Seven persons P, Q, R, S, T, U and V are standing on different steps of a vertical ladder, one person per step. P is higher up the ladder than T but lower than R. Q stands exactly in the middle position. V is somewhere between P and Q. T is between Q and U, and U is between T and S. Based on these conditions, who is standing on the bottom step of the ladder?

Difficulty: Medium

Correct Answer: S

Explanation:


Introduction / Context:
This arrangement problem involves seven people standing on different steps of a ladder. The ladder is vertical and each person occupies exactly one distinct step. Various relative position clues are given. The question asks who is at the very bottom, so we need to determine the full order from bottom to top or at least enough of it to identify the lowest person.


Given Data / Assumptions:

  • Persons: P, Q, R, S, T, U, V.
  • Q stands in the middle, so Q is on the 4th step if there are 7 steps.
  • P is higher than T but lower than R.
  • V is between P and Q.
  • T is between Q and U.
  • U is between T and S.
  • We assume bottom step is the lowest and top step is the highest, and that up means a higher step number.


Concept / Approach:
We interpret each relational statement as an inequality in vertical order. Placing Q in the middle gives us a fixed reference point. Then we use the between relationships to form chains like S above U above T and T above Q or Q above T depending on the order. By carefully testing and combining these chains, we can derive a unique sequence of all seven persons on the ladder.


Step-by-Step Solution:
Step 1: Place Q on the 4th step (middle position).Step 2: T is between Q and U, and U is between T and S. This implies S is above U and U is above T, or S is below U and U is below T. But since T must be between Q and U and U between T and S, the consistent chain from bottom to top becomes S, U, T, Q or Q, T, U, S. However, T is said to be between Q and U, so Q and U must be on opposite sides of T. Combined with U between T and S, the correct chain is S (bottom), U, T, Q upward.Step 3: P is higher than T but lower than R. Since T is below Q in our chain, P must be above T and can be placed above Q or just above T if consistent with other constraints.Step 4: V is between P and Q. This means Q and P are on opposite sides of V. Because Q is already fixed in the middle, V must lie between Q and P in the vertical order.Step 5: A consistent full arrangement that satisfies all conditions is from bottom to top: S, U, T, Q, V, P, R.Step 6: In this arrangement, S is clearly on the bottom step.


Verification / Alternative check:
Check all conditions against S, U, T, Q, V, P, R. Q is in the middle (4th). P is higher than T but lower than R. V is between P and Q. T is between Q and U, and U is between T and S. All relationships hold without contradiction, which confirms that the derived ordering is valid and unique for the purpose of identifying the lowest person.


Why Other Options Are Wrong:
R is at the top in the valid ordering, not at the bottom. U and T are both above S. No arrangement with R, U, or T at the bottom can satisfy all the given between and middle position constraints at the same time. Therefore, options B, C, and D are inconsistent with the conditions when checked systematically.


Common Pitfalls:
Many candidates misinterpret the phrase between and treat it as simply below or above. Another common mistake is to forget that Q must be exactly in the middle. Without fixing Q first, it becomes difficult to handle the chain of between relationships. Drawing a vertical ladder diagram with labelled steps often makes such puzzles much easier to solve.


Final Answer:
The person who stands on the bottom step of the ladder is S.

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