Direction: Study the following information carefully and answer the question…
2020
Direction: Study the following information carefully and answer the question given below.
A certain number of persons sit in a linear row. All of them face the north direction. P sits third to the right of S. Only three persons sit between P and Q. U sits third to the left of Q. U sits fifth from the left end of the row. R sits third to the left of U. Only three persons sit between W and T, who is an immediate neighbour of R. Only six persons sit to the right of W. M sits immediately to the left of O. Only three persons sit between M and H. O does not sit to the left of P. H does not sit at the extreme end of the row.
Who among the following persons sits exactly between R and Q?
- A.
T
- B.
M
- C.
P
- D.
H
- E.
U
Attempted by 2 students.
Show answer & explanation
Correct answer: E
Concept
In a linear-row puzzle, fix every clue to an absolute seat number by starting from the one clue that gives a definite position, then chain the relative clues ("k-th to the left/right", "only n persons between") off it. "Only n persons sit between X and Y" means the seat gap |X-Y| = n+1; "k-th to the right" means add k to the seat number. "Exactly between" two seats means their single middle seat, which exists only when the two seats are an even number of seats apart (so the gap is even).
Building the row (left to right, all facing north)
U is fifth from the left end, so U is at seat 5 — the anchor.
R is third to the left of U, so R = 5 − 3 = seat 2.
U is third to the left of Q, so Q = 5 + 3 = seat 8.
T is an immediate neighbour of R (seat 2) and three persons sit between W and T (gap 4). Taking T at seat 3 gives W at seat 7, which fits the next clue.
Only six persons sit to the right of W, so with W at seat 7 the row has 7 + 6 = 13 seats.
Three persons sit between P and Q (gap 4), so P is at seat 4 or seat 12. If P were seat 12, then S = P − 3 = seat 9, and "O is not left of P" would force O into seat 12 or 13; seat 12 is P and O = seat 13 would need M at seat 12 (also P) — impossible. So P = seat 4, and S = P − 3 = seat 1.
M is immediately left of O and three persons sit between M and H (gap 4). Placing M at seat 10, O at seat 11 satisfies "O is not left of P" (11 ≥ 4); H at seat 6 then keeps three persons between M and H with H away from both extreme ends.
Final arrangement
Seats marked "?" are occupied by unnamed persons (the row holds 13 people but only ten are named in the clues).
Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Person | S | R | T | P | U | H | W | Q | ? | M | O | ? | ? |
Answering the question
R is at seat 2 and Q is at seat 8 — six seats apart, so the span has exactly one middle seat at (2 + 8) / 2 = seat 5, which is occupied by U. So U sits exactly between R and Q.
Cross-check
The seats strictly between R and Q are 3, 4, 5, 6, 7, and their exact centre is seat 5 = U. Every other named person either touches only one endpoint of the span or lies outside it, so none of them is the midpoint.