**Direction for the questions: (1- 5:) **Five students P,Q,R,S and T are scheduled to undergo counseling interviews within a seven day period starting from Sunday to Saturday. Exactly one student undergoes counseling interview per day. The schedule must accommodate the following conditions:

1. P is to receive exactly two interviews; the second interview must be scheduled for the fourth day after the day of the first interview.

2. Q is to receive exactly one interview.

3. R is to receive exactly one interview, which must be scheduled for either the day before or the day after the day of P’s first interview

4. S is to receive exactly one interview, which must be scheduled for a day any time before the day of P’s second interview.

5. T is to receive exactly one interview, which must be scheduled for the third day after the day of Q’s interview

**Question 1:** If Q’s interview is to schedule for the first day of the week, which of the following pairs ‘of Students cannot be scheduled for consecutive days.

(a) Q,P

(b) P,T

(c) Q,R

(d) R,S

**Question 2:** Any of the five students could be scheduled for the first day of week except

(a) P

(b) Q

(c) R

(d) T

**Question 3:** Which of the following is a possible schedule, including the open day for which no student is schedule, from Sunday to Saturday of the week?

(a) R,P,Q,S,T,P, open day

(b) Q, P, R, T, open day, P, S

(c) P,Q,R,S,T, Open day

(d) R,P,S,Q, open day, P,T

**Question 4:** The day of Q’s interview must be no more than how many days after P’s first interview:

(a) 1

(b) 2

(c) 3

(d) 4

**Question 5:** If the condition that the second interview for P must be scheduled for the fourth day after the day of the first interview is removed, the maximum number of days between P’s first interview and Q’s first interview can be:

(a) 1

(b) 2

(c) 3

(d) 4

### Answers and Explanations

**Answer 1 : (d)**

Applying the new condition to the problem, the original table reduces to the following:

From the above table, we can say that option (d) cannot be satisfied.

**Answer 2 : (d)**

From the given information, we can draw the following table of possible interview schedules per day (the table lists the candidates that can give an interview on a particular day)

P1 means the first Interview for P and P2 refers to the second interview.

R before P1 or After P1

S < P2

T scheduled on the 3^{rd} day after Q

So, from the above table, we can say that T’s interview cannot be scheduled for Sunday.

**Answer 3 : (d)**

1st option is out because R must be interviewed the day before or the day after P’s first interview. Here, this condition is violated. Second option is also gone because T ‘s condition is violated. Third option is out because T is to receive interview for the third day after B but here it is being violated. So the correct answer for the question is option d.

**Answer 4 : (c)**

If P is interviewed on Sunday, then Q must be interviewed on Tuesday or Wednesday which implies T gets his turn on Friday or Saturday. Thus maximum number of days should be 2 between P’s first Interview and Q’s interview. If we shift P’s first interview to any other place, then Q’s place is consequently shifted and T’s conditions cannot be satisfied. So the right option for the question is option (c)

**Answer 5 : (d)**

In this case, the following sequence can be build:

The maximum number of days possible = 4 Since both P and Q are at the extreme ends, this is the maximum possible answer.

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