The average weight of 100 students in a class is 32 kg. The average weight of the first 49 students is 30 kg and the average weight of the last 50 students is 34 kg. What is the weight (in kg) of the 50th student?

Introduction / Context:
This question tests understanding of averages, overlapping groups, and how to recover an individual value from combined average information. It is a classic aptitude problem involving average weights of different subsets of a class.

Given Data / Assumptions:
- Total number of students = 100. - Average weight of all 100 students = 32 kg. - Average weight of the first 49 students = 30 kg. - Average weight of the last 50 students = 34 kg. - The term "first" and "last" refer to some fixed ordering of students, and student number 50 does not belong to both groups simultaneously.

Concept / Approach:
Average weight is defined as total weight divided by number of students. We can convert each average into a total weight for that group. The first 49 and the last 50 students together cover all 100 students plus possibly one overlap, but in this wording it is natural to interpret that the first 49 are students 1 to 49, and the last 50 are students 51 to 100. Then the 50th student is not included in either partial group. We use total sums to recover the missing weight.

Step-by-Step Solution:
Step 1: Total weight of all 100 students = 32 * 100 = 3200 kg. Step 2: Total weight of the first 49 students = 30 * 49 = 1470 kg. Step 3: Total weight of the last 50 students = 34 * 50 = 1700 kg. Step 4: Combine the two partial totals: 1470 + 1700 = 3170 kg. Step 5: The combined total of these two groups represents the weight of all 100 students except the 50th student, because the first group covers students 1 to 49 and the second group covers students 51 to 100. Step 6: Therefore, total weight of the 99 students counted in the two groups = 3170 kg. Step 7: Weight of the 50th student = total weight of all 100 students minus the total of the 99 students in the two groups. Step 8: Weight of 50th student = 3200 - 3170 = 30 kg.

Verification / Alternative check:
We can verify by imagining that the 50th student weighs 30 kg and checking consistency. If student 50 has weight 30 kg, then the total becomes 3170 + 30 = 3200 kg, which matches the given average of 32 kg. The average of the subsets remains unchanged, since they did not include student 50 in the starting interpretation. Hence the result fits all stated conditions and is consistent.

Why Other Options Are Wrong:
Option A (25 kg): Would lead to total 3170 + 25 = 3195 kg and the overall average would become 31.95 kg, not 32 kg. Option C (32 kg): Would give total 3170 + 32 = 3202 kg, which is inconsistent with the given overall average. Option D (33 kg): Would result in total 3170 + 33 = 3203 kg, again inconsistent. Option E (40 kg): Clearly produces too large a total and a larger overall average than 32 kg.

Common Pitfalls:
A frequent error is to assume that the 50th student is included in both subgroups and then double counted. That interpretation would require careful subtraction of the overlap, but the wording here suggests that the last 50 students are a block separate from the first 49. Another common mistake is to average the two given averages directly without considering the different group sizes. Always convert averages to totals first, then manipulate those totals to find missing values.

Final Answer:
The weight of the 50th student is 30 kg.