Direction: Read the following information carefully and answer the questions given below. A certain number of people are sitting in a straight line facing north with equal distance between adjacent persons. Seven persons sits between T and P. U sits second to the right of W. Two persons sits between U and T. W sits second from the left end. S sits second to the left of Q. Q sits third to the left of P. V sits second to the left of X, who sits exactly between Q and U. P sits immediate left of R, who sits one of the extreme ends.
How many persons sits to the right of Q?
Four
This problem requires us to determine the seating arrangement of people in a straight line based on a set of clues and then find the number of people sitting to the right of a specific person, Q.
Step-by-Step Solution
- Analyze the Fixed Positions:
- "W sits second from the left end." This places W at position 2. Let's represent the line as:
_ W _ _ _ ... - "U sits second to the right of W." Since W is at 2, U is at position 2 + 2 = 4. Arrangement:
_ W _ U _ ... - "P sits immediate left of R, who sits one of the extreme ends." This means R is at the rightmost end (position N), and P is immediately to its left (position N-1). Arrangement:
... P R - "Q sits third to the left of P." If P is at N-1, Q is at (N-1) - 3 = N-4. Arrangement:
... Q _ _ P R
- "W sits second from the left end." This places W at position 2. Let's represent the line as:
- Connect U and Q using X:
- "X, who sits exactly between Q and U." This means the number of people between Q and X is the same as between X and U.
- We have U at 4 and Q at N-4. Since N must be greater than 8 for Q to be to the right of U, the order is U ... X ... Q.
- The midpoint position for X is calculated as the average of U's and Q's positions: Position(X) = (Position(U) + Position(Q)) / 2 = (4 + (N-4)) / 2 = N/2.
- For X's position to be an integer, N must be even.
- "V sits second to the left of X." Position(V) = Position(X) - 2 = N/2 - 2 = (N-4)/2.
- Incorporate the T clues:
- "Two persons sits between U and T." This means the difference in their positions is 3. Since U=4, T can be at 4-3=1 or 4+3=7.
- "Seven persons sits between T and P." This means the difference in their positions is 8. Position(P) = N-1.
- Case 1: If T=1. P must be at 1+8=9. Since P=N-1, N-1=9 => N=10.
- Case 2: If T=7. P must be at 7+8=15. Since P=N-1, N-1=15 => N=16.
- Test the Cases and Place S:
- Test Case N=10: T=1, U=4, P=9, R=10, Q=6. X=10/2=5. V=(10-4)/2=3. The arrangement is
T W V U X Q _ _ P R. Now use the clue "S sits second to the left of Q." Q is at 6, so S should be at 4. However, U is already at position 4. This case leads to a conflict. - Test Case N=16: T=7, U=4, P=15, R=16, Q=12. X=16/2=8. V=(16-4)/2=6. The clue "S sits second to the left of Q" means S is at 12-2=10. Let's check for conflicts: Positions occupied are W=2, U=4, V=6, T=7, X=8, S=10, Q=12, P=15, R=16. All positions are unique and valid. This arrangement is consistent with all clues.
- Test Case N=10: T=1, U=4, P=9, R=10, Q=6. X=10/2=5. V=(10-4)/2=3. The arrangement is
- Determine the Final Arrangement (N=16):
The deduced positions are: W(2), U(4), V(6), T(7), X(8), S(10), Q(12), P(15), R(16). The arrangement looks like:
_ W _ U _ V T X _ S _ Q _ _ P R(filling in knowns). The total number of people (N) is 16. - Answer the Question: The question asks: "How many persons sits to the right of Q?" Q is at position 12. The total number of positions is 16. The number of positions to the right of Q is N - Position(Q) = 16 - 12 = 4. These positions are 13, 14, 15, and 16, occupied by unnamed people, P, and R.
Final Answer
There are Four persons sitting to the right of Q.
Similar Questions
Who faces W?
How many students are between W and R when counted from the left of W?
The same number of students are sitting between Y and ____ as that of between U and W.
Who is sitting to the immediate right of Q?
Who is sitting third to the left of V?
Four of the following five are alike in a certain way based on their seating position and thus form a group. Which of the following does not belong to the group?
Who is sitting opposite Q?
How many persons sits in the row?
Who sits third to the right of U?
Which of the following statements is true regarding M?
Important Questions from Seating Arrangement
Five friends, Bhumika, Rashi, Shweta, Vibha and Arunima, are sitting in a row facing east. Bhumika is sitting between Vibha and Shweta. Rashi is second to the left of Shweta. Who is sitting at the south end?
O, P, Q, R, S, T and U are sitting in a row facing north. U is sitting to the immediate right of T. Q is sitting in between R and O. P, who is on the extreme right, is sitting to the immediate right of O. S is sitting to the immediate left of R. Who is sitting in the middle of the row ?
Six friends are sitting in a straight line. E is 4th from the right. E is between B and D. A is adjacent to B. D is adjacent to C. D is between E and C. F is adjacent to C. Who is sitting between F and D?
In hall there are seven children (including girls and boys) P, Q, R, S, T, U and V. They sit on three benches I, II and III. Such that at least two children on each bench and at least one girl on each bench. R who is a girl child, does not sit with P, T and S. U the boychild sit with only Q. P sits on the bench I with his best friends. V sits on the bench III. T is the brother of R. Who sits with R?
- Five people Palak, Karol, Risha, Saloni and Tishaare travelling in a car. The car has two seats in the front and three at the back. Rishais driving the car. Palak wants to sit at one of the window seats at the back of the car. Tisha wants to sit next to Palak. Karol hates Tisha and will not sit with Tisha. Who is sitting next to the driver ?
