# Logical Reasoning – The Humanities department of a college is planning to organize

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students – A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.
The following additional facts are also known.

1. Seminars by students from Economics are scheduled in each of the four slots.
2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.
3. F is an Anthropology student whose seminar is scheduled at 10:30 am.
4. The seminar of a Sociology student is scheduled at 9:00 am.
5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.
6. P, who is guiding both B and C, has students scheduled in the first two slots.
7. A and G are scheduled in two consecutive slots.
Q.1 Which one of the following statements is true?
1. Two seminars are scheduled in the first slot.
2. Three seminars are scheduled in the last slot.
3. Three seminars are scheduled in the first slot.
4. Only one seminar is scheduled in the second slot.

Q.2 Who all are NOT guiding any Economics students?
1. P, Q and R
2. P, Q and S
3. Q, R and S
4. P, R and S

Q.3 Which of the following statements is necessarily true?
1. H is an Economics student.
2. B is scheduled in the first slot.
3. S is guiding F.
4. Q is guiding G.

Q.4 If D is scheduled in a slot later than Q’s, then which of the following two statement(s) is(are) true?
(i) E and H are guided by T.
(ii) G is guided by Q.

1. Both (i) and (ii)
2. Only (ii)
3. Only (i)
4. Neither (i) nor (ii)

Q.5 If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?
1. Both D and H are guided by T.
2. Exactly one of D and H is guided by T.
3. At least one of D and H is guided by T.
4. Neither D nor H is guided by T.

Q.6 If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?
1. D is guided by T.
2. F is guided by S.
3. E is guided by R
4. G is guided by Q.

Solutions:

From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .
T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.
From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

Let the divide the slots available and room no in a table as below:

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 Room 2 A R Room 3 F

Now lets arrange the students and their guide as per information given in corresponding column  –

As in each slot there is one economics students and A and G are scheduled to be in consecutive slot so G must be in slot 2 along with B ( As they can’t be in slot 4 , because F is already there) so the table will look like –

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 T G A R R Room 3 T F

From here we can say there will be 1 seminor in slot 3, 2 each in slot 1 and slot 4 and 3 in slot 2.

Q.1 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .

T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.

From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

Let the divide the slots available and room no in a table as below:

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 Room 2 A R Room 3 F

Now lets arrange the students and their guide as per information given in corresponding column  –

As in each slot there is one economics students and A and G are scheduled to be in consecutive slot so G must be in slot 2 along with B ( As they can’t be in slot 4 , because F is already there) so the table will look like –

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 G A R Room 3 T F

Q.2 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .
T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.
From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

So P, Q, S are not guiding any economics students.

Q.3 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .

T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.

From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

H is an economics student is correct.

Q.4 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .

T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.

From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

Let the divide the slots available and room no in a table as below:

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 Room 2 A R Room 3 F

Now lets arrange the students and their guide as per information given in corresponding column  –

As in each slot there is one economics students and A and G are scheduled to be in consecutive slot so G must be in slot 2 along with B ( As they can’t be in slot 4 , because F is already there) so the table will look like –

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 G A R Room 3 T F

From here we can say there will be 1 seminor in slot 3, 2 each in slot 1 and slot 4 and 3 in slot 2.

Now ,

If D is scheduled in a slot later than Q’s. Then F must be guided by S. So G  will be guided by Q thus D will be in slot 4.Following arrangement will be possible.

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 H/E T G Q A R D R Room 3 E/H T F S

So both statements are correct.

Q.5 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .

T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.

From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

Let the divide the slots available and room no in a table as below:

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 Room 2 A R Room 3 F

Now lets arrange the students and their guide as per information given in corresponding column  –

As in each slot there is one economics students and A and G are scheduled to be in consecutive slot so G must be in slot 2 along with B ( As they can’t be in slot 4 , because F is already there) so the table will look like –

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 G A R Room 3 T F

From here we can say there will be 1 seminor in slot 3, 2 each in slot 1 and slot 4 and 3 in slot 2.

Now , If E and Q are both scheduled in the same slot. Then they both can be either in slot 2 or slot 4 and following possibilities will be there

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 H T G Q A R D R Room 3 E T F S

Or

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 H/D T G S A R E R Room 3 D/H T F Q

So option c) is correct.

Q.6 From point 5 and 6 , it is clear that B, G and C are Sociology students and P is a guide of Sociology .

T is Economics guide so as R as from point 2 – A is guided by R and A is an Economics students.

From the information following table can be made –

 Department (S, G) Students Guide Economics (4 , 2) A, D, E , H T , R Sociology (3, 2) B, G, C P, S/Q Anthropology department (1,1) F Q/S

Let the divide the slots available and room no in a table as below:

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 Room 2 A R Room 3 F

Now lets arrange the students and their guide as per information given in corresponding column  –

As in each slot there is one economics students and A and G are scheduled to be in consecutive slot so G must be in slot 2 along with B ( As they can’t be in slot 4 , because F is already there) so the table will look like –

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 G A R Room 3 T F

From here we can say there will be 1 seminor in slot 3, 2 each in slot 1 and slot 4 and 3 in slot 2.

Now , If D is scheduled in the slot immediately before Q’s,then Q must be in slot 2 and D in slot 1 and following possibility will be there,

 9:00 – 9:30 9:30 – 10:00 10:00 – 10:30 10:30 – 11:00 Student Guide Student Guide Student Guide Student Guide Room 1 C P B P Room 2 D T G Q A R E/H R Room 3 H/E T F S

Option) 1 is correct option.

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