In a class of 66 students there are 33 girls and 33 boys. The average weight of the girls is 61 kg and the average weight of the entire class is 66 kg. What is the average weight (in kg) of the boys in the class?

Introduction / Context:
This question checks understanding of how to work with averages when a group is split into two equal parts. You are given the average weight of the whole class and the average weight of the girls. Using this information, you have to determine the average weight of the boys in the class, which involves careful manipulation of totals derived from averages.

Given Data / Assumptions:
• Total number of students = 66.• Number of girls = 33, so number of boys = 33.• Average weight of girls = 61 kg.• Average weight of the full class = 66 kg.• We assume all given averages are correct and based on the same unit of kilograms.

Concept / Approach:
The key concept is that average = total sum of weights divided by number of students. If we know the average of the whole class and of a subgroup (girls), then we can find the sum of weights of the whole class and the girls, and by subtraction we get the total weight of the boys. Finally, dividing by the number of boys gives the average weight of the boys.

Step-by-Step Solution:
Step 1: Total weight of all 66 students = 66 * 66 = 4356 kg.Step 2: Total weight of the 33 girls = 33 * 61 = 2013 kg.Step 3: Total weight of the 33 boys = total weight of class minus total weight of girls = 4356 - 2013 = 2343 kg.Step 4: Average weight of the boys = total weight of boys divided by number of boys = 2343 / 33.Step 5: Compute 2343 / 33. Since 33 * 70 = 2310 and 2343 - 2310 = 33, we have 2343 = 33 * 71.Step 6: Therefore, average weight of boys = 71 kg.

Verification / Alternative check:
If the average of boys is 71 kg and average of girls is 61 kg, then the combined average with equal numbers of boys and girls is (61 + 71) / 2 = 132 / 2 = 66 kg, which matches the given class average. This consistency confirms that our answer is correct.

Why Other Options Are Wrong:
72: This would make the combined average greater than 66 kg, which contradicts the given overall average.73: This is even larger and increases the overall average far beyond 66 kg.69: This is too low and would pull the combined average below 66 kg when mixed with 61 kg for girls.

Common Pitfalls:
One common mistake is to simply take the difference of averages or average the given averages directly, without considering group sizes. Another error is to divide by the wrong number of boys. Always convert averages into totals and then back to averages after performing the required subtractions.

Final Answer:
The average weight of the boys is 71 kg.