DirectionsRead the following information carefully and answer the question…
2024
Directions
Read the following information carefully and answer the question that follows.
Eight persons — A, B, C, D, E, F, G and H — are sitting in a circular arrangement, all facing the centre. Each person holds a distinct card number from 2 to 9.
Note: The difference between the card numbers of any two adjacent persons is more than 1.
C sits sixth to the right of the person whose card number is a prime number.
Two persons sit between G and the person who sits second to the right of C.
The person whose card number is a multiple of 5 is an immediate neighbour of G.
F sits third to the right of the person whose card number is a multiple of 5.
The person sitting opposite the person whose card number is 5 has a card number two less than G's card number.
The person whose card number is 8 sits second to the left of F.
One person sits between H and the person who has card number 6.
A is an immediate neighbour of the person who has card number 6, and A's own card number is a multiple of 3.
B's card number is not 2, 5 or 8.
The person who sits second to the left of A has card number 4.
The difference between the card numbers of C and A equals B's card number.
D is an immediate neighbour of the person who has card number 3.
D is not an immediate neighbour of A or H, and D does not sit opposite H or F.
E is an immediate neighbour of G.
What is the sum of the card numbers of C, G and H?
- A.
25
- B.
20
- C.
23
- D.
21
- E.
None of these
Show answer & explanation
Correct answer: D
Concept
In a circular seating puzzle, you solve by anchoring on the most restrictive clue — here, the unique card values (the only multiple of 5 is 5; the multiple of 3 that A holds; the single 6 and 8) — then propagate fixed offsets ('sixth to the right', 'third to the right', 'second to the left') around the ring. All persons face the centre, so 'to the right' is one consistent rotational direction; on an 8-seat circle 'sixth to the right' equals 'second to the left'. Each placement is forced by combining a position clue with a value clue.
Step-by-step deduction
Card values are unique, so the only multiple of 5 is 5 itself and the only multiple of 3 that A can hold is 3, 6 or 9. The multiple-of-5 person (card 5) is a neighbour of G, and F sits third to the right of that person; the person opposite card 5 holds a card two less than G.
A is adjacent to the 6-card person, so A is not the 6 itself; combined with 'A holds a multiple of 3', A must be 3 or 9. The person two seats to A's left holds 4. Taking A = 9 is the only choice that lets a 4 sit two places to its left without violating the 'adjacent difference more than 1' rule, fixing A = 9.
The 8-card person sits second to the left of F, and C sits sixth to the right of the prime-card person (equivalently second to that person's left on an 8-seat circle). Testing the four primes 2, 3, 5, 7, only 7 places C consistently with the multiple-of-5 and 8-card positions, so the 7-card person is fixed and C is six seats to its right.
Now apply 'exactly one person between H and the 6-card person' and the D-clues ('D neighbours the 3-card person; D is not adjacent to A or H and not opposite H or F'). These leave only one consistent placement, pinning H, B = 3, D = 5 and E.
Reading off the now-fixed ring, the card numbers are forced uniquely (see table). The seating is unique up to mirror reflection, and both mirror images give the same card-to-person mapping.
Final arrangement (clockwise)
Person | Card number |
|---|---|
C | 6 |
A | 9 |
H | 7 |
B | 3 |
D | 5 |
G | 8 |
E | 2 |
F | 4 |
Cross-check
Verify the closing constraints: |C − A| = |6 − 9| = 3 = B's card ✓; the person opposite card 5 (D) holds 6 = G − 2 = 8 − 2 ✓; every adjacent pair differs by more than 1 (6-9, 9-7, 7-3, 3-5, 5-8, 8-2, 2-4, 4-6) ✓. The arrangement is unique.
Result
Sum of the card numbers of C, G and H = 6 + 8 + 7 = 21.