Tabulation and Arrangement Based Reasoning

Welcome to a crucial section of the Reasoning Ability for your SBI PO exam. In this topic, we will delve into problems that require you to organize and arrange given information, often presented in a tabular format or through a series of statements. These questions test your logical deduction, analytical skills, and your ability to systematically process information to arrive at a definitive conclusion. The key is to break down complex scenarios into manageable parts and build a coherent picture.

Understanding Tabulation

Tabulation, in the context of reasoning problems, involves organizing data into rows and columns, much like a spreadsheet or a table. You will typically be given a set of individuals, objects, or entities, and several attributes or characteristics associated with them. Your task is to correctly match each entity with its corresponding attributes by carefully analyzing the given clues.

Common Elements in Tabulation Problems:

  • Entities: These are the main subjects of the problem (e.g., people, cities, brands, subjects, days of the week).
  • Attributes: These are the characteristics or properties associated with the entities (e.g., age, salary, color, profession, location, hobbies).
  • Clues: These are statements that provide information, either directly or indirectly, linking entities to attributes or stating relationships between them.

Steps to Solve Tabulation Problems:

  1. Identify Entities and Attributes: First, clearly list down all the entities and all the attributes mentioned in the problem.
  2. Create a Grid/Table: Draw a grid with entities as rows and attributes as columns (or vice-versa, whichever seems more logical). This table will serve as your workspace.
  3. Process Direct Clues: Go through each clue and fill in the table with definite information. If a clue states "Person A likes Red," mark 'Yes' or the attribute directly in the corresponding cell.
  4. Process Negative Clues: Use clues that state what is NOT true. If "Person B does not like Blue," mark 'No' or a cross ('X') in that cell. This is as important as filling in positive information.
  5. Deduce Indirect Information: This is where the real reasoning comes in. If you know Person C is not a Doctor and not an Engineer, and there are only three professions (Doctor, Engineer, Teacher), then Person C must be a Teacher. Mark this deduction.
  6. Elimination: As you fill in information, use elimination. If Person D likes Green, then no other person can like Green (assuming each attribute is unique to one entity). Similarly, if Person E is a Teacher, they cannot be a Doctor or Engineer.
  7. Review and Verify: Once you think you have completed the table, re-read all the clues and check if your final arrangement satisfies every single condition.

Example Scenario for Tabulation:

Five friends – Amit, Bharat, Chandan, Deepak, and Eshan – live in five different cities – Delhi, Mumbai, Chennai, Kolkata, and Bangalore. Each of them likes a different fruit – Apple, Banana, Cherry, Date, and Elderberry. The clues are: 1. Amit does not live in Delhi or Mumbai. 2. The person who lives in Chennai likes Apple. 3. Eshan likes Elderberry and lives in Bangalore. 4. Chandan likes Banana but does not live in Kolkata. 5. Deepak lives in Mumbai. 6. The person who lives in Kolkata likes Date. 7. Bharat does not like Cherry.

Solving the Example:

Let's create a table. Entities: Amit, Bharat, Chandan, Deepak, Eshan. Attributes: Cities (Delhi, Mumbai, Chennai, Kolkata, Bangalore), Fruits (Apple, Banana, Cherry, Date, Elderberry).

Step 1: Initial Table Setup

Name City Fruit
Amit
Bharat
Chandan
Deepak
Eshan

Step 2: Processing Direct Clues and Deductions

  • Clue 3: Eshan likes Elderberry and lives in Bangalore.
  • Clue 5: Deepak lives in Mumbai.
  • Clue 4: Chandan likes Banana but does not live in Kolkata.
  • Clue 2: The person who lives in Chennai likes Apple.
  • Clue 6: The person who lives in Kolkata likes Date.

From Clue 4, Chandan likes Banana. Since Eshan likes Elderberry and Deepak lives in Mumbai (we don't know his fruit yet), Chandan cannot be Eshan or Deepak. Chandan's city cannot be Kolkata. So Chandan could live in Delhi, Mumbai, Chennai, or Bangalore. But Eshan is in Bangalore. Deepak is in Mumbai. So Chandan can be in Delhi or Chennai.

From Clue 2, Chennai <-> Apple. From Clue 6, Kolkata <-> Date.

From Clue 1, Amit does not live in Delhi or Mumbai. Eshan is in Bangalore. Deepak is in Mumbai. So Amit can live in Chennai, Kolkata, or Delhi. But Amit doesn't live in Delhi or Mumbai. So Amit can live in Chennai or Kolkata.

Let's consolidate:

  • Eshan: Bangalore, Elderberry
  • Deepak: Mumbai, ?
  • Chandan: ?, Banana (Not Kolkata)
  • Amit: ?, ? (Not Delhi, Not Mumbai)
  • Bharat: ?, ?

Cities remaining for Amit, Bharat, Chandan: Delhi, Chennai, Kolkata. Fruits remaining for Amit, Bharat, Deepak: Apple, Cherry, Date.

If Amit lives in Chennai, he likes Apple (Clue 2). If Amit lives in Kolkata, he likes Date (Clue 6). So Amit likes either Apple or Date.

Chandan likes Banana. His city is not Kolkata. His city can be Delhi or Chennai. If Chandan is in Chennai, he likes Apple. But Chandan likes Banana. So Chandan cannot be in Chennai. Therefore, Chandan must be in Delhi.

Now we have:

  • Eshan: Bangalore, Elderberry
  • Deepak: Mumbai, ?
  • Chandan: Delhi, Banana
  • Amit: ?, ? (Not Delhi, Not Mumbai)
  • Bharat: ?, ?

Remaining cities for Amit and Bharat: Chennai, Kolkata. Remaining fruits for Amit, Bharat, Deepak: Apple, Cherry, Date.

Amit cannot live in Delhi or Mumbai. Amit can live in Chennai or Kolkata. If Amit lives in Chennai, he likes Apple. If Amit lives in Kolkata, he likes Date.

So, Amit lives in either Chennai (likes Apple) or Kolkata (likes Date).

Let's consider Deepak. He lives in Mumbai. Fruits left are Apple, Cherry, Date. He cannot like Apple (Chennai) or Date (Kolkata). So Deepak must like Cherry.

Now we have:

  • Eshan: Bangalore, Elderberry
  • Deepak: Mumbai, Cherry
  • Chandan: Delhi, Banana
  • Amit: ?, ? (Not Delhi, Not Mumbai)
  • Bharat: ?, ?

Remaining cities: Chennai, Kolkata. Remaining fruits: Apple, Date.

Since Chennai <-> Apple, and Kolkata <-> Date.

Amit cannot live in Delhi or Mumbai. So Amit lives in Chennai or Kolkata. If Amit lives in Chennai, he likes Apple. If Amit lives in Kolkata, he likes Date.

Bharat does not like Cherry (Clue 7). Cherry is taken by Deepak. So this clue is consistent.

We need to place Amit and Bharat in Chennai and Kolkata, and assign Apple and Date. Since Amit is not in Delhi or Mumbai, and Chandan is in Delhi, and Deepak is in Mumbai, and Eshan is in Bangalore, the remaining cities are Chennai and Kolkata. Amit must be in one of these. Bharat must be in the other.

If Amit is in Chennai, he likes Apple. Then Bharat must be in Kolkata and likes Date.

If Amit is in Kolkata, he likes Date. Then Bharat must be in Chennai and likes Apple.

Let's re-check all clues. Clue 1: Amit not Delhi/Mumbai (Ok). Clue 2: Chennai likes Apple (Ok). Clue 3: Eshan likes Elderberry, Bangalore (Ok). Clue 4: Chandan likes Banana, not Kolkata (Ok, Chandan in Delhi). Clue 5: Deepak in Mumbai (Ok). Clue 6: Kolkata likes Date (Ok). Clue 7: Bharat not Cherry (Ok).

Both scenarios seem plausible based on the clues given. However, in typical exam questions, there's usually a unique solution. Let's assume the question implies a unique assignment. The standard approach is to fill what's certain. Let's trace again carefully.

1. Eshan: Bangalore, Elderberry.

2. Deepak: Mumbai, ?

3. Chandan: ?, Banana. Not Kolkata. Cities left: Delhi, Chennai, Kolkata. So Chandan is in Delhi or Chennai.

4. Amit: ?, ?. Not Delhi, Not Mumbai. Cities left: Delhi, Chennai, Kolkata. So Amit is in Chennai or Kolkata.

5. Bharat: ?, ?

6. Chennai <-> Apple. Kolkata <-> Date. Delhi <-> ? (Fruit not assigned). Mumbai <-> ? (Fruit not assigned).

7. From 3 & 4, Chandan and Amit must occupy Chennai and Kolkata (or Delhi and one of Chennai/Kolkata).

If Chandan is in Chennai, he likes Apple. But he likes Banana. So Chandan is NOT in Chennai. Chandan must be in Delhi. Since Chandan is in Delhi, and Amit is not in Delhi or Mumbai, Amit must be in Chennai or Kolkata.

So far:

  • Eshan: Bangalore, Elderberry
  • Deepak: Mumbai, ?
  • Chandan: Delhi, Banana
  • Amit: Chennai or Kolkata, Apple or Date
  • Bharat: Chennai or Kolkata, Apple or Date

Cities left: Chennai, Kolkata. Fruits left: Apple, Date, Cherry.

Amit is in Chennai or Kolkata. If Amit is in Chennai, he likes Apple. If Amit is in Kolkata, he likes Date.

Deepak lives in Mumbai. His fruit must be one of Apple, Date, Cherry. Since Apple is for Chennai and Date is for Kolkata, Deepak must like Cherry. So Deepak: Mumbai, Cherry.

Now fruits left: Apple, Date. Cities left: Chennai, Kolkata.

Amit is in Chennai or Kolkata. Bharat is in Chennai or Kolkata.

Chennai <-> Apple. Kolkata <-> Date.

If Amit is in Chennai, he likes Apple. Then Bharat must be in Kolkata and likes Date.

If Amit is in Kolkata, he likes Date. Then Bharat must be in Chennai and likes Apple.

Let's check Clue 7: Bharat does not like Cherry. This is satisfied in both cases.

It seems the problem might be underspecified or I'm missing a subtle deduction. However, the process of filling the table and using elimination is the core skill.

Let's assume a standard setup where each clue contributes to a unique solution. The most common way this is resolved is by ensuring all entities and attributes are uniquely placed. The setup implies distinct assignments. Let's re-evaluate the constraints.

Let's construct the final table based on common exam logic where a unique solution is intended. The most direct deductions lead us to:

  • Eshan: Bangalore, Elderberry
  • Deepak: Mumbai, Cherry
  • Chandan: Delhi, Banana

Remaining: Amit, Bharat; Chennai, Kolkata; Apple, Date.

Chennai <-> Apple

Kolkata <-> Date

Amit is not in Delhi or Mumbai. So Amit must be in Chennai or Kolkata.

Bharat must be in the remaining city (Chennai or Kolkata).

If Amit is in Chennai, he likes Apple. Then Bharat is in Kolkata and likes Date.

If Amit is in Kolkata, he likes Date. Then Bharat is in Chennai and likes Apple.

Both assignments satisfy all conditions. This means the question would likely ask something that is true in *both* scenarios (e.g., "Who lives in Delhi?" or "Who likes Banana?"). If it asked "Who likes Apple?", there would be ambiguity between Amit and Bharat depending on the city assignment.

For the purpose of learning, let's assume one of these is the intended outcome. Often, there's a final clue that resolves this, or the question is designed to have multiple valid arrangements, and questions are based on common elements.

Understanding Arrangement Based Reasoning

Arrangement problems deal with the linear or circular positioning of people or objects based on given conditions. These can be further categorized into:

1. Linear Arrangement:

In this type, items or people are arranged in a straight line. This could be a row of people sitting on a bench, cars parked in a line, or books on a shelf. The key is to determine positions from left to right or right to left.

2. Circular Arrangement:

Here, items or people are arranged in a circle or around a circular table. The challenge is that there's no fixed starting or ending point, and directions (clockwise/anticlockwise, left/right relative to facing center or outwards) are crucial.

Steps to Solve Arrangement Problems:

  1. Understand the Setup: Determine if it's a linear or circular arrangement. Identify the number of entities and the total positions.
  2. Identify Fixed Points: Look for clues that give absolute positions (e.g., "A is at the extreme left") or fixed relationships (e.g., "A is sitting next to B").
  3. Process Relative Positions: Use clues that describe relative positions (e.g., "A is two places to the left of B," "C is sitting somewhere between D and E").
  4. Handle Directions (Circular): For circular arrangements, pay close attention to whether people are facing the center or outwards. "Left" and "Right" are relative to the direction they are facing.
    • Facing Center: Your left is their right, and your right is their left.
    • Facing Outwards: Your left is their left, and your right is their right.
  5. Use Visual Aids: Draw a line or a circle with placeholders for positions. Fill in information as you deduce it.
  6. Combine Clues: Integrate information from multiple clues. If Clue 1 says "A is next to B" and Clue 2 says "B is next to C," you can deduce a sequence like A-B-C or C-B-A.
  7. Elimination: If a position is ruled out for one person, it becomes available for another.
  8. Test Possibilities: Sometimes, you might have two possible arrangements. Test both against all clues. If one violates a clue, the other is correct. If both are valid, the questions asked should have answers that are common to both arrangements.

Example Scenario for Linear Arrangement:

Six people – P, Q, R, S, T, and U – are standing in a row facing North. 1. Q is exactly in the middle of P and S. 2. R is not at either end of the row. 3. U is standing to the immediate right of R. 4. P is standing at the extreme left end. 5. T is standing somewhere to the left of R.

Solving the Example:

We have 6 positions: _ _ _ _ _ _ (Left to Right, North facing)

Step 1: Direct Placement

  • Clue 4: P is at the extreme left end.
  • Positions: P _ _ _ _ _

Step 2: Using Relative Positions

  • Clue 1: Q is exactly in the middle of P and S. Since P is at position 1, P _ Q _ S. This means P, Q, S are in positions 1, 3, 5 or 1, 2, 3 (not possible as Q is middle) or 1, 4, 7 (not possible as only 6 positions). So, P is at 1, Q is at 3, S is at 5.
  • Positions: P _ Q _ S _

Step 3: Incorporating Other Clues

  • The remaining people are R, T, U. The remaining positions are 2, 4, 6.
  • Clue 3: U is to the immediate right of R. This means they are together as R U.
  • Clue 2: R is not at either end. So R cannot be at position 1 (already P) or position 6. R could be at 2 or 4.
  • Clue 5: T is somewhere to the left of R.

Let's test R's position:

  • If R is at position 2: Then U is at position 3 (immediate right). But position 3 is taken by Q. So R cannot be at position 2.
  • If R is at position 4: Then U is at position 5 (immediate right). But position 5 is taken by S. Wait, Clue 3 says "immediate right of R". Let's re-read carefully. "U is standing to the immediate right of R."
  • Let's re-evaluate Clue 1: Q is exactly in the middle of P and S. This implies P and S are equidistant from Q. If P is at 1, and Q is at 3, then S must be at 5. (1, 3, 5). This is correct.
  • Positions: P _ Q _ S _ (1, 2, 3, 4, 5, 6)
  • Remaining positions: 2, 4, 6. Remaining people: R, T, U.
  • Clue 3: U is to the immediate right of R. So, R U must occupy two adjacent slots. Possible pairs are (2,3), (3,4), (4,5), (5,6). Out of these, only (2,3), (3,4), (4,5), (5,6) are adjacent slots. But positions 3 and 5 are already taken. So R U must be in (2,3) or (4,5) or (5,6). None of these work because positions 3 and 5 are occupied. This means my interpretation of Clue 1 might be too rigid, or there's an error in my deduction.

Let's re-think Clue 1: "Q is exactly in the middle of P and S." This means the number of people between P and Q is the same as between Q and S. If P is at 1, and there are 'x' people between P and Q, then there are 'x' people between Q and S. Total positions: P (1) + x + Q + x + S = 1 + 2x + 2. This must be <= 6. If x=0, P Q S (positions 1,2,3). If x=1, P _ Q _ S (positions 1,3,5). If x=2, P _ _ Q _ _ S (positions 1,4,7 - too many). So, P, Q, S are in positions 1, 3, 5. This seems correct.

Let's re-check Clue 3: "U is standing to the immediate right of R." This means R and U are adjacent, with U on R's right. So, R U.

Remaining positions: 2, 4, 6. Remaining people: R, T, U.

Possible adjacent slots for R U within {2, 4, 6}: None. This implies R or U must occupy one of the already filled slots (3 or 5), which is not possible, or my placement of P, Q, S is wrong.

Let's consider the possibility that P, Q, S are not necessarily in the order P-Q-S. What if it's S-Q-P? If P is at the extreme left (pos 1), this order is not possible.

Let's assume the clue implies P and S are at the ends of a segment, and Q is exactly in the middle of that segment. With P at 1, and 6 total positions: Possible arrangements for P, Q, S: - P _ Q _ S _ (1, 3, 5) - This was my initial thought. - P _ _ Q _ _ S (1, 4, 7) - Impossible (7 positions) - P Q S _ _ _ (1, 2, 3) - Q is not "in the middle" of P and S if they are adjacent. Middle implies at least one person on each side. - P _ _ _ Q _ S (1, 5, 6) - No, Q is not in the middle. So, (1, 3, 5) for P, Q, S seems the only logical interpretation for "Q is exactly in the middle of P and S" when P is at the extreme left.

Let's revisit Clue 3: "U is standing to the immediate right of R." This means R and U are adjacent. R U. Clue 2: R is not at either end (so not 1 or 6). R can be 2, 3, 4, 5. Clue 5: T is somewhere to the left of R.

Current state: P _ Q _ S _ (Positions 1, 3, 5 occupied by P, Q, S). Positions 2, 4, 6 are free for R, T, U.

From Clue 2, R cannot be at 6. So R can be at 2 or 4.

Case 1: R is at position 2.

  • Then U must be at position 3 (immediate right). But position 3 is Q. This case is impossible.

Case 2: R is at position 4.

  • Then U must be at position 5 (immediate right). But position 5 is S. This case is also impossible.

This indicates a potential issue with the problem statement or my interpretation of "middle". Let's consider another interpretation of "Q is exactly in the middle of P and S". It could mean the number of people between P and S is 2x, and Q is at position x+1 from P.

Let's assume the problem meant "Q is somewhere between P and S". No, "exactly in the middle" is specific.

Let's consider P, Q, S could be in order P _ _ Q _ S (1, 4, 6). Number of people between P and Q is 2. Number of people between Q and S is 1. Not middle. P _ Q _ _ S (1, 3, 6). Between P and Q is 1. Between Q and S is 2. Not middle.

What if "middle" refers to the count of people, not necessarily physical slots? If P and S are at ends of a group, Q is the center person. If P is at 1, and S is at 4, then Q is at 2 or 3. No, this is not "exactly in the middle".

Let's go back to P, Q, S at 1, 3, 5. This is the most standard interpretation.

P _ Q _ S _ (1, 3, 5)

Remaining slots: 2, 4, 6. Remaining people: R, T, U.

Clue 3: U is to the immediate right of R (R U). This pair must fit into adjacent slots.

Clue 2: R is not at ends (not 1 or 6). So R can be 2, 3, 4, 5. Since 3 and 5 are taken, R can be 2 or 4.

Clue 5: T is to the left of R.

If R is at 2: U must be at 3. But 3 is Q. Impossible.

If R is at 4: U must be at 5. But 5 is S. Impossible.

There seems to be a contradiction. Let me re-read "Q is exactly in the middle of P and S". Maybe it implies that P and S are separated by exactly one person, and Q is that person? No, that would be "Q is between P and S". "Exactly in the middle" implies symmetry.

Let's assume the clue meant "Q is adjacent to P and S". No, that's not standard. Could "middle" refer to the indices? P=1, S=5. Middle index is (1+5)/2 = 3. Q is at 3. This aligns with P _ Q _ S _.

Let's consider the possibility that the clue means "Q is between P and S, and the number of people between P and Q is equal to the number of people between Q and S." This is the standard interpretation.

Let's assume there is a typo in Clue 3 or Clue 1, or maybe Clue 4.

If we ignore Clue 1 for a moment and use others:

  • Clue 4: P _ _ _ _ _
  • Clue 2: R is not 1 or 6.
  • Clue 3: R U must be together. Possible slots for R U: (2,3), (3,4), (4,5), (5,6). R cannot be 6. So R U could be (2,3), (3,4), (4,5), (5,6). R cannot be at 6. If R U is at (5,6), R is at 5, U is at 6. This is possible. If R U is at (4,5), R is at 4, U is at 5. Possible. If R U is at (3,4), R is at 3, U is at 4. Possible. If R U is at (2,3), R is at 2, U is at 3. Possible.
  • Clue 5: T is to the left of R.

Let's try fitting R U into available slots {2,3,4,5,6} given R is not 6.

Possibility A: R U is at (5,6). So P _ _ _ R U. Remaining slots {2,3,4} for Q, S, T. Clue 5: T is left of R. T is in {2,3,4}. This is fine. Clue 1: Q is middle of P and S. P=1. S=?. Q=?. If S=4, Q needs to be middle. (1+4)/2 = 2.5. Not integer. If S=3, Q needs to be middle. (1+3)/2 = 2. So P Q S _ R U (1,2,3,4,5,6). Check Clue 1 again: Q is exactly middle of P and S. P=1, Q=2, S=3. Number of people between P and Q is 0. Number of people between Q and S is 0. This is "exactly in the middle". So P Q S R U. Remaining person is T. Where does T fit? T must be left of R. T could be 4. So P Q S T R U. Let's check all clues: 1. Q middle of P and S? P=1, Q=2, S=3. Yes (0 people between each). 2. R not at ends? R=5. Yes. 3. U immediate right of R? R=5, U=6. Yes. 4. P extreme left? P=1. Yes. 5. T left of R? T=4, R=5. Yes. This arrangement works: P Q S T R U.

Let's try another possibility for R U.

Possibility B: R U is at (4,5). So P _ _ R U _. Remaining slots {2,3,6} for Q, S, T. Clue 5: T is left of R (T in {2,3}). Clue 1: Q middle of P and S. P=1. S=?. Q=?. S must be at 6 (only remaining slot). P=1, S=6. Middle position is (1+6)/2 = 3.5. Not integer. So this arrangement P _ _ R U S is not possible with Clue 1.

Possibility C: R U is at (3,4). So P _ R U _ _. Remaining slots {2,5,6} for Q, S, T. Clue 5: T is left of R (T=2). So P T R U _ _. Remaining slots {5,6} for Q, S. Clue 1: Q middle of P and S. P=1. S=?. Q=?. If S=5, Q=(1+5)/2=3. But R is at 3. Impossible. If S=6, Q=(1+6)/2=3.5. Impossible.

Possibility D: R U is at (2,3). So P R U _ _ _. Remaining slots {4,5,6} for Q, S, T. Clue 5: T is left of R. This is impossible as R is at 2, and P is at 1. There's no slot left of R except P's slot.

So, the only valid arrangement found is P Q S T R U.

Let's double check Clue 1 interpretation again. "Q is exactly in the middle of P and S". The interpretation P Q S (1,2,3) works if "middle" means 0 people on either side. This is a valid interpretation in competitive exams. So the arrangement P Q S T R U is correct.

Final arrangement: P Q S T R U

Positions: 1 2 3 4 5 6

Example Scenario for Circular Arrangement:

Eight friends – A, B, C, D, E, F, G, H – are sitting around a circular table, facing the center. 1. A is sitting second to the left of G. 2. D is an immediate neighbor of A. 3. F is sitting third to the left of C. 4. E is not sitting next to G or A. 5. B is sitting exactly opposite to H. 6. D is sitting third to the left of B.

Solving the Example:

We have 8 positions around a circle. Let's number them 1 to 8 clockwise. Assume G is at position 1. All are facing the center.

Step 1: Place G and use Clue 1

  • Let G be at position 1.
  • Clue 1: A is second to the left of G. Facing center, left of G is position 8, second left is position 7. So, A is at 7.
  • Positions: G(1) _ _ _ _ _ A(7) _ (8)

Step 2: Use Clue 2 and Clue 6

  • Clue 2: D is an immediate neighbor of A. A is at 7. Neighbors are 6 and 8. So D is at 6 or 8.
  • Clue 6: D is sitting third to the left of B. Let's test positions for D.
  • If D is at 6: B must be at position 4 (third left of 4 is 1, then 8, then 7... no wait. Left of 4 is 3, 2, 1. So D=6 is third left of B=4? No. Third left of B means B is at X, then left is X-1, X-2, X-3. So D=X-3. If D=6, then 6=X-3 => X=9. Not possible. Let's count clockwise: Pos 1 is right of Pos 8. Pos 8 is left of Pos 1. If B is at X, then 1st left is X-1, 2nd left is X-2, 3rd left is X-3 (all modulo 8, adjusting for 1-based index). If D=6, and D is 3rd left of B. Then B is 3rd right of D. Right of 6 is 7, 8, 1. So B is at 1. But G is at 1. So D cannot be at 6.
  • Let's try D at 8. If D=8, and D is 3rd left of B. Then B is 3rd right of D. Right of 8 is 1, 2, 3. So B is at 3.
  • Let's check this: B=3. 1st left is 2, 2nd left is 1, 3rd left is 8. Yes, D=8 is 3rd left of B=3.
  • So, we have: G(1), B(3), A(7), D(8).
  • Positions: G(1) _ B(3) _ _ _ A(7) D(8)

Step 3: Use Clue 3

  • Clue 3: F is sitting third to the left of C.
  • Remaining positions: 2, 4, 5, 6. Remaining people: C, E, F, H.
  • Let's try placing C.
  • If C=2: 1st left=1, 2nd left=8, 3rd left=7. F=7. But A is at 7. Impossible.
  • If C=4: 1st left=3, 2nd left=2, 3rd left=1. F=1. But G is at 1. Impossible.
  • If C=5: 1st left=4, 2nd left=3, 3rd left=2. F=2. This is possible. So C=5, F=2.
  • If C=6: 1st left=5, 2nd left=4, 3rd left=3. F=3. But B is at 3. Impossible.
  • So, C=5 and F=2 seems to be the only possibility for this clue.
  • Positions: G(1) F(2) B(3) _ C(5) _ A(7) D(8)

Step 4: Place remaining people and check remaining clues

  • Remaining positions: 4, 6. Remaining people: E, H.
  • Clue 5: B is sitting exactly opposite to H. B is at 3. Opposite position in 8 people circle is 3 + 4 = 7 or 3 - 4 = -1 (which is 7). So H should be at 7. But A is at 7. This is a contradiction.

Let me recheck the opposite calculation. In an 8-person circle, opposite means 4 positions away. If B is at 3, then 1st neighbor is 2, 2nd is 1, 3rd is 8, 4th is 7. So B(3) is opposite A(7). Clue 5 says B is opposite H. So H must be at 7. But A is at 7. There is a contradiction.

This means my initial placement of G at 1 was arbitrary, but the relative positions should hold. Let's re-evaluate Clue 5 and 6 first, as they are absolute relationships.

Let's restart, placing B first.

Let B be at position 1.

  • Clue 5: B is opposite H. So H is at position 5. (1+4=5).
  • Clue 6: D is third to the left of B. Left of 1 is 8, 7, 6. So D is at 6.
  • Positions: B(1) _ _ _ H(5) D(6) _ _
  • Remaining positions: 2, 3, 4, 7, 8. Remaining people: A, C, E, F, G.
  • Clue 2: D is neighbor of A. D is at 6. Neighbors are 5 and 7. H is at 5. So A must be at 7.
  • Positions: B(1) _ _ _ H(5) D(6) A(7) _ _
  • Remaining positions: 2, 3, 4, 8. Remaining people: C, E, F, G.
  • Clue 1: A is second to the left of G. A=7. Second left of G means G is second right of A. Right of A(7) is 8, 1. So G is at 1. But B is at 1. Contradiction.

There seems to be an inherent contradiction in the clues provided for the circular arrangement problem. Let me check standard interpretations again.

Let's assume the numbering is 1-8 clockwise. Facing center.

1. A is 2nd left of G. If G is at X, A is at X-2.

2. D is neighbor of A. D = A-1 or D = A+1.

3. F is 3rd left of C. If C is at Y, F is at Y-3.

4. E not neighbor of G or A.

5. B opposite H. If B is at Z, H is at Z+4 (mod 8).

6. D is 3rd left of B. If B is at Z, D is at Z-3.

From 5 and 6: If B is at Z, H is at Z+4, and D is at Z-3.

Let's try placing B. Let B = 1.

  • H = 1+4 = 5.
  • D = 1-3 = -2 => -2+8 = 6. So D = 6.
  • Arrangement: B(1) _ _ _ H(5) D(6) _ _
  • From 2: D=6 is neighbor of A. Neighbors of 6 are 5 and 7. H=5, so A must be 7.
  • Arrangement: B(1) _ _ _ H(5) D(6) A(7) _ _
  • From 1: A=7 is 2nd left of G. So G must be 2nd right of A. Right of 7 is 8, then 1. So G = 1. But B=1. Contradiction again.

Let's try placing G first.

Let G = 1.

  • From 1: A is 2nd left of G. A = 1-2 = -1 => -1+8 = 7. So A = 7.
  • Arrangement: G(1) _ _ _ _ _ A(7) _ (8)
  • From 2: D is neighbor of A. Neighbors of 7 are 6 and 8. So D = 6 or D = 8.
  • From 4: E is not neighbor of G(1) or A(7). E cannot be 8, 2, 6.
  • From 5: B opposite H.
  • From 6: D is 3rd left of B.

Case 1: D = 6.

  • Arrangement: G(1) _ _ _ _ D(6) A(7) _ (8)
  • From 6: D=6 is 3rd left of B. B must be 3rd right of D. Right of 6 is 7, 8, 1. So B = 1. But G=1. Contradiction.

Case 2: D = 8.

  • Arrangement: G(1) _ _ _ _ _ A(7) D(8)
  • From 6: D=8 is 3rd left of B. B must be 3rd right of D. Right of 8 is 1, 2, 3. So B = 3.
  • Arrangement: G(1) _ B(3) _ _ _ A(7) D(8)
  • Now check Clue 5: B opposite H. B=3. Opposite is 3+4=7. So H=7. But A=7. Contradiction.

It appears there is a genuine contradiction in the problem statement as provided. Let's assume a slight modification to make it solvable, for learning purposes. Suppose Clue 1 was "A is sitting second to the RIGHT of G".

Let G = 1.

  • Modified Clue 1: A is 2nd right of G. Right of 1 is 2, 3. So A = 3.
  • Arrangement: G(1) _ A(3) _ _ _ _ _
  • Clue 2: D is neighbor of A. Neighbors of 3 are 2 and 4. So D = 2 or D = 4.
  • Clue 5: B opposite H.
  • Clue 6: D is 3rd left of B.

Case A: D = 2.

  • Arrangement: G(1) D(2) A(3) _ _ _ _ _
  • From 6: D=2 is 3rd left of B. B is 3rd right of D. Right of 2 is 3, 4, 5. So B = 5.
  • Arrangement: G(1) D(2) A(3) _ B(5) _ _ _
  • From 5: B=5 is opposite H. Opposite of 5 is 1. So H = 1. But G=1. Contradiction.

Case B: D = 4.

  • Arrangement: G(1) _ A(3) D(4) _ _ _ _
  • From 6: D=4 is 3rd left of B. B is 3rd right of D. Right of 4 is 5, 6, 7. So B = 7.
  • Arrangement: G(1) _ A(3) D(4) _ _ B(7) _
  • From 5: B=7 is opposite H. Opposite of 7 is 3. So H = 3. But A=3. Contradiction.

The original problem statement for the circular arrangement has contradictory clues. This is unusual for well-designed exam questions. However, the METHODOLOGY of solving remains the same: place knowns, use relative positions, combine clues, deduce, and check for contradictions.

Exam Strategy for Tabulation & Arrangement:

  • Read Carefully: Understand every word, especially "immediate," "exactly," "not," "between," "left," "right," "opposite."
  • Start with Definite Clues: Begin with clues that give absolute positions or strong links.
  • Use a Table/Diagram: A visual representation is key. Don't try to solve complex arrangements in your head.
  • Cross-check: After placing each person/attribute, check if it contradicts any previous clue.
  • Manage Time: These can be time-consuming. If stuck, move to the next question and come back later. Sometimes, re-reading after a break reveals a missed deduction.
  • Focus on the Question: Once the arrangement/table is complete, answer ONLY what is asked. Don't try to deduce extra information.

Common Pitfalls and How to Avoid Them:

  • Misinterpreting "Left/Right": Always consider the direction people are facing (center/outwards for circular, North/South/East/West for linear).
  • Confusing "Next to" with "Immediate Next to": "Next to" can mean adjacent or separated by others, while "immediate next to" implies adjacency.
  • Ignoring Negative Information: Clues like "X does not like Y" or "A is not next to B" are as valuable as positive ones for elimination.
  • Assuming Order: Do not assume the order of entities unless explicitly stated or deduced.
  • Calculation Errors: Especially in circular arrangements with opposite positions or counting positions to the left/right. Double-check your counts.

Mastering tabulation and arrangement problems requires consistent practice. With each problem you solve, you'll become faster and more adept at spotting the crucial links and making accurate deductions. Remember to stay calm, work systematically, and trust your logical reasoning.