P, Q, R, S, T, U and V sit around a circular table facing the centre. Only one person sits between U and P when counted from the right of U. Only one person sits between P and R. Only one person sits between U and Q. Only two people sit between V and R. Only one person sits between T and Q. How many people sit between T and V when counted from the left of T?2
Correct Answer :
1
Solution :
The correct answer is Option 1 (1).
Let us analyze the step-by-step arrangement of the 7 people (P, Q, R, S, T, U, and V) sitting around a circular table facing the centre:
1. Total positions: 7 seats around a circle. Since everyone faces the centre, "right" means anti-clockwise and "left" means clockwise.
2. Placement of U and P: "Only one person sits between U and P when counted from the right of U."
This means going anti-clockwise from U, there is one empty seat, and then P. So if U is at position 1, P is at position 3.
3. Placement of Q: "Only one person sits between U and Q."
Q can either be 2 positions to the right of U or 2 positions to the left of U. Since position 3 (2 positions to the right of U) is occupied by P, Q must be 2 positions to the left of U (position 6).
4. Placement of R: "Only one person sits between P and R."
P is at position 3. R can be at position 1 or position 5. Since U is at position 1, R must be at position 5.
5. Placement of V: "Only two people sit between V and R."
With 7 people in a circle, sitting 2 people away from R in one direction means sitting 3 people away in the other direction. Let's check:
- 2 seats away from R (pos 5) clockwise gives position 2.
- 2 seats away from R (pos 5) anti-clockwise gives position 1 (which is occupied by U).
Therefore, V must be at position 2.
6. Placement of T: "Only one person sits between T and Q."
Q is at position 6. T can be at position 4 or position 1 (occupied by U). Thus, T must be at position 4.
7. Placement of S: The remaining vacant seat is position 7, which must be occupied by S.
Summary of Seating Order (Clockwise / Left direction starting from U at 1):
Position 1: U
Position 2: V
Position 3: P
Position 4: T
Position 5: R
Position 6: Q
Position 7: S
Final Question: "How many people sit between T and V when counted from the left of T?"
Starting from T (position 4) and moving to the left (clockwise):
- The person immediately to the left of T is P (position 3).
- The next person is V (position 2).
Thus, counting from the left of T to V, there is exactly 1 person (P) sitting between them.
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