Refer to the data below and answer the questions that follow: A got five movie…
2024
Refer to the data below and answer the questions that follow: A got five movie tickets as a gift in a contest. He and his four friends B , C, D and E decide to go for the movie. Three of the tickets were first row tickets numbered 101, 102 & 103 and the other two were second row tickets numbered 201 and 202 from left to right, respectively. A and B do not sit in the same row. D and E are sitting next to each other. The person sitting to the right of E is not a member belonging to the group. The unit digit of the ticket numbers of A and C are the same. Who is sitting on seat number 102?
- A.
A
- B.
C
- C.
B
- D.
D
Show answer & explanation
Correct answer: D
Concept: In a row-and-seat puzzle, first apply any clue that forces an END-OF-ROW position (such as "no one sits to the right/left"), since that pins one person absolutely; then use the shared-attribute and different-row clues to eliminate arrangements for the rest.
Application:
Seats: Row 1 has tickets 101, 102, 103 (left to right); Row 2 has tickets 201, 202 (left to right).
"The person sitting to the right of E is not a member of the group" — since all five seats belong to the group, this is possible only if E has no seat at all to the right, i.e. E sits at the end of a row: ticket 103 or ticket 202.
D and E sit next to each other, so D takes the seat immediately to E's left in that row — ticket 102 if E is at 103, or ticket 201 if E is at 202.
Test E = 202, D = 201: the remaining three (A, B, C) would occupy 101, 102, 103, whose units digits are 1, 2, 3 — all different. Since A and C must share a units digit, this case fails.
So E = 103 and D = 102. The remaining three (A, B, C) occupy 101, 201, 202, whose units digits are 1, 1, 2 respectively — only 101 and 201 match, so {A, C} = {101, 201} and B = 202.
A and B cannot share a row. If A were 201, then A (Row 2) and B = 202 (Row 2) would be in the same row — not allowed. So A = 101 (Row 1), C = 201 (Row 2), and B = 202 (Row 2), which is a different row from A.
Cross-check: A (101) and B (202) are in different rows — holds. D (102) and E (103) are adjacent — holds. The seat to the right of E (103) does not exist, so no group member sits there — holds. A (101) and C (201) share the units digit 1 — holds. Every clue is satisfied.
Result: the final arrangement is A–101, D–102, E–103, C–201, B–202. Seat number 102 is occupied by D.