60 students were shortlisted for their Personal Interview by the Indian School of Management. But the interview process was to be conducted online and hence students were sent the KOOM meeting link for the same. All the 60 students were to join the KOOM common room at 9:00 AM sharp and then the admission co-ordinators would send in a certain number of students to different waiting rooms- X, Y and Z prior to their one on one interviews with the panellists. There were 3 panellists- A, B and C who were conducting interviews for the candidates waiting in the rooms X, Y and Z respectively. The capacity for the waiting rooms X, Y and Z were 5, 10 and 15 respectively. 
The 60 students were given a rank from 1 to 60 based on their composite score and it is known that no two students got the same score. To start off the interviews, the ones with top 5 ranks are sent to panellist A. The 10 below them are sent to B and students ranked 16 to 30 were sent to C. When the last person from the waiting room X, Y and Z gives an interview, the next set of students are immediately sent to the waiting room as soon as the interview gets over and the priority is maintained as students with higher ranks are sent to X, Y and Z respectively if the interviews of the previous batch end simultaneously. 
It is known that:
1. Panellist A takes an interview for 15 minutes and takes a break of 5 minutes only after interviewing 3 candidates 
2. Panellist B takes an interview for 10 minutes and takes a break of 5 minutes after interviewing 5 students.
3. Panellist C takes an interview of 5 minutes and takes a break of 5 minutes after interviewing 4 students.
4. Lunch break is scheduled between 12:00 noon to 12:30 PM and students are not cut abruptly if their interview began before 12:00 noon, i.e. the interviewers take the break only after finishing the interview if it started before 12:00 noon.
5. Batches of 5, 10 and 15 students enter the waiting room together such that students who enter the waiting room at a time have continuous ranks. For example, if the interviewer X is ending up the interview of the last student from the previous batch, 5 students with continuous ranks (say 21-25) enter the waiting room X together.
6. Students allotted to a particular waiting room is only interviewed by the designated interviewer and is not interviewed by anyone else even if the other interviewer is free.
7. If panellist A goes into the lunch break after having interviewed 1 student, he will again take his 5 minute break after interviewing 2 students post the lunch break so as to satisfy the condition 1 always. The same applies for panellist B and C who follow conditions 2 and 3 respectively.
Which of the following ranked students was interviewed by panellist C?
  • a)
    35
  • b)
    45
  • c)
    55
  • d)
    60
Correct answer is option 'B'. Can you explain this answer?

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Answers

Pioneer Academy
Jan 18, 2022
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.
Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.
And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.
A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.
So, a map of the first few students will look like:
Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.
We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.
Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.
Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.
We do not require N.
Interviewer A interviews students ranked from 1 to 5, 31 to 35.
Interviewer B interviews students ranked from 6 to 15 and 51 to 60.
Interviewer C interviews students ranked from 16 to 30 and 36 to 50.

An updated table will look like:
We can break down the interviews of students ranked 41 to 50 for interviewer C as:
Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.
So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.

Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.So, a map of the first few students will look like:Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.We do not require N.Interviewer A interviews students ranked from 1 to 5, 31 to 35.Interviewer B interviews students ranked from 6 to 15 and 51 to 60.Interviewer C interviews students ranked from 16 to 30 and 36 to 50.An updated table will look like:We can break down the interviews of students ranked 41 to 50 for interviewer C as:Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.
Students ranked from 1 to 5 will be interviewed by A and thus are moved to the waiting room X.Similarly, students ranked 6 to 15 (10 students) will be interviewed by B and are moved to waiting room Y.And students ranked 16 to 30 (15 students) will be interviewed by C and are moved to waiting room Z.A takes a break after every 3 interviews. B and C take breaks after every 5 and 4 interviews respectively.So, a map of the first few students will look like:Here, M, N, X and Y are the ranks of the students. M to M+4 are the set of 5 students who will be interviewed once the interview of the student ranked 5th gets over and similarly for others.We see that interviewer A finishes his first batch of interviews first (at 10:20) and hence M must be 31. Students ranked 31 to 35 move to waiting room X.Next to finish interviewing his/her first batch of interviewees is B (at 10:30) and hence Y=36. Students ranked from 36 to 50 will move into waiting room Z.Finally, interviewer Y will get the next 10 students ranked from 51 to 60 and hence X=51.We do not require N.Interviewer A interviews students ranked from 1 to 5, 31 to 35.Interviewer B interviews students ranked from 6 to 15 and 51 to 60.Interviewer C interviews students ranked from 16 to 30 and 36 to 50.An updated table will look like:We can break down the interviews of students ranked 41 to 50 for interviewer C as:Each set of 4 consecutively ranked students will be interviewed in 20 minutes. The fifth student will be interviewed after 20+5(break) minutes= 25 minutes.So, the interview of student ranked 41 starts at 11:05 am and that of student ranked 45 starts at 11:05+25= 11:30 am. Similarly the interview of student ranked 49 starts at 11:55 am and so on.