Sanjeev scored the highest marks in the class. Rahul scored more marks than Nirbhay but fewer marks than Sameer. Arpit scored more marks than Rahul. If there are exactly five students Sanjeev, Rahul, Nirbhay, Sameer and Arpit, who obtained the 4th rank in the class?

Introduction / Context:
This ranking question is based on comparative statements about examination marks. Instead of providing exact scores, the problem gives relative information such as higher marks and lower marks among the five students. You are asked to find who occupies the 4th rank when the students are arranged in order of decreasing marks. Such questions test logical ordering skills and the ability to work with inequalities involving several individuals.

Given Data / Assumptions:
- Students: Sanjeev, Rahul, Nirbhay, Sameer and Arpit. - Sanjeev scored the highest marks in the class. - Rahul scored more than Nirbhay but fewer than Sameer, giving Sameer > Rahul > Nirbhay. - Arpit scored more marks than Rahul, so Arpit > Rahul. - No contradictions are implied, and all five students have distinct scores. - We must find who stands at the 4th position when ordered from highest marks to lowest marks.

Concept / Approach:
The core idea is to build an order from the given inequalities. Sanjeev is known to be the topper, so he occupies rank 1. Among the remaining four students, we know that Sameer is above Rahul, and Rahul is above Nirbhay. We also know that Arpit is above Rahul, but we do not initially know whether Arpit is above or below Sameer. However, regardless of this detail, the relative positions of Rahul and Nirbhay are fixed, and that is enough to identify the student at 4th place.

Step-by-Step Solution:
Step 1: Place Sanjeev first, since he has the highest marks overall. Step 2: From the relation Sameer > Rahul > Nirbhay, we know that among these three, Nirbhay must be below Rahul, and Rahul must be below Sameer. Step 3: From Arpit > Rahul, we know Arpit is above Rahul. There are two possibilities: - Possibility 1: Arpit is above Sameer, so the order (top to bottom) is Sanjeev, Arpit, Sameer, Rahul, Nirbhay. - Possibility 2: Arpit is between Sameer and Rahul, so the order is Sanjeev, Sameer, Arpit, Rahul, Nirbhay. Step 4: In both possibilities, the student at the 4th position from the top is Rahul. Thus his rank is 4th regardless of the exact position of Arpit relative to Sameer.

Verification / Alternative check:
To further verify, you can assign sample marks that respect all inequalities. For example, in the first possibility, let Sanjeev have 95, Arpit 90, Sameer 88, Rahul 80 and Nirbhay 70. All given relations hold, and Rahul is 4th. In the second possibility, let Sanjeev have 95, Sameer 92, Arpit 88, Rahul 80 and Nirbhay 70. Again, all relations hold and Rahul is 4th. The fact that different consistent assignments still place Rahul at rank 4 confirms that his position is fixed by the data.

Why Other Options Are Wrong:
- Sameer is always ranked above Rahul and cannot be 4th. - Nirbhay is always below Rahul and therefore has rank 5 in every consistent ordering. - Arpit is above Rahul and therefore must be ranked either 2nd or 3rd, not 4th. - The conclusion is fully determined, so the option stating that it cannot be determined is incorrect.

Common Pitfalls:
Many students attempt to force a single linear order too early or assume that the position of Arpit relative to Sameer must be specified. They may also misread the phrase scored more than and reverse the inequality. Another frequent mistake is to assume that because one comparison is not completely specified, the entire ranking cannot be determined, which is not true here. Focusing on the relative position of Rahul and Nirbhay within all possible orders leads to the correct answer.

Final Answer:
The student who obtained the 4th rank in the class is Rahul.