In A Class Of 60 Students, 40% Of The Students Passed In Reasoning, 5% Of The Students Failed In Quants And Reasoning, And 20% Of The Students Passed In Both The Subjects. Find The Number Of Student Passed Only In Quants? A)17 )33123 D)37 E) None

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Introduction

In this problem, we are given a class of 60 students with specific pass and fail rates in two subjects: Reasoning and Quants. We need to find the number of students who passed only in Quants. To solve this problem, we will use the principle of set theory and Venn diagrams to visualize the relationships between the students who passed and failed in each subject.

Given Information

  • 40% of the students passed in Reasoning.
  • 5% of the students failed in Quants and Reasoning.
  • 20% of the students passed in both the subjects.

Step 1: Calculate the Number of Students Passed in Reasoning

First, let's calculate the number of students who passed in Reasoning. We know that 40% of the students passed in Reasoning, and there are 60 students in total.

# Calculate the number of students passed in Reasoning
total_students = 60
pass_reasoning_percentage = 40
pass_reasoning = (pass_reasoning_percentage / 100) * total_students
print("Number of students passed in Reasoning:", pass_reasoning)

Step 2: Calculate the Number of Students Passed in Both Subjects

Next, let's calculate the number of students who passed in both Reasoning and Quants. We know that 20% of the students passed in both subjects.

# Calculate the number of students passed in both subjects
pass_both_percentage = 20
pass_both = (pass_both_percentage / 100) * total_students
print("Number of students passed in both subjects:", pass_both)

Step 3: Calculate the Number of Students Failed in Quants and Reasoning

Now, let's calculate the number of students who failed in Quants and Reasoning. We know that 5% of the students failed in Quants and Reasoning.

# Calculate the number of students failed in Quants and Reasoning
fail_quants_reasoning_percentage = 5
fail_quants_reasoning = (fail_quants_reasoning_percentage / 100) * total_students
print("Number of students failed in Quants and Reasoning:", fail_quants_reasoning)

Step 4: Calculate the Number of Students Passed Only in Quants

Finally, let's calculate the number of students who passed only in Quants. We can use the principle of set theory to find this value.

# Calculate the number of students passed only in Quants
pass_quants = pass_reasoning - pass_both
print("Number of students passed only in Quants:", pass_quants)

Conclusion

In this problem, we used the principle of set theory and Venn diagrams to find the number of students who passed only in Quants. We calculated the number of students passed in Reasoning, passed in both subjects, failed in Quants and Reasoning, and finally, passed only in Quants.

Answer

The number of students passed only in Quants is 24.

Discussion

This problem requires a good understanding of set theory and Venn diagrams. The student needs to be able to visualize the relationships between the students who passed and failed in each subject and use the principle of set theory to find the number of students who passed only in Quants.

Tips and Variations

  • To make this problem more challenging, you can add more conditions, such as students who passed in one subject but failed in another.
  • You can also use different percentages or numbers of students to make the problem more realistic.
  • To make this problem easier, you can provide more information or hints to help the student solve it.

References

  • Set Theory
  • Venn Diagrams
  • Mathematics
    Frequently Asked Questions (FAQs) on Finding the Number of Students Passed Only in Quants =============================================================================================

Q: What is the main concept used to solve this problem?

A: The main concept used to solve this problem is the principle of set theory, specifically the use of Venn diagrams to visualize the relationships between the students who passed and failed in each subject.

Q: How do I calculate the number of students passed in Reasoning?

A: To calculate the number of students passed in Reasoning, you need to multiply the total number of students by the percentage of students who passed in Reasoning. In this case, the total number of students is 60, and the percentage of students who passed in Reasoning is 40%.

Q: What is the significance of the 20% of students who passed in both subjects?

A: The 20% of students who passed in both subjects is important because it represents the intersection of the two sets (Reasoning and Quants). This means that these students have passed in both subjects, and we need to subtract this value from the total number of students who passed in Reasoning to find the number of students who passed only in Quants.

Q: How do I calculate the number of students failed in Quants and Reasoning?

A: To calculate the number of students failed in Quants and Reasoning, you need to multiply the total number of students by the percentage of students who failed in Quants and Reasoning. In this case, the total number of students is 60, and the percentage of students who failed in Quants and Reasoning is 5%.

Q: What is the relationship between the number of students passed in Quants and the number of students passed only in Quants?

A: The number of students passed in Quants is equal to the number of students passed only in Quants plus the number of students who passed in both subjects. This is because the students who passed in both subjects are counted twice (once in each set), so we need to subtract this value from the total number of students passed in Quants to find the number of students who passed only in Quants.

Q: Can I use this method to solve problems with different numbers of students or percentages?

A: Yes, you can use this method to solve problems with different numbers of students or percentages. The key is to understand the principle of set theory and how to use Venn diagrams to visualize the relationships between the students who passed and failed in each subject.

Q: What are some common mistakes to avoid when solving this type of problem?

A: Some common mistakes to avoid when solving this type of problem include:

  • Not understanding the principle of set theory and how to use Venn diagrams.
  • Not calculating the number of students passed in both subjects correctly.
  • Not subtracting the number of students passed in both subjects from the total number of students passed in Reasoning.
  • Not considering the intersection of the two sets (Reasoning and Quants).

Q: How can I practice solving this type of problem?

A: You can practice solving this type of problem by:

  • Using different numbers of students or percentages.
  • Adding more conditions, such as students who passed in one subject but failed in another.
  • Using different types of problems, such as finding the number of students who failed in both subjects.
  • Practicing with online resources or worksheets.

Q: What are some real-world applications of this concept?

A: Some real-world applications of this concept include:

  • Marketing and sales: understanding the relationships between different customer segments and how to target them effectively.
  • Finance: understanding the relationships between different financial instruments and how to manage risk.
  • Education: understanding the relationships between different student groups and how to provide targeted support.

Q: Can I use this concept to solve problems in other subjects, such as science or history?

A: Yes, you can use this concept to solve problems in other subjects, such as science or history. The key is to understand the principle of set theory and how to use Venn diagrams to visualize the relationships between different concepts or groups.