In a class, P has more marks than Q, and R does not have the least marks. S has more marks than T and T has more marks than P. Who among P, Q, R, S and T has the least marks?

Introduction / Context:
This question is a ranking puzzle based on marks obtained by five students P, Q, R, S and T. You are given relative comparisons, such as who has more marks than whom, and one condition about who is not at the bottom. The goal is to use these comparisons to determine which student has the least marks in the group. This type of question tests logical ordering and careful interpretation of comparative statements.

Given Data / Assumptions:

• P has more marks than Q.
• R does not have the least marks.
• S has more marks than T.
• T has more marks than P.
• All five students have different marks; there are no ties.
• We want to identify the student with the lowest marks.

Concept / Approach:
To solve this, convert the verbal statements into inequalities and then arrange the students in order from lowest to highest marks. Any statement like “X has more marks than Y” can be written as X > Y. By chaining these comparisons and applying the condition that R is not the least, we can narrow down the possible positions for each student and see who must be at the bottom.

Step-by-Step Solution:
Step 1: From “P has more marks than Q”, we write P > Q.Step 2: From “T has more marks than P”, we write T > P. Combining these two, we get T > P > Q, so Q is below P and T in the ranking.Step 3: From “S has more marks than T”, we get S > T. Combining this with the previous chain gives S > T > P > Q, placing Q at the bottom of this partial order so far.Step 4: The statement “R does not have the least marks” means R cannot be at the lowest position in the class. R can be anywhere above the bottom.Step 5: Since Q is already lowest among P, Q, S and T, and R is not allowed to be the least, R must be above Q in the ranking.Step 6: Therefore the only student who can occupy the least position is Q, because everyone else, including R, must be above Q based on the given comparisons.

Verification / Alternative check:
To double check, construct a possible ordering that satisfies all constraints. For example, a valid order from lowest to highest marks could be Q, R, P, T, S. In this example P > Q holds, T > P holds, S > T holds and R is not the least. There are many possible exact numerical marks that match these inequalities, but in all consistent orders Q is always at the bottom, while the exact positions of R, P, T and S above Q can vary as long as the inequalities are maintained.

Why Other Options Are Wrong:
P cannot be the least because he has more marks than Q. T and S cannot be the least because each has more marks than someone who is already above Q. R is explicitly stated as not having the least marks. This rules out P, S, T and R as candidates for the lowest position, leaving only Q as the correct answer.

Common Pitfalls:
One common mistake is to forget the condition that R is not the least and focus only on the chain S > T > P > Q, leading to confusion about R. Another pitfall is misreading “more marks than” and accidentally reversing the inequality. Writing down the relationships symbolically and then building a consistent order from bottom to top helps avoid these errors.

Final Answer:
The student who has the least marks in the class is Q.