Logical Reasoning

Optimization

Medium

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 9:00am, 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.

Seminars by students from Economics are scheduled in each of the four slots.

A's is the only seminar that is scheduled at 10:00 am. A is guided by R.

F is an Anthropology student whose seminar is scheduled at 10:30 am.

The seminar of a Sociology student is scheduled at 9:00 am.

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.

P, who is guiding both B and C, has students scheduled in the first two slots.

A and G are scheduled in two consecutive slots.

Which one of the following statements is necessarily true?

Three seminars are scheduled in the first slot.

Two seminars are scheduled in the first slot.

Only one seminar is scheduled in the second slot.

Three seminars are scheduled in the last slot.

✅ Correct Option: 2

Slide 1/10

Understanding the set :

There are 8 students : A, B, C, D, E, F, G and H

a) Four of them are from Economics

b) three from Sociology and

c) one from Anthropology department

Each student is guided by one among P, Q, R, S and T

a) Two by P, R, T each

b) one by Q and S 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

at the most three seminars can be scheduled in a slot.

This is a table set;

In this you are needed to find the slot, subject and guide of each student using clues given.

	A	B	C	F	G
Guide	R	P	P
Subject		Sociology		Anthropology	Sociology
Slot	10 : 00	$x$		10 : 30	$x$

Let's first fill the data we can directly add from the clues.

Clue 3 says,

F is an Anthropology student whose seminar is scheduled at 10:30 am.

Also, clue 2 says,

A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.

Clue 5 says,

B and G are both Sociology students, whose seminars are scheduled in the same slot (Let that be " $x$ ")

Clue 6 says,

P, who is guiding both B and C.

	A	B	C	F	G
Guide	R	P	P
Subject	Economics	Sociology		Anthropology	Sociology
Slot	10 : 00	$x$		10 : 30	$x$

Clue 7 says,

Seminars by students from Economics are scheduled in each of the four slots.

We know, A’s is the only seminar that is scheduled at 10:00 am (clue 2)

Therefore, A has Economics subject.

	A	B	C	F	G
Guide	R	P	P
Subject	Economics	Sociology		Anthropology	Sociology
Slot	10 : 00	9 : 30		10 : 30	9 : 30

Clue 7 says,

A and G are scheduled in two consecutive slots.

We know, A is in 10:00 slot

Therefore, G will be in 9:30 or 10:30 slot.

But we know, B, G, and an Economics student will be in the same slot.

Also, F who is Anthropology student is already in 10:30 slot.

In a slot maximum 3 seminars can be there

=> F can't be with B, G

Therefore, B, G, and Economics student slot will be 9:30.

	A	B	C	F	G
Guide	R	P	P
Subject	Economics	Sociology		Anthropology	Sociology
Slot	10:00	9:30	9:00	10:30	9:30

Clue 6 says,

P, who is guiding both B and C, has students scheduled in the first two slots.

Now, We know, B has seminar scheduled at 9 : 30

=> C will have seminar at 9 : 00.

	A	B	C	F	G
Guide	R	P	P
Subject	Economics	Sociology		Anthropology	Sociology
Slot	10:00	9:30	9:00	10:30	9:30

Now, We have three students scheduled at 9:30

Also, we have 1 student scheduled at 10:00 (who is the only one of his slot)

And, F student scheduled at 10:30 (An anthropology student)

Therefore, there will be one more person at 10:30 from economics background. (Clue 1)

Now, at 9:00

We have a sociology student at 9:00 (clue 4)

And, according to clue 1, we will have one Economics student as well

Therefore,

We have; 9:00 - 2 students

9 :30 - 3 students

10:00 - 1 student

10:30 - 2 students

	A	B	C	F	G
Guide	R	P	P
Subject	Economics	Sociology	Sociology	Anthropology	Sociology
Slot	10:00	9:30	9:00	10:30	9:30

Now, For C,

It is given Each student is guided by a guide belonging to their department.

=> P is from Sociology

=> C is also from sociology.

	A	B	C	D	E	F	G	H
Guide	R	P	P
Subject	Economics	Sociology	Sociology	Economics	Economics	Anthropology	Sociology	Economics
Slot	10:00	9:30	9:00			10:30	9:30

We know,

a) Four of studetns are from Economics

b) three from Sociology and

c) one from Anthropology department

Therefore, remaining three students left will be from Economics.

	A	B	C	D	E	F	G	H
Guide	R	P	P	R/T	R/T	Q/S	S/Q	R/T
Subject	Economics	Sociology	Sociology	Economics	Economics	Anthropology	Sociology	Economics
Slot	10:00	9:30	9:00			10:30	9:30

Now, we know,

Each student is guided by a guide belonging to their department.

=> R is an economics guide

therefore, 2 economics student will be guided by him

Now, there are 2 more economics slot,

Therefore, there will be one more guide for economics

he will be T.

(as T has guided 2 students)

Therefore, Q and S who has guided 1 student each,

Will guide one Anthropology student and one sociology student.

	A	B	C	D	E	F	G	H
Guide	R	P	P	R/T	R/T	Q/S	S/Q	R/T
Subject	Economics	Sociology	Sociology	Economics	Economics	Anthropology	Sociology	Economics
Slot	10:00	9:30	9:00			10:30	9:30

Slot	Students
9:00	2
9:30	3
10:00	1
10:30	2