Question 1

Circular seating arrangement – six persons A, B, C, D, E, F sit at equal distances around a round table facing the centre. F sits opposite E and exactly between A and D (i.e., F has A and D as immediate neighbours). C sits to the immediate right of …

Accepted Answer

Introduction / Context:Seating-arrangement questions test the ability to translate relational clues (left/right/opposite/between) into a consistent circular map. Here, six people sit around a table facing the centre. We must determine who sits immediately beside A using the given positional constraints about F, E, C and A.Given Data / Assumptions:All six (A, B, C, D, E, F) face the centre and are equally spaced.F is opposite E.F is between A and D (i.e., A–F–D or D–F–A consecutively).C is immediately to the right of E.C is opposite A.Concept / Approach:In a circle facing the centre, “right of X” is the next clockwise seat from X. “Opposite” is three seats away (since 6 seats). “Between A and D” means F has A on one side and D on the other, so F’s immediate neighbours are A and D.Step-by-Step Solution:1) Place A arbitrarily (circular symmetry allows this) and enforce “C opposite A”, so C is three seats from A.2) Since F is between A and D, put F next to A; D must then be on F’s other side.3) Place E opposite F (given). With E fixed, place C immediately to the right of E (clockwise from E).4) The remaining seat belongs to B.5) Reading off A’s neighbours in the final consistent layouts gives B on one side and F on the other.Verification / Alternative check:Try the symmetric rotation (start A at a different seat). All valid rotations still force A’s neighbours to be B and F. Hence the answer is invariant under rotation.Why Other Options Are Wrong:F and D: F is a neighbour, but D is not adjacent to A in the consistent placements.E and F / E and C: E and C end up across or away from A due to opposite/right constraints.B and D: D is separated from A by F.Common Pitfalls:A frequent mistake is reversing “right of” when facing the centre, or misreading “between” as “somewhere in the arc”. Here, “between” means immediate adjacency on both sides of F.Final Answer:B and F

Question 2

Five students A, B, C, D, E sit in a circle facing each other. E sits between A and D (i.e., E has A and D as immediate neighbours). Also, A is to the immediate right of B. Who sits to the immediate left of B?

Accepted Answer

Introduction / Context:This is a small-circle seating question (five seats). The goal is to translate the minimal clues into a unique relative placement and identify who sits to B’s immediate left (counterclockwise from B when all face the centre).Given Data / Assumptions:People: A, B, C, D, E; all face the centre.E is between A and D (so E’s immediate neighbours are A and D).A is to the immediate right of B (A is the next clockwise seat from B).Concept / Approach:In a circle facing the centre, “right of X” means the next seat clockwise from X. With five seats, we can fix B’s seat without loss of generality (rotational symmetry) and build the circle using the constraints.Step-by-Step Solution:1) Place B at an arbitrary position and put A immediately to B’s right (clockwise).2) Place E such that its two neighbours are A and D. This forces two consecutive seats around E to be A and D in some order.3) Fill the remaining seat with C.4) Read off the person to B’s immediate left (the counterclockwise neighbour of B).5) In the consistent arrangement that satisfies both clues, the person to B’s immediate left is C.Verification / Alternative check:Because of rotational symmetry, try starting B at a different seat. The relative mapping remains equivalent, and the identity of the left neighbour of B remains C.Why Other Options Are Wrong:A: A is explicitly to B’s right, not left.B: One cannot be to one’s own immediate left in a seating puzzle.D / E: Under the enforced adjacencies around E, neither D nor E occupies B’s left seat in any valid arrangement.Common Pitfalls:Confusing “left” and “right” while facing the centre is common. Remember: facing inward, clockwise is right; counterclockwise is left.Final Answer:C

Question 3

Six friends sit in a circle facing the centre: Kenny, Danny, Michael, Bobby, Johnny, Roger. Kenny is to the immediate left of Danny. Michael sits between Bobby and Johnny (i.e., both are Michael’s immediate neighbours). Roger sits between Kenny and …

Accepted Answer

Introduction / Context:We must place six named friends around a circular table (all facing the centre) so that the local adjacency constraints are satisfied. Then we identify the person to Michael’s immediate right (clockwise side).Given Data / Assumptions:Kenny is to the immediate left of Danny.Michael has Bobby and Johnny as immediate neighbours (Michael sits between them).Roger sits between Kenny and Bobby (i.e., Roger’s immediate neighbours are Kenny and Bobby).Concept / Approach:For circular arrangements facing the centre, “left of X” means the next counterclockwise seat from X. “Between” means immediate adjacency on both sides. We construct the ring by chaining the mandatory adjacencies, watching for consistency and avoiding contradictions.Step-by-Step Solution:1) Start from Michael: his neighbours must be Bobby and Johnny in some order.2) Place Kenny and Danny so that Kenny is exactly to the left (counterclockwise) of Danny.3) Insert Roger so that Roger’s two neighbours are Kenny and Bobby. This further restricts where Bobby can be relative to Kenny and Roger—and, via step (1), relative to Michael.4) Complete the circle with the remaining person in the only consistent seat.5) After satisfying all constraints, check the person immediately to Michael’s right (clockwise seat).Verification / Alternative check:Try the mirror possibility for Michael’s neighbours (swap Bobby and Johnny). In each consistent configuration, the person to Michael’s immediate right is the same: Bobby. Multiple symmetric solutions (rotations) exist, but they all give the same right neighbour for Michael.Why Other Options Are Wrong:Danny / Kenny / Johnny / Roger cannot occupy Michael’s immediate right without breaking one of the strict adjacencies (Kenny–Danny order, Roger between Kenny and Bobby, or Michael between Bobby and Johnny).Common Pitfalls:Mixing up “left of” with “right of” when everyone faces the centre; also reading “between” as a broad positional description rather than immediate adjacency.Final Answer:Bobby

Question 4

Six friends sit in a circle facing the centre: Runa, Charu, Pari (females) and Varun, Manu, Prakash (males). Manu is between Varun and Prakash (both immediate neighbours). Charu is between Pari and Runa (both immediate neighbours). Varun and Pari si…

Accepted Answer

Introduction / Context:This circular seating puzzle mixes adjacency, opposition, and gender cues. We must determine the unique identity of the person to Prakash’s immediate right (clockwise next seat) while everyone faces the centre.Given Data / Assumptions:People: Runa (F), Charu (F), Pari (F), Varun (M), Manu (M), Prakash (M).Manu is between Varun and Prakash (Manu’s immediate neighbours are Varun and Prakash).Charu is between Pari and Runa (Charu’s immediate neighbours are Pari and Runa).Varun and Pari are opposite each other (three seats apart).The person to the immediate right of Runa is male.Concept / Approach:Facing the centre, “right of X” is the next clockwise seat from X. “Between” means immediate adjacency on both sides. “Opposite” in a 6-seat circle is three seats away. We build the circle by respecting all three constraint types simultaneously.Step-by-Step Solution:1) Place Varun and Pari opposite each other to satisfy the opposition constraint.2) Place Manu so that his two neighbours are exactly Varun and Prakash (this forces Prakash next to Manu).3) Place Charu so that Charu’s two neighbours are Pari and Runa, which in turn locks where Runa must go.4) Apply the gender cue: the person to Runa’s immediate right must be male; this prunes mirror-image placements and fixes the unique arrangement up to rotation.5) Read the person sitting immediately to the right (clockwise) of Prakash; it is Pari.Verification / Alternative check:Test the symmetric alternative (swap sides for the “between” relations). In all consistent rotations that satisfy the “Runa’s right is male” condition, the identity of the person to Prakash’s right remains Pari.Why Other Options Are Wrong:Manu / Varun: Their adjacencies are already fixed relative to Prakash; neither can occupy the immediate-right seat without breaking “Manu between Varun and Prakash”.Charu / Runa: Both are female; arrangements forcing either on Prakash’s right violate the “Runa’s right is male” or the “Charu between Pari and Runa” conditions.Common Pitfalls:Confusing clockwise with counterclockwise “right”, and treating “between” loosely rather than as immediate adjacency. Another mistake is forgetting that opposite seats are exactly three steps apart in a 6-seat circle.Final Answer:Pari

Question 5

Eight persons — A, B, C, D, E, F, G, and H are sitting around a circular table facing toward the center, but not necessarily in the same order. Also, each of them is holding number cards from 2 to 9 (one card per person). The numbers on their cards …

Accepted Answer

Concept & Logic: This is a circular arrangement puzzle with a dual-variable twist (persons and distinct cards from 2 to 9). The golden rule here is that consecutive numbered cards cannot be adjacent. Facing the center means "Left" is clockwise and "Right" is anti-clockwise. Step-by-Step Solution: 1. Deduce A and E's cards: • A holds a card divisible by 2 and 4, so A \in \{4, 8\}. • Card 4 is opposite 8. • If A = 8, the person to A's immediate right holds 9. Since 8 and 9 are consecutive, they cannot be adjacent. Thus, A MUST be 4. • Consequently, the person opposite A holds 8. • E holds an even number >4, meaning E \in \{6, 8\}. Since A and 8 are opposite, E must be the one holding 8 to satisfy all conditions. 2. Build the circle (Positions 1 to 8, Anti-Clockwise = Right): • Let A(4) be at Pos 1. • E(8) is opposite at Pos 5. • Person with 9 is immediately right (anti-clockwise) of A \rightarrow Pos 2 holds 9. • Person with 3 is 2nd to the right of E(8). From Pos 5, 2nd right is Pos 7. So, Pos 7 holds 3. 3. Place remaining cards (2, 5, 6, 7): • Person with 2 is 3rd to the left (clockwise) of person with 6. • Placing 6 at Pos 6 puts 2 at Pos 3. This validly avoids consecutive adjacencies. • Only 5 and 7 remain for Pos 4 and Pos 8. Putting 7 at Pos 4 makes it adjacent to E(8) (violating the consecutive rule). Thus, 7 is at Pos 8, and 5 is at Pos 4. 4. Map the remaining Persons: • B is 2nd left of person with 7 (Pos 8). 2nd left (clockwise) of 8 is 6. Thus, B is at Pos 6 (holding 6). • D and opposite have a difference of 3. The only opposite pairs with a difference of 3 are at Pos 2 (9) and Pos 6 (6). Since B is at Pos 6, D must be at Pos 2 (holding 9). • G + immediate right = 11. At Pos 8, G(7) + right person A(4) = 11. So G is at Pos 8. • C holds a prime and is not adjacent to B(6) or 9. Pos 4 holds a prime (5) and is adjacent to 2 and 8, satisfying this. Thus, C is at Pos 4. • F and H interchangeably occupy the remaining Pos 3 (holding 2) and Pos 7 (holding 3). 5. Evaluate Options: • G is at Pos 8. The person holding 3 is at Pos 7. Positions 7 and 8 are adjacent. This statement is true. Exam Strategy & Shortcut: Always start with the most restrictive negative constraints. The "no consecutive adjacent numbers" rule instantly solves the A=4 vs A=8 dilemma, creating a rigid anchor for the entire puzzle. Common Pitfall: Confusing Left and Right in a circular arrangement. When everyone faces the center, Left is always Clockwise, and Right is always Anti-Clockwise. Final Answer: Therefore, the correct answer is G and the person holding card numbered 3 are seated adjacent to each other.

Question 6

Eight persons — A, B, C, D, E, F, G, and H are sitting around a circular table facing toward the center, but not necessarily in the same order. Also, each of them is holding number cards from 2 to 9 (one card per person). The numbers on their cards …

Accepted Answer

Concept & Logic: To determine exact positions in an advanced circular arrangement, every variable must be strictly defined by the clues. If the clues do not uniquely distinguish two or more entities, their exact positions remain ambiguous. Step-by-Step Solution: 1. Establish the base arrangement: Following the core deductions from the puzzle, we can map the cards and most people to 8 positions (anti-clockwise sequence 1 through 8): • Pos 1: A (holds 4) • Pos 2: D (holds 9) • Pos 3: ? (holds 2) • Pos 4: C (holds 5) • Pos 5: E (holds 8) • Pos 6: B (holds 6) • Pos 7: ? (holds 3) • Pos 8: G (holds 7) 2. Identify missing entities: The only people left to place are F and H. The only positions left are Position 3 and Position 7. 3. Analyze remaining clues: • We have exhausted all given clues (adjacency, sum, differences, consecutive card restrictions). • Neither F nor H is explicitly or implicitly constrained to a specific card or position among the two remaining slots. • Therefore, F could be at Position 3 (holding 2) with H at Position 7 (holding 3), OR vice versa. 4. Answer the specific question: The question asks who is immediately to the left of the person holding 7. • The person holding 7 is G at Position 8. • "Left" in a center-facing circle is clockwise. The position immediately clockwise to Position 8 is Position 7. • Position 7 is occupied by either F or H. Since we cannot confirm which one, the answer cannot be determined. Exam Strategy & Shortcut: When you reach the end of a puzzle derivation and two variables are left with no unused clues, do not waste time re-reading the prompt hoping to find a hidden meaning. Trust your extraction process; "Cannot be determined" is frequently the correct answer for exactly this reason. Common Pitfall: Guessing between the remaining variables based on alphabetical order or arbitrary assumptions instead of objectively acknowledging the ambiguity. Final Answer: Therefore, the correct answer is Can't be determined.

Question 7

Eight persons — A, B, C, D, E, F, G, and H are sitting around a circular table facing toward the center, but not necessarily in the same order. Also, each of them is holding number cards from 2 to 9 (one card per person). The numbers on their cards …

Accepted Answer

Concept & Logic: This question relies on accurately mapping the specific pairs of individuals sitting diametrically opposite each other in an 8-person circular table. Step-by-Step Solution: 1. Locate B in the arrangement: • The puzzle states B is second to the left of the person holding card 7. • Through full derivation, we established that G holds 7 and sits at Position 8. • Left is clockwise. Second to the left of Position 8 is Position 6. Therefore, B is seated at Position 6. 2. Determine B's card: • The clues dictate that the person holding 2 is third to the left of the person holding 6. This perfectly aligns with Position 3 (holding 2) and Position 6 (holding 6). So, B holds the card numbered 6. 3. Identify the opposite position: • In an evenly spaced 8-person circle, a person at position P is opposite the person at position P+4 (or P-4). • Opposite Position 6 is Position 2. 4. Identify the occupant of Position 2: • Based on our primary derivation, A(4) is at Pos 1, and the person with 9 is immediately to A's right (anti-clockwise) at Pos 2. • Furthermore, the difference between D and the person opposite D is 3. The cards at Pos 2 (9) and Pos 6 (6) have a difference of exactly 3. Since B is at Pos 6, D must be at Pos 2, holding the card numbered 9. • Thus, the person opposite B holds the card 9. Exam Strategy & Shortcut: If you have successfully mapped out the table, this is a simple lookup question. Always draw a clear, large diagram of the circle on your scratch paper to ensure opposite pairs are visually perfectly aligned, eliminating calculation errors. Common Pitfall: A common mistake is misidentifying opposite pairs by counting incorrectly around the circle. Always remember the P+4 rule for an 8-person table. Final Answer: Therefore, the correct answer is 9.

Question 8

Eight persons — A, B, C, D, E, F, G, and H are sitting around a circular table facing toward the center, but not necessarily in the same order. Also, each of them is holding number cards from 2 to 9 (one card per person). The numbers on their cards …

Accepted Answer

Concept & Logic: Conditional questions introduce a temporary new rule that resolves previous ambiguities. Here, the "If..." clause allows us to finally fix the specific positions of the remaining undetermined variables (F and H) before executing a final arithmetic step. Step-by-Step Solution: 1. Resolve the F/H ambiguity: • The base arrangement dictates that A holds the card numbered 4. • The conditional clue states: A + H = 7. • Substituting A's value: 4 + H = 7 \Rightarrow H = 3. • From our initial derivation, the cards 2 and 3 were distributed between F and H at Positions 3 and 7. Since H = 3, H must be seated at the position holding 3 (Position 7). • Consequently, F is seated at the position holding 2 (Position 3). 2. Identify C's card number: • Based on the main puzzle derivation, C sits at Position 4 and holds the card numbered 5. 3. Locate the person second to the left of E: • E is seated at Position 5 (holding 8). • Facing the center, "Left" is clockwise. • Moving clockwise from Position 5: The first left is Position 4, and the second left is Position 3. • We established in Step 1 that Position 3 is occupied by F, who holds the card numbered 2. 4. Calculate the final difference: • The difference between C's card and F's card (2nd left of E). • Difference = |5 - 2| = 3. Exam Strategy & Shortcut: Focus precisely on what the question is asking. You don't necessarily need the whole circle for the final step. Once you realize E is at 5 and its 2nd left is 3, you only need the card value at Position 3 (which is 2) and C's card value (which is 5). The identity of H resolving to 3 just confirms that Pos 3 is indeed 2. Common Pitfall: Forgetting the direction rule for circular arrangements (Left = Clockwise, Right = Anti-clockwise). If you mistakenly went anti-clockwise from E, you would land on Position 7 (card 3), leading to a difference of 5-3 = 2, which is an incorrect trap option. Final Answer: Therefore, the correct answer is 3.

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