In a slip test, K secures the 15th rank from the top and the 44th position from the bottom among the students who passed. Four students did not take the test and three students failed. What is the total strength of the class (total number of students)?

Introduction:
This question tests ranking logic (top and bottom positions) combined with additional students who were absent or failed. A key rule: if someone is k-th from the top and m-th from the bottom in the same group, then total in that group is k + m - 1. Here, the group is “students who passed.” After finding how many passed, we add those who did not take the test and those who failed to obtain the total class strength.

Given Data / Assumptions:

• K is 15th from the top among those who passed
• K is 44th from the bottom among those who passed
• Absent students (did not take test) = 4
• Failed students = 3
• Total class = passed + absent + failed

Concept / Approach:
Compute passed students using: passed = 15 + 44 - 1. Then include the 4 absent and 3 failed students to get the overall class strength. The -1 avoids counting K twice (once from top and once from bottom).

Step-by-Step Solution:
Number of passed students = 15 + 44 - 1 = 58 Total students in class = passed + absent + failed = 58 + 4 + 3 = 65

Verification / Alternative check:
If 58 students passed and K is 15th from the top, then there are 14 passed students above K. If K is 44th from the bottom, then there are 43 passed students below K. Total passed = 14 + 1 + 43 = 58, consistent. Adding 7 non-passed participants (4 absent + 3 failed) gives 65 total students.

Why Other Options Are Wrong:
62, 63, 64, and 66 come from forgetting the -1 in ranking totals, or forgetting to add absent/failed students, or adding only one of the two extra groups.

Common Pitfalls:
Using 15 + 44 (forgetting -1), mixing “passed” group with total class directly, or treating absent students as part of passed rankings.

Final Answer:
The total strength of the class is 65.