The average weight of 100 students in a school 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 of the 50th student in kilograms?

Introduction / Context:
This question checks your understanding of averages and overlapping groups. One hundred students have a known average weight. You are told the average weight of the first 49 students and the average of the last 50 students. The 50th student does not belong to either of these two groups, and you must use the total information to find that student weight. This pattern appears frequently in aptitude tests.

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.
- We are asked to find the weight of the 50th student alone.

Concept / Approach:
The key idea is that average multiplied by the number of students gives the total weight. We first compute the total weight of all 100 students. Then we compute the total weight of the first 49 students and the total of the last 50 students. The 50th student is not part of these two groups, so if we add the sums of the first 49 and last 50 we have accounted for all students except the 50th. This observation allows us to isolate the 50th student weight by simple subtraction.

Step-by-Step Solution:
Step 1: Total weight of all 100 students = 100 * 32 = 3200 kg.Step 2: Total weight of the first 49 students = 49 * 30 = 1470 kg.Step 3: Total weight of the last 50 students = 50 * 34 = 1700 kg.Step 4: Notice that the last 50 students are students numbered 51 to 100. The 50th student is not included in this group.Step 5: If we add the total weights of the first 49 and the last 50 students, we get 1470 + 1700 = 3170 kg.Step 6: The total weight of all 100 students is 3200 kg, which includes the 50th student, but the sum 3170 kg does not.Step 7: Therefore, weight of the 50th student = 3200 - 3170 = 30 kg.

Verification / Alternative check:
We can quickly verify consistency. If the 50th student weighs 30 kg, then the total of the first 49 plus the 50th is 1470 + 30 = 1500 kg for the first 50 students, giving an average of 1500 / 50 = 30 kg. The last 50 students have a total weight of 1700 kg and an average of 34 kg as given. Combined, 1500 + 1700 = 3200 kg, and the overall average remains 3200 / 100 = 32 kg, matching the question statement.

Why Other Options Are Wrong:
Weights like 25 kg, 32 kg or 33 kg for the 50th student lead to total weights that no longer produce an overall average of 32 kg when combined with the given subgroup totals. Simple substitution and recomputation of the total would show that the resulting averages do not match what the problem describes.

Common Pitfalls:
Some learners mistakenly assume that the 50th student is included in both subgroups or in neither and attempt more complicated setups. The key is to recognize that the first group covers students 1 to 49 and the second group covers 51 to 100, so the 50th student is missing from both. Once this is clear, the subtraction approach becomes straightforward and reliable.

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