In a class, Sanjeev ranks seventh from the top and twenty eighth from the bottom. How many students are there in the class altogether?

Introduction / Context:
This ranking question checks understanding of how positions from the top and bottom of a list relate to the total number of students. It is a classic type of reasoning problem where one student's two ranks, from opposite ends, are used to calculate the total class strength.

Given Data / Assumptions:

• Sanjeev is 7th from the top of the class.
• Sanjeev is 28th from the bottom of the same class.
• All students are arranged in one linear order (for example by marks).
• There are no ties in rank and Sanjeev is counted only once.

Concept / Approach:
When the position of the same person from the top and from the bottom is known, the total number of students can be obtained by adding the two positions and subtracting 1. The subtraction of 1 is necessary because the student in question has been counted once in each rank and must not be double counted when calculating the total strength.

Step-by-Step Solution:
Step 1: Note Sanjeev's rank from the top: 7. Step 2: Note Sanjeev's rank from the bottom: 28. Step 3: Apply the formula: total students = rank from top + rank from bottom - 1. Step 4: Substitute the values: total students = 7 + 28 - 1. Step 5: Compute 7 + 28 = 35. Step 6: Now subtract 1: 35 - 1 = 34. Step 7: Therefore, there are 34 students in the class.

Verification / Alternative check:
Imagine writing all the students in a line and numbering them from 1 at the top to 34 at the bottom. If Sanjeev is 7th from the top, he stands at position 7. Counting from the bottom, positions would be 34 at the bottom, then 33, 32, and so on. The position 7 from the top corresponds to 34 - 7 + 1 = 28 from the bottom, which matches the given value, so the total of 34 is consistent.

Why Other Options Are Wrong:
Options 33, 35, and 36 are inconsistent with the formula and would not produce matching ranks of 7 from the top and 28 from the bottom for the same student.

Common Pitfalls:
Students sometimes forget to subtract 1 and instead use only the sum of the two ranks, which double counts the student in question. Others misinterpret ranks as distances between students. Remember that ranks include the person and refer to positions, so the formula with minus 1 is essential.

Final Answer:
There are 34 students in the class.