Directions: Read the following information carefully and answer the questions given below:
Nine containers - P, Q, R, S, T, U, V, W, and X - are placed one above another in a single vertical stack, but not necessarily in the same order. Container R is placed fourth from the top of the stack. Only three containers are placed between container R and container Q, where container Q is kept below container R. Container U is kept immediately below container Q. Container W is placed at the top of the stack. Only one container is placed between container W and container T. Container P is placed immediately above container T. Two containers are kept between container S and container Q. Container X is placed immediately below container S. Container V is placed between container X and container Q.
If all the containers are reordered in alphabetical order from bottom to top, how many containers will remain in their original positions?
Correct Answer :
One
Solution :
The correct option is One.
Step-by-step arrangement of the stack:
There are 9 containers positioned from top (Position 1) to bottom (Position 9).
1. Position of R: Container R is placed 4th from the top of the stack.
⇒ Position 4 = R
2. Position of Q: Only 3 containers are placed between R and Q, where Q is below R.
⇒ Position of Q = 4 + 3 + 1 = 8
⇒ Position 8 = Q
3. Position of U: Container U is placed immediately below Q.
⇒ Position 9 = U
4. Position of W: Container W is placed at the top of the stack.
⇒ Position 1 = W
5. Position of T: Only one container is placed between W and T.
⇒ Position 3 = T
6. Position of P: Container P is placed immediately above T.
⇒ Position 2 = P
7. Positions of S, X, and V:
• Two containers are kept between S and Q. Since Q is at Position 8, S is placed at Position 5 (8 - 2 - 1 = 5).
⇒ Position 5 = S
• Container X is placed immediately below S.
⇒ Position 6 = X
• Container V is placed between X and Q.
⇒ Position 7 = V
Original Stack (From Top to Bottom):
Position 1: W
Position 2: P
Position 3: T
Position 4: R
Position 5: S
Position 6: X
Position 7: V
Position 8: Q
Position 9: U
Reordering in alphabetical order from bottom to top:
The alphabetical list of containers is: P, Q, R, S, T, U, V, W, X.
Placing them starting from Position 9 (Bottom) up to Position 1 (Top):
Position 9 (Bottom): P
Position 8: Q
Position 7: R
Position 6: S
Position 5: T
Position 4: U
Position 3: V
Position 2: W
Position 1 (Top): X
Comparison of Original and Reordered Positions:
• Position 1: W → X (Changed)
• Position 2: P → W (Changed)
• Position 3: T → V (Changed)
• Position 4: R → U (Changed)
• Position 5: S → T (Changed)
• Position 6: X → S (Changed)
• Position 7: V → R (Changed)
• Position 8: Q → Q (Unchanged)
• Position 9: U → P (Changed)
Only container Q at Position 8 remains in its original position. Hence, only One container remains unchanged.
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