In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?a)38b)35c)32d)22e)20Correct answer is option 'D'. Can you explain this answer?

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In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?

a)
38
b)
35
c)
32
d)
22
e)
20

Correct answer is option 'D'. Can you explain this answer?

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Verified Answer

In a certain class of 66 students, 30 students study Science, 40 stude...

Given:

Total number of students = 66

Students who take:
- Science = 30
- Humanities = 40
- Dance = 40
- None of these 3 subjects = 0

Maximum possible number of students who study all 3 subjects = x

To find: X – N = ?

Approach:

To answer the question, we need to find the value of x

We’ll visually represent the given information to analyze the maximum possible overlap for 3 subjects.

Working Out:

The shaded part represents the students who study all three subjects: Science, Humanities, and Dance.

In the problem, the shaded part is labeled as x, which represents the maximum number of students who study all three subjects.

Analyzing the Maximum possible overlap for the 3 subject

To maximize x, i.e. to minimize the other overlap regions, among the sets, let’s consider the number of students who study only two subjects to be 0
- So, number of students who study only Science = 30 – x
- Number of students who study only Humanities = 40 -x
- Number of students who study only Dance = 40 – x

So, number of students who study only 1 subject + Number of students who study all the 3 subjects = 66

(30-x) + (40-x) + (40- x) + x = 66

2x = 44

x = 22

Getting to the answer
- So, the maximum number of students who can study all the 3 subjects is 22

Looking at the answer choices, we see that the correct answer is Option D

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In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?a)38b)35c)32d)22e)20Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?a)38b)35c)32d)22e)20Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain class of 66 students, 30 students study Science, 40 students study Humanities and 40 students study Dance. If all the students studied at least one of the subjects, then what is the maximum possible number of students who study all the three subjects?a)38b)35c)32d)22e)20Correct answer is option 'D'. Can you explain this answer?.

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