In a class there are five students P, Q, R, S and T with different heights. P has height more than only one student. Q has height more than S and P but not more than R. S has height more than P. R is not the shortest. Who has the maximum height in the class?

Introduction / Context:
This reasoning puzzle involves comparing the heights of five students P, Q, R, S and T. You are given several statements about who is taller than whom and asked to conclude who is the tallest. Questions like this test your ability to translate verbal comparisons into an ordered ranking and to keep track of multiple conditions at the same time.

Given Data / Assumptions:

• There are five students: P, Q, R, S and T.
• P has height more than only one student, so P is second from the bottom in height.
• Q has height more than S and P but not more than R.
• S has height more than P.
• R is not the smallest student.
• All five heights are distinct; no two students have exactly the same height.

Concept / Approach:
The key idea is to convert each statement into ordering information and then combine these pieces into one consistent sequence. When a student is described as being taller than only one other student, that fixes their approximate position. Then we use the remaining inequalities to position each of the others relative to that student and to one another. Finally, we identify the top of the order, which corresponds to the student with maximum height.

Step-by-Step Solution:
Step 1: P has height more than only one student. Therefore in the ordered list from shortest to tallest, P must be second from the bottom. That means exactly one student is shorter than P and three are taller.Step 2: The student who is shorter than P must be one of Q, R, S or T. However, S is taller than P, so S cannot be shorter. Q is also taller than P, so Q cannot be shorter. R is not the smallest, so R cannot be the one at the very bottom.Step 3: The only remaining possibility for the shortest student is T. Thus, from shortest to taller, the ordering starts as T, then P.Step 4: S has height more than P, so S must be somewhere above P in the order. Q has height more than S and P but not more than R, which means Q is taller than both S and P but still not taller than R. Since heights are distinct, this implies Q is below R and above S.Step 5: From this we can build the order from bottom to top as: T (shortest), P, S, Q and then R on top. R is taller than Q, and Q is taller than S and P, while T is the only one shorter than P.

Verification / Alternative check:
You can verify by checking each original condition against the final ordering T, P, S, Q, R. P is taller than only T, which matches the first condition. S is taller than P, which is also correct. Q is taller than S and P but shorter than R, which fits the second condition. R is not the smallest, since T is smaller and even P is smaller. All given statements are satisfied with R as the tallest.

Why Other Options Are Wrong:
If Q were the tallest, then the statement that Q is not more than R would be violated because Q would exceed everyone, including R. If S or T were the tallest, they would contradict the clear indications that Q and R are above them in the implied ordering. Therefore options a, c and d cannot be correct.

Common Pitfalls:
One common mistake is to misread “more than only one student” and place P at the wrong position, such as second tallest instead of second shortest. Another pitfall is to assume that “not more than R” means equal to R, which is impossible here because all heights are distinct. Always build a complete ordered list and then check each condition carefully.

Final Answer:
The student with the maximum height in the class is R.