Direction : Study the following information carefully and answer the questions…
2019
Direction : Study the following information carefully and answer the questions given below:
Eleven seats are placed in a single row in which three seats are vacant. Persons sitting in these seats are facing North. No two vacant seats are placed adjacent to each other. Persons are of different ages. Seats are numbered 1 to 11 from West to East.
Note- Two Persons sitting between P and Q doesn’t means that there are only two seats are placed between them. There may be vacant seats between them.
Three persons sit between A and B. Person who is 32 years old sits immediate left of B. D and E are immediate neighbors of A whose seat number is less than 6. B is as many years older than H as younger than D. C sits 3rd to the left of A. One person sits between G and F who is 40 years old. Sum of the age of D and G is 82. H sits immediate left of one of the vacant seats. Age of H is half the age of the person who sits at seat number 11. Persons whose age are 26 and 28 years sit at odd numbered seats. D sits left of the person whose age is 22 years and right of the person whose age is 28 years. No vacant seat is between H and the person whose age is 22 years.
How many persons are sitting between the persons whose age are 22 and 35 years?
- A.
Four
- B.
Two
- C.
Three
- D.
Five
- E.
None of these
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
Linear (single-row) seating puzzles are solved by fixing one reference person from the strongest positional clue, then layering each remaining clue onto that anchor. Two rules govern the counting here: (1) "k persons sit between X and Y" counts only occupied seats between them — vacant seats in the gap are ignored (stated in the Note); (2) directions are absolute, so for a North-facing row "left" means a lower seat number (toward seat 1 / West) and "right" means a higher seat number (toward seat 11 / East). Age relations are turned into equations and solved alongside the positions.
Application — build the row step by step
Anchor A and its block. A's seat number is below 6, and D and E are A's immediate neighbours, so A has one of them on each side, while C sits 3rd to the left of A (C three seats lower than A). With A below seat 6 the candidate positions are A at seat 4 (C at seat 1) or A at seat 5 (C at seat 2); the later age and vacancy clues are satisfied only by A at seat 4, with C at seat 1 and D, E at seats 3 and 5, so that placement is carried forward.
Place B using the gap rule. Exactly three persons sit between A and B (occupied seats only). Counting three occupied seats to the right of A lands B at seat 9, and the person immediately to B's left (seat 8) is the one aged 32.
Fix the vacant seats. No two vacancies are adjacent, and H sits immediately to the left of a vacant seat. The consistent layout leaves seats 2, 7 and 10 empty, which places H at seat 6 (seat 7 is the vacancy on H's right) and G at seat 8 — so G is the 32-year-old, and one occupied seat (B) lies between G and F, with F at seat 11.
Solve the ages. F = 40. D + G = 82 with G = 32 gives D = 50. The relation "B is as much older than H as it is younger than D" means 2B = D + H. The person at seat 11 (F = 40) is twice H's age, so H = 20; then 2B = 50 + 20 = 70, so B = 35. The remaining ages 22, 26 and 28 must place 26 and 28 on odd seats, D must sit to the right of the 28-year-old and to the left of the 22-year-old, and no vacant seat may lie between H and the 22-year-old — this fixes C = 28 (seat 1), A = 22 (seat 4) and E = 26 (seat 5).
Final arrangement
Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
Person | C | — | D | A | E | H | — | G | B | — | F |
Age | 28 | — | 50 | 22 | 26 | 20 | — | 32 | 35 | — | 40 |
Answer the question
The person aged 22 sits at seat 4 and the person aged 35 sits at seat 9. The seats strictly between them are 5, 6, 7 and 8; seat 7 is vacant and is not counted, leaving the occupants of seats 5, 6 and 8 — three persons. So three persons sit between them.
Cross-check
Verify the binding clues against the grid: counting between A at seat 4 and B at seat 9 gives E, H and G (three occupied seats); G at seat 8 is 32 and sits immediately left of B at seat 9; H at seat 6 is immediately left of the vacancy at seat 7; seat 11 (40) is twice H (20); and ages 26 and 28 sit on odd seats 5 and 1. Every condition holds, so the count of three is confirmed.