CAT 2022 | DILR Set 1
Q.1 to Q.5
DIRECTIONS for the question: Read the information given below and answer the question that follows.
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.
- Only one goal was scored in every even numbered match.
- Harita scored more goals than Bimla.
- The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
- Bimla scored a goal in Match 1 and one each in three other consecutive matches.
- 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.
- The match in which the highest number of goals was scored was unique and it was not Match 5.
1. How many goals were scored in Match 7?
- 1
- 2
- 3
- Cannot be determined
First, we have to figure out the highest number of goals scored by whom.
As we have to make total 12 goals.
Harita score minimum of total 5 goals as she scored more than Bimla.So, Bimla scores a total of 4 goals.
Therefore, Amla and Sarita scores either 1,2 or 2,1 goals.
Now, we have total 12 goals
We have two options for the same
3 1 2 1 1 1 2 1....(1st case)
Or
4 1 1 1 2 1 1 1...(2nd case)
Now, it is not possible that there are total 3 goals in the first match so 1st case is cancelled
In match 7 only 1 goal is scored : Option 1
2. Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
- 3, 1, 2, 1
- 5, 1, 0, 1
- 3, 2, 1, 2
- 4, 1, 2, 1
First, we have to figure out the highest number of goals scored by whom.
As we have to make total 12 goals.
Harita score minimum of total 5 goals as she scored more than Bimla.So, Bimla scores a total of 4 goals.
Therefore, Amla and Sarita scores either 1,2 or 2,1 goals.
Now, we have total 12 goals
We have two options for the same
3 1 2 1 1 1 2 1....(1st case)
Or
4 1 1 1 2 1 1 1...(2nd case)
Correct sequence of goals is 4,1,2,1 : Option 4
3. 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.
- None of the statements
- Statement-1 only
- Both the statements
- Statement-2 only
Statement 1 : Total 3 vacant spaces are available where a total of 3 goals are to be scored.Now, the combination of Amla and Sarita goals is 2 or 1.Therefore, if Amla scores a goal then Sarita cannot score a goal and if Sarita scores a goal then Amla cannot.So, this is true. Statement 2 : Harita’s goals have already been scored as she is the highest goal scorer and the places where Harita is not scoring goal are the places where Sarita would score the goal.Hence, this statement is also true. Therefore both the statements are true : Option 3
4. 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.
- Statement-2 only
- None of the statements
- Both the statements
- Statement-1 only
Statement 1 : In first match, 4 goals are scored i.e 3 by Harita and 1 by Bimla.If Amla scores in 2nd match then Sarita scores in 3rd match. In the 4th match Harita is scoring the goal.In 5th,6th & 7th match, Bimla scored a goal each. In 8th match Harita scores a goal.So, in every match atleast one player scored a goal. Statement 2 : Amla scores either 1 or 2. Bimla scores 4. Harita scores 3. Sarita scores 2. Hence,no two players scored goals in the same number of matches. Therefore, none of the statements is false.
5. 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.
- Both the statements
- Statement-2 only
- None of the statements
- Statement-1 only
Statement 1 : If Harita scored in 3 matches then Sarita scores 2. Therefore, Amla scores 1.Then Bimla scores in 4 matches.Now, Amla may or may not score good in consecutive matches. Statement 2 : If Harita scored in 3 matches then Sarita scores 2. Therefore, Amla scores 1.Then Bimla scores in 4 matches. Now, Bimla may or may not score goals in consecutive matches. Therefore, none of the statements is true.
CAT 2022 | DILR Set 2
Q.6 to Q.10
DIRECTIONS for the question: Read the information given below and answer the question that follows.
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:
- Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
- Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
- Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.
6. How many tokens did Qahira receive?
7. Who among the following definitely received a token from Bithi but not from Dhanavi
- Rasheeda
- Pragnyaa
- Tantra
- Qahira
8. How many tokens did Chhaya award?
9. How many tokens did Smera receive?
10. Which of the following could be the amount of funding that Tantra received?
(a) Rs. 66,000
(b) Rs. 165,000
- Only (b)
- Only (a)
- Neither (a) nor (b)
- Both (a) and (b)
CAT 2022 | DILR Set 3
Q.11 to Q.15
DIRECTIONS for the question: Read the information given below and answer the question that follows.
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:
- 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.
- 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.
- 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.
- 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.
- 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.
11. How many boys are there in the class?
0.7(0.6b + 6) = b – x
0.42 b + 4.2 = b – x
0.58b = 4.2 + x
b has to be a natural number if 4.2 is in the table of 48.
Multiplying it by 100
58b = 420 + 100x
For ‘b’ to be a natural number x = 19, b = 40
Which means b = 40
0.6g = 9 – y
Therefore g can be 10 or 5 and y can be 6 or 3
Now making the complete table again with this information
No of boys = b + 10 = 40 + 10 = 50
12. 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.
- Neither I nor II
- Both I and II
- Only I
- Only II
13. What fraction of the class are interested in attending a 2-day event?
- 7/13
- 2/3
- 9/13
- 7/10
14. What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?
- 5
- 4 or 6
- 6
- 5 or 6
15. How many female dancers are interested in attending a 2-day event?
- 2
- 1
- 0
- Cannot be determined
CAT 2022 | DILR Set 4
Q.16 to Q.20
DIRECTIONS for the question: Read the information given below and answer the question that follows.
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.)
16. 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?
- 9:06 am
- 9:13 am
- 9:11 am
- 9:01 am
First we need to find the time taken from all terminals to all junctions through stations
M → R = 2 +2 + 2 + 2(3 stations gap is 4) + 3(every station stop ) = 11 min
P →T = 2 + 2 + 2 + 2 + 3 (same as above) = 11 min
R → S = 2 + 2 + 2+ 2 + 2 + 2 + 2 + 2 + 2 + 2(9 stations so gap is 10) + 9(9 stations ) = 20 min + 9 min = 29 min
T →V = symmetrical as R → S = 20 + 9 = 29 min
S →N = 2 + 2 + 2 + 2 + 2 + 2 + 5 = 12 + 5 = 17 min
V → Q = 12 + 5 = 17 min
A→R = 3 + 3 + 3 + 2 = 11 min
C→S = 3 + 3 + 3 + 2 = 11 min
R→T = 3 + 3 + 3 + 3 + 3 = 15 min
S→V = 3 +3 + 3 + 3 + 3 = 15 min
T → B = 3 +3 + 3(for north south direction train takes 3 minutes) + 2 = 11 min
V → D = 3 + 3 + 3 + 2 = 11 min
Hari is ready to board at 8:05 am from station M to N. As he has to reach at the earliest so he has to go straight from M → N via R and S.
Now we know a train would leave at 6 am then 6:10 as a train leaves after every 10 minutes in the east west direction and so on. We have to find which train will he board close to 8:05 am. So, he will board a train which will leave at 8:10 as the train at 8:00 am would have already left. Therefore, he has to wait for 5 minutes
M→N = 5min(he waited) + (M →R) + (R →S) + (S →N) = 5 + 11 + 29 + 17 = 66 min
8:05 + 66 min = 9 :11 am : Option 3
17. If Priya is ready to board a train at 10:25 am from station T, then when is the earliest that she can reach station S?
- 11:12 am
- 11:28 am
- 11:22 am
- 11:07 am
If Priya is ready to board at 10:25 from station T, we need to check whether there is a train from P or B around 10:25 am. As BT path has less number of stations which is 2 so we will take BT path. If a train leaves at 10:00 from B it will take 11 minutes to reach T i.e 10:11 and it would leave at 10:13 so Priya won’t be able to catch this train. If train leaves at 10:10 from B it will reach T at 10:21 and would leave at 10:23 so again she won’t be able to catch this train also. If train leaves at 10:20 from B it will reach at 10:31 and leave at 10:33 which means Priya had to wait for 8 minutes and board this train. 8 min + (T→ R) + (R → S) = 8 min + 15 min + 29 min = 52 min which means she would reach S at 10:33 + 52 min = 11:25 am which is not in option. So, we will check the other option As we know for every north-south direction the train can leave after every 15 minutes also. If the train leaves from B at 10:15 then it will reach T at 10:26. It would leave at 10:28 from station T. So, Priya had waited for 3 minutes. 3 min + (T→R) + (R → S) = 3 + 15 + 29 = 47 minutes which means she would reach station S at 10:25 + 47 min = 10:25 + 35 min + 12 min = 11:12 min which is option 1
18. 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?
- 11:39 pm
- 11:43 pm
- 11:49 am
- 11:35 pm
Haripriya has to reach station S late via station R if she must reach station B before 1 am Using option 1 : 11:39 We have to find when the train would have left N. Suppose the train would have left around 11:20 then it would reach S at 11:37. It would leave station S at 11:39. So, she will board the train at 11:39 from S (S→R) + 2 + (R→T) + 2 + (T→B) =11:39 + 29 + 2 + 17 + 2 + 11 = 11:39 + 61 = 11:39 + 21 + 40 = 12:40 pm which is the latest time by which she would reach station S If we take option 4 i.e 11 : 35, then the train would have left N at 11:10 then it will take 17 min to reach S which is at 11:27 which will be left at 11:29.So, it is impossible for Haripriya to catch this train at 11:35. Similarly if we taken option 2 i.e 11:43 then train would have left N at 11:30 minimum which will reach S at 11:47 so it is impossible for Haripriya to catch this train .Because if the train left N at 11:20 then it will reach 11:37 which will leave at 11:39 which is again impossible to catch again. Therefore latest time to reach before 1 am is 12:41 am
19. What is the minimum number of trains that are required to provide the service on the AB line (considering both north and south directions)?
For minimum number of trains we need to check that by the time first train reach at the other terminal, we keep on sending the trains. For AB line total time taken = A→R→T→B = 11 + 2 + 15 + 2 + 11 + 15 = 56 min For BA line total time taken B→T→R→A = 15 + 11 + 2 + 15 + 2 + 11 = 56 min Total time for AB + BA = 56 + 56 = 112 min For north south direction we can send trains after every 15 mins Total number of trains = 112/15 = 7.4 approx, which implies there are more than 7 gaps, so 8 trains can be sent. Therefore 8 trains is the answer
20. What is the minimum number of trains that are required to provide the service in this city?
Total number of trains that required to provide in the city can be calculated through total number of trains across all the roots For east-west root trains leave after every 10 minutes and rest of 15 minutes is also given after reaching the last terminal M→R→S→N = 11 + 2 + 29 + 2 + 17 = 61 min P→T→V→Q = 11 + 2 + 29 + 2 + 17 = 61 min For east west trains total time = (61 + 61 + 15) = 76 minutes each for MN and PQ Total time = 76×2 = 152 Every train comes after 10 minutes, number of trains =152/10 = 15.2 as gap is more than 15 so number of trains in east-west direction = MN + PQ = 16 + 16 = 32 trains Similarly, for north-south direction trains leave after every 15 minute and rest of 15 minutes is same A→R→T→B = C→S→V→D = 11 + 2 + 15 + 2 + 11 + 15 = 56 min + 56 min = 112 min Number of trains = 112/15 = 7.4 approx implies more than 7 gaps are there so number of trains each side = 8 Total trains north-south direction = 8 + 8 = 16 Therefore, total number of trains = trains in north-south direction + trians in east-west direction = 16 + 32 = 48
