Question

In a class of 30 students, the average weight of boys is \(20 \mathrm{~kg}\) and the average weight of the girls is \(25 \mathrm{~kg}\). The fraction of boys out of the total students of the class is : (a) \(\frac{4}{5}\) (b) \(\frac{5}{6}\) (c) \(\frac{3}{4}\) (d) data insufficient

Short answer

Answer: (d) Data insufficient

Step-by-step solution

Test option (a) - 4/5

If the fraction of boys is \(\frac{4}{5}\), this means there are \(\frac{4}{5} * 30 = 24\) boys in the class which leaves \(30 - 24 = 6\) girls in the class. However, we cannot determine the total weight of girls and boys, so the information is not enough to confirm the answer.

Test option (b) - 5/6

If the fraction of boys is \(\frac{5}{6}\), this means there are \(\frac{5}{6} * 30 = 25\) boys in the class which leaves \(30 - 25 = 5\) girls in the class. The same logic as for option (a) applies here, and the information is not enough to confirm the answer.

Test option (c) - 3/4

If the fraction of boys is \(\frac{3}{4}\), this means there are \(\frac{3}{4} * 30 = 22.5\) boys in the class which is not possible as the number of boys must be an integer. So this option is not valid.

Conclusion

Since we cannot determine the fraction of boys with the information given, the answer is (d) data insufficient.

Key concepts

Fractions in Aptitude

Fractions are an integral part of aptitude problems. They provide a way to represent parts of a whole, which is especially useful when analyzing groups within a total number, such as a class of students divided into boys and girls. In aptitude tests, understanding fractions can help you divide and manage quantities effectively.

• Fractions show the relationship between a part and a whole.
• They can be expressed as a ratio of one number over another, such as \(\frac{1}{2}\), \(\frac{3}{4}\), etc.
• In the context of the exercise, each fraction option implies different compositions of boys, requiring calculations to verify feasibility.

Grasping fractions enables better aptitude problem-solving and helps in assessing different possibilities effectively.

Weights and Averages

Averages offer insights into data sets by providing a central value around which individual values are distributed. This concept is particularly useful when analyzing weights, such as the average weight of boys and girls in understanding the distribution of weights.

• The average weight is calculated by dividing the total weight by the number of individuals.
• It gives a simplified view of the entire group, helping to identify typical values easily.
• In problems involving weight, averages allow you to predict and compare the weights of different groups, facilitating a better understanding of how these groups relate to each other.

Weights and averages help identify trends and make comparisons where precise data might not be available.

Step-by-step Problem Solving

Approaching problems step-by-step is crucial for breaking down complex questions. By analyzing each part of a problem, you can methodically test possibilities, as demonstrated in the exercise where each fraction was assessed independently.

• Identify what is known and what needs to be found.
• Test each option logically by plugging in values, just like testing each fraction.
• Ensure to check for logical consistency and errors, such as the need for a whole number count of boys.

This approach makes problem-solving more manageable, as it provides structure and precision to the process. Ensuring every aspect is checked carefully increases the likelihood of finding the correct answer.

Insufficient Data Analysis

Identifying when data is insufficient is a key skill in problem-solving. It involves recognizing limitations in given information, which may prevent arriving at a definitive answer or solution.

• Acknowledge the constraints imposed by the information provided.
• Evaluate each option to see if the available data can lead to a reliable conclusion.
• Recognize when additional data is needed to resolve ambiguities or inconsistencies.

In the given exercise, realizing the answer is based on insufficient data reflects excellent analytical skills, shedding light on the ability to discern data gaps and preventing incorrect conclusions.