) = 30% of 60% of (10 + x)
⇒ 2 + b + 4 = × × (10 + x)
⇒ 6 + b = × (10 + x)
Here b has to be an integer, hence (10 + x) should be completely divisible by 50.
∴ x should be 40 or 90 or 140 and so on.
But since b cannot be greater than 4, x should be 40 and b = 3.
From (5): The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.
This is only possible when 2 female singers while no female dance is interested in a 2-day event.
From (3): 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
⇒ 0 + 2 = × (0 + 2 + females interested in a 2-day event who are neither singer nor dancer)
females interested in a 2-day event who are neither singer nor dancer = 3
Which of the following can be determined from the given information?
I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.
II. The number of female dancers who are interested in attending a 1-day event.
Consider the solution to first question of this set.
Number of male dancers who are interested in attending a 1-day event has to be more than or equal to number of male dancers who are interested in attending a 2-day event i.e., 5 or 6.
Answer the next 5 questions based on the information given below:
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only.
Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.
Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.
The following additional facts are known:
1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.
From (1): Fathima awarded tokens to everyone except Qahira,
∴ Fatima must have awarded token number 3 to everyone and Qahira received tokens whose product is 77.
From (1): Adhara awarded tokens to no one except Pragnyaa
∴ Adhara must have awared token 13 and Pragnyaa received tokens whose product is 390.
From (2): Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
∴ Rashida must have received 4 tokes whose product can only be 210. Also, since Esther did not give her the token, hence Esther must have distributed token number 11.
From (3): Dhanavi awarded a token to Qahira but not to Smera.
∴ Dhanavi must have awared token number 7.
From (3): Bithi awarded a token to Smera but not to Qahira
∴ Bithi/Chhaya could have awared token 2/5 in any order.
If Bithi gives token number 2 to S/T, then Chhaya will given token number 5 to T/S and vice-a-versa.
Answer the next 5 questions based on the information given below:
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.
The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.
1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.
16.
CAT 2022 LRDI Slot 1
| DI - Games & Tournaments
Total 12 goals were scored by 4 players such that each player scored at least one goal and distinct number of total goals.
There are two possibilities for this:
12 = 1 + 2 + 3 + 6
12 = 1 + 2 + 4 + 5
From (1): Only one goal was scored in every even numbered match.
From (5): An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
Let the number of goals scored in Match 3 and 7 be x each.
From (6): The match in which the highest number of goals was scored was unique and it was not Match 5.
⇒ Highest goals were scored in Match 1.
From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
From (2): Harita scored more goals than Bimla.
⇒ Bimla scored at least 4 goals while Harita scored at least 5 goals.
∴ 12 = 1 + 2 + 4 + 5
⇒ Bimla scored 4 goals while Harita scored at 5 goals.
From (3): The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
∴ Harita can score maximum 1 goal each in Match 4 and 5, hence she scores 3 goals in one more Match.
The only match Harita can score 3 goals is Match 1 since highest numbers of goals are scored in Match 1.
From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
∴ Three consecutive matches Bimla can score in are Match 5, 6 and 7.
Now, a + 1 + x + 1 + b + 1 + x + 1 = 12
⇒ a + b + 2x = 8
[Match 7: x has to be greater than or equal to 1.]
Case 1: x = 1
⇒ a + b = 6
⇒ a = 4 and b = 2 [a has to be uniquely highest and a, b ≠ x]
Case 2: x = 2
⇒ a + b = 4
Rejected as minimum value of a is 4 and that of b is 1.
∴ x = 1, a = 4 and b = 2
Amla or Sarita could have scored 1 or 2 goal in any order.
Which of the following statement(s) is/are true? Statement-1: Amla and Sarita never scored goals in the same match. Statement-2: Harita and Sarita never scored goals in the same match.
19.
CAT 2022 LRDI Slot 1
| DI - Games & Tournaments
Which of the following statement(s) is/are false? Statement-1: In every match at least one player scored a goal. Statement-2: No two players scored goals in the same number of matches.
20.
CAT 2022 LRDI Slot 1
| DI - Games & Tournaments
If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true? Statement-1: Amla scored goals in consecutive matches. Statement-2: Sarita scored goals in consecutive matches.
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