Seating ArrangementsPYQ May 25Question 4052 of 145
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In a class, there are seven students (including boys and girls) A, B, C, D, E, F and G. They sit on three benches I, II and III, such that at least two students on each bench and at least one girl on each bench. C who is a girl student, does not sit with A, E and D. F the boy student sits with only B. A sits on the bench I with his best friends. G sits on the bench III. E is the brother of C. Which of the following is the group of girls?

Options

ABCG
BBFC
CBCD
DCDF
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Correct Answer

✅ Option c — BCD

All Options:

  • ABCG
  • BBFC
  • CBCD
  • DCDF

Detailed Solution & Explanation

Let us analyze the students, their gender, and their placement on the benches I, II, and III step-by-step:
1. **Benches and Capacities**:
There are 7 students (A, B, C, D, E, F, G) and 3 benches. Each bench must have at least 2 students. Thus, the distribution of students on the benches must be 3,2,2\displaystyle 3, 2, 2.

2. **Gender Requirement**:
Each of the three benches must have at least one girl student.

3. **Analyzing F and B's Bench**:
- "F the boy student sits with only B."
This means F\displaystyle F and B\displaystyle B sit together on a bench with no other students. Thus, their bench contains exactly 2 students: B\displaystyle B and F\displaystyle F.
- Since F\displaystyle F is a boy, and each bench must contain at least one girl, B\displaystyle B must be a girl student.

4. **Determining the Benches**:
- "A sits on the bench I with his best friends." Since "friends" is plural, Bench I must have at least 3 students.
- "G sits on the bench III."
- Since Bench I has 3 students, and the bench containing B\displaystyle B and F\displaystyle F has exactly 2 students, B\displaystyle B and F\displaystyle F must be on Bench II.
- Thus, Bench II consists of {B,F}\displaystyle \{B, F\}.

5. **Placing C, D, and E**:
- "C who is a girl student, does not sit with A, E and D."
- Since C\displaystyle C cannot sit with A\displaystyle A (who is on Bench I) and cannot sit on Bench II (which only has B\displaystyle B and F\displaystyle F), C\displaystyle C must be on Bench III.
- Since G\displaystyle G is on Bench III, the students on Bench III are {C,G}\displaystyle \{C, G\} (exactly 2 students).
- The remaining students D\displaystyle D and E\displaystyle E cannot sit with C\displaystyle C (on Bench III) and cannot sit on Bench II. Thus, they must sit on Bench I with A\displaystyle A.
- So, Bench I consists of {A,D,E}\displaystyle \{A, D, E\}.

6. **Determining Genders of A, D, and E**:
- "E is the brother of C." This means E\displaystyle E is a boy.
- "A sits on the bench I with his best friends." The pronoun "his" indicates that A\displaystyle A is a boy.
- Since Bench I consists of {A,D,E}\displaystyle \{A, D, E\} and must have at least one girl, and both A\displaystyle A and E\displaystyle E are boys, D\displaystyle D must be a girl.

7. **Identifying the Group of Girls**:
From our deductions:
- C\displaystyle C is a girl (given).
- B\displaystyle B is a girl (deduced from Bench II).
- D\displaystyle D is a girl (deduced from Bench I).

Thus, the group of girls is B, C, D.

Hence, **Option C** is the correct answer.

About This Chapter: Seating Arrangements

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Linear & Circular Seating Arrangements

A crucial part of the Logical Reasoning section. It tests spatial reasoning through linear arrangements (people sitting in a row) and circular arrangements. Students must decode right/left orientation based on the direction individuals face (North, South, or Center).

View Official ICAI Syllabus

Exam Strategy Tip

Always use abbreviations (A, B, C) and draw the diagram immediately. The key trick is to never start with a 'relative' clue; always start with a fixed, concrete clue (e.g., 'A sits at the extreme right').

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