Study the following information and answer the question that follows. Five…
2021
Study the following information and answer the question that follows.
Five persons — D, K, M, O and L — sit in a row (left to right), and each likes a different colour: Red, White, Purple, Yellow and Green. Only two persons sit after the one who likes Red. One person sits between D and the one who likes Red. The number of persons sitting after D equals the number of persons sitting before the one who likes White. The one who likes Purple sits before the one who likes White and after the one who likes Yellow, but not immediately after the one who likes Yellow. O sits before L and after M, and M does not like Green. K sits between M and O.
The number of persons between O and L is the same as the number of persons between which of the following pairs?
- A.
M-O
- B.
D-K
- C.
K-L
- D.
M-K
- E.
O-D
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept
A linear-arrangement puzzle is solved by first fixing the clue that admits the fewest positions, then layering the remaining clues until exactly one seating survives. “Exactly n persons after X” in a row of five fixes X's seat directly; “as many persons after A as before B” and “not immediately after” are gap equalities and gap inequalities that pin the rest. Once the unique line is built, a “gap between two persons” question is answered by counting seats strictly between them.
Application — building the line (seats 1 to 5, left to right)
Only two persons sit after the colour Red, so Red is at seat 3.
One person sits between D and Red (seat 3), so D is at seat 1 or seat 5.
Persons after D equal persons before White. If D were at seat 5, persons after D would be 0, forcing White at seat 1 — but then Purple (before White) has no seat. So D is at seat 1, giving 4 persons after D, hence White is at seat 5.
Yellow < Purple < White(5), with Purple not immediately after Yellow, so the only fit is Yellow at seat 2 and Purple at seat 4; Green then takes seat 1 (D).
M is before O before L, and K is between M and O. With D fixed at seat 1, the block M–K–O occupies seats 2, 3, 4 (M=2, K=3, O=4) and L takes seat 5. M at seat 2 likes Yellow, satisfying “M does not like Green.”
The unique line is therefore:
Seat | Person | Colour |
|---|---|---|
1 | D | Green |
2 | M | Yellow |
3 | K | Red |
4 | O | Purple |
5 | L | White |
Answering the question
O is at seat 4 and L is at seat 5, so they are adjacent — there are 0 persons between O and L. We need the pair that also has 0 persons between them. M is at seat 2 and K is at seat 3, which are adjacent, so the pair M and K has 0 persons between them, matching the O–L gap.
Cross-check
Verify the other gaps against the line: M and O are at seats 2 and 4 (one person between), D and K at seats 1 and 3 (one person between), K and L at seats 3 and 5 (one person between), O and D at seats 4 and 1 (two persons between). Only the M–K pair shares the O–L gap of 0, confirming the result.