Reasoning: How to Solve Uncertain Number of Persons in Arrangements

Introduction This topic typically carries 5-10 marks in competitive exams, and mastering it can make a huge difference in your overall score. So, let's dive into how to solve uncertain number of persons in arrangements.

WHAT YOU NEED TO KNOW FIRST To solve uncertain number of persons in arrangements, you need to know the following basic concepts:

1. Direction Chart: A direction chart is a diagram that shows the direction of each person in the arrangement. It's essential to draw a direction chart to understand the arrangement.
2. BODMAS: BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It's a rule to follow when solving mathematical expressions.
3. Sitting Arrangement Conventions: Familiarize yourself with common sitting arrangement conventions, such as 'North' being the direction towards the top of the diagram.

CRYSTAL‑CLEAR METHOD (Step‑by‑Step) To solve uncertain number of persons in arrangements, follow these steps:

1. Read the question carefully: Understand what the question is asking and what information is given.
2. Draw a direction chart: Draw a direction chart to visualize the arrangement.
3. Identify the unknowns: Identify the unknowns in the arrangement, such as the number of persons or their positions.
4. Use BODMAS: Use BODMAS to solve mathematical expressions in the arrangement.
5. Apply sitting arrangement conventions: Apply common sitting arrangement conventions to understand the arrangement.
6. Use logical deductions: Use logical deductions to eliminate options and arrive at the correct answer.

WORKED EXAMPLES

Example 1 – Easy

Five friends - A, B, C, D, and E - are sitting in a row. A is sitting to the left of C. B is sitting to the right of D. E is sitting at one of the ends. How many possible arrangements are there?

Step-by-Step Reasoning

1. Draw a direction chart with five positions.
2. Identify the unknowns: the positions of A, B, C, D, and E.
3. Use BODMAS: No mathematical expressions are given.
4. Apply sitting arrangement conventions: A is sitting to the left of C, and B is sitting to the right of D.
5. Use logical deductions: Since E is sitting at one of the ends, there are two possible arrangements: E-A-C-B-D and E-D-B-C-A.
6. Calculate the total number of possible arrangements: 2.

What we learned: When there are no mathematical expressions, focus on applying sitting arrangement conventions and using logical deductions to arrive at the correct answer.

Example 2 – Medium

Four friends - P, Q, R, and S - are sitting in a row. P is sitting to the left of Q. R is sitting to the right of S. The number of persons sitting between P and Q is twice the number of persons sitting between R and S. How many possible arrangements are there?

Step-by-Step Reasoning

1. Draw a direction chart with four positions.
2. Identify the unknowns: the positions of P, Q, R, and S.
3. Use BODMAS: The number of persons sitting between P and Q is twice the number of persons sitting between R and S.
4. Apply sitting arrangement conventions: P is sitting to the left of Q, and R is sitting to the right of S.
5. Use logical deductions: Let's assume there are x persons sitting between R and S. Then, there are 2x persons sitting between P and Q. Since there are four positions, x + 2x + 1 = 4 (the +1 is for the person sitting between R and S). Solving for x, we get x = 1. Therefore, there is one person sitting between R and S, and two persons sitting between P and Q.
6. Calculate the total number of possible arrangements: 2.

What we learned: When there are mathematical expressions, use BODMAS to solve them and apply logical deductions to arrive at the correct answer.

Example 3 – Exam‑Style

Five friends - A, B, C, D, and E - are sitting in a row. A is sitting to the left of C. B is sitting to the right of D. E is sitting at one of the ends. The number of persons sitting between A and C is twice the number of persons sitting between B and D. How many possible arrangements are there?

Step-by-Step Reasoning

1. Draw a direction chart with five positions.
2. Identify the unknowns: the positions of A, B, C, D, and E.
3. Use BODMAS: The number of persons sitting between A and C is twice the number of persons sitting between B and D.
4. Apply sitting arrangement conventions: A is sitting to the left of C, and B is sitting to the right of D.
5. Use logical deductions: Let's assume there are x persons sitting between B and D. Then, there are 2x persons sitting between A and C. Since there are five positions, x + 2x + 1 = 5 (the +1 is for the person sitting between B and D). Solving for x, we get x = 1. Therefore, there is one person sitting between B and D, and two persons sitting between A and C.
6. Calculate the total number of possible arrangements: 2.

What we learned: When there are multiple unknowns and mathematical expressions, use BODMAS to solve them and apply logical deductions to arrive at the correct answer.

Common Mistakes

MISTAKE → WHY IT HAPPENS → CORRECT APPROACH

1. Not drawing a direction chart: Not drawing a direction chart can lead to confusion and incorrect answers.
2. Not identifying the unknowns: Not identifying the unknowns can lead to incorrect assumptions and answers.
3. Not using BODMAS: Not using BODMAS can lead to incorrect mathematical expressions and answers.
4. Not applying sitting arrangement conventions: Not applying sitting arrangement conventions can lead to incorrect assumptions and answers.
5. Not using logical deductions: Not using logical deductions can lead to incorrect answers and assumptions.

EXAM TRAPS

Trap → How to Spot it → How to Avoid it

1. Trick questions: Trick questions can be identified by reading the question carefully and understanding what is being asked.
2. Misleading information: Misleading information can be identified by carefully reading the question and understanding what is being asked.
3. Complex arrangements: Complex arrangements can be avoided by breaking them down into simpler arrangements and using logical deductions.

TIME‑SAVING SHORTCUTS

1. Elimination tricks: Elimination tricks can be used to eliminate options and arrive at the correct answer.
2. Diagram hacks: Diagram hacks can be used to visualize the arrangement and arrive at the correct answer.
3. Pattern recognition: Pattern recognition can be used to identify common arrangements and arrive at the correct answer.

1‑MINUTE RECAP Hey there, it's the night before the exam, and you're feeling confident. Let's quickly recap how to solve uncertain number of persons in arrangements.

First, read the question carefully and understand what is being asked. Then, draw a direction chart to visualize the arrangement. Identify the unknowns and use BODMAS to solve mathematical expressions. Apply sitting arrangement conventions and use logical deductions to arrive at the correct answer.

Remember, elimination tricks, diagram hacks, and pattern recognition can be used to save time and arrive at the correct answer. Don't forget to avoid common mistakes and exam traps.

You got this! Go out there and ace that exam.