NIMCET 2017 Logical Reasoning Question 83 with Solution

Question 83

Logical Reasoning Puzzles Easy

Three are six teacher A, B, C, D , E and F in a school, Each teacher has to teach two subjects, one compulsory and the other optional. D’s optional is History, while three others have it as a compulsory subject, E and F have Physics as one of their subjects, F‘s compulsory subject in Mathematics, which is an optional subject of both C and E, History and English are A’s subject but in term of compulsory and optional subjects, they are reserved of D’s Chemistry is an optional subject of one of the teachers. There is only one female teacher, who has English as her compulsory subject. What is compulsory subject of B?

(A) Physics

(B) Chemistary

(C) Englilsh

(D) History

View Dynamic Solution & Explanation ▼

Correct Solution: Option D

Step-by-step Solution:

Step-by-Step Logical Deduction

To solve this complex puzzle, the most effective method is to create a table and populate it step-by-step as we process each clue.

Initial Table Setup

Teacher	Gender	Compulsory Subject	Optional Subject
A
B
C
D
E
F

Analyzing the Clues

From "D's optional is History" and "History and English are A's subject...they are reserved [reversed] of D's", we can deduce:
- D has Optional: History and Compulsory: English.
- A has the reverse: Compulsory: History and Optional: English.
From "There is only one female teacher, who has English as her compulsory subject", we know that D is the female teacher. All others are male.
From "F's compulsory subject is Mathematics" and "E and F have Physics", we deduce F's subjects: Compulsory: Maths, Optional: Physics.
From "which [Mathematics] is an optional subject of both C and E" and "E and F have Physics", we deduce E's subjects: Optional: Maths, Compulsory: Physics.
The same clue tells us C has Optional: Maths.

Intermediate Table

After applying the clues above, our table looks like this:

Teacher	Gender	Compulsory Subject	Optional Subject
A	Male	History	English
B	Male	?	?
C	Male	?	Maths
D	Female	English	History
E	Male	Physics	Maths
F	Male	Maths	Physics

Final Deductions

We still need to fill the subjects for B and the compulsory subject for C. Let's look at the remaining constraints:

We need a total of three teachers with History as a compulsory subject. We currently only have one (A). This means two more compulsory slots are for History.
We need one teacher with Chemistry as an optional subject.

C needs a compulsory subject. The only available compulsory subject slot is History. Therefore, C's compulsory subject is History.

B needs a compulsory and an optional subject. The last remaining compulsory slot is History, and the last remaining optional slot is Chemistry. These must belong to B.

Conclusion

After all deductions, B's subjects are Compulsory: History and Optional: Chemistry.

Therefore, the compulsory subject of B is History.