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Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is
Correct answer is '52'. Can you explain this answer?
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Each of 74 students in a class studies at least one of the three subj...
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It is given that the number of students studying H equals that studying E.
Let 'x' be the total number of students who studied H, and H and P but mot E. We can also say that the same will be the number of students who studied E, and E and P but not H. Therefore,
x + 20 + 10 + x = 74
x = 22
Hence, the number of students studying H = 22 + 10+ 20 = 52
Most Upvoted Answer
Each of 74 students in a class studies at least one of the three subj...
Given information:
- There are 74 students in the class.
- Each student studies at least one of the three subjects: H, E, and P.
- 10 students study all three subjects.
- 20 students study H and E, but not P.
- Every student who studies P also studies H or E or both.
- The number of students studying H is equal to the number of students studying E.
Step 1: Understand the given information
Let's break down the information given to gain a better understanding:
- There are 74 students in total.
- Each student studies at least one subject, so the number of students studying H, E, or P will be greater than or equal to 74.
- 10 students study all three subjects, so they are included in the count for H, E, and P.
- 20 students study H and E, but not P. This means there are 20 students who study H and E, but not P, and they are not included in the count for P.
- Every student who studies P also studies H or E or both. This implies that there are no students who study only P.
- The number of students studying H is equal to the number of students studying E.
Step 2: Solve the problem
Let's assume the number of students studying all three subjects (H, E, and P) is x.
- Since there are 10 students studying all three subjects, x = 10.
- The number of students studying H and E, but not P, is given as 20.
- The number of students studying H and P, but not E, can be calculated as follows:
- The total number of students studying H is x + 20 (students studying H and E, but not P).
- The number of students studying H and P is x (students studying all three) + 20 (students studying H and E, but not P) - 74 (total students) = x + 20 - 74.
- Since the number of students studying H is equal to the number of students studying E, we can equate the calculations for H and E:
- x + 20 = x + 20 - 74
- Simplifying the equation, we get 0 = -74
- This implies that the given information is not consistent, and there is no unique solution.
Step 3: Conclusion
The given information is contradictory, and there is no unique solution for the number of students studying H. Therefore, we cannot determine the exact number of students studying H based on the given information.
- There are 74 students in the class.
- Each student studies at least one of the three subjects: H, E, and P.
- 10 students study all three subjects.
- 20 students study H and E, but not P.
- Every student who studies P also studies H or E or both.
- The number of students studying H is equal to the number of students studying E.
Step 1: Understand the given information
Let's break down the information given to gain a better understanding:
- There are 74 students in total.
- Each student studies at least one subject, so the number of students studying H, E, or P will be greater than or equal to 74.
- 10 students study all three subjects, so they are included in the count for H, E, and P.
- 20 students study H and E, but not P. This means there are 20 students who study H and E, but not P, and they are not included in the count for P.
- Every student who studies P also studies H or E or both. This implies that there are no students who study only P.
- The number of students studying H is equal to the number of students studying E.
Step 2: Solve the problem
Let's assume the number of students studying all three subjects (H, E, and P) is x.
- Since there are 10 students studying all three subjects, x = 10.
- The number of students studying H and E, but not P, is given as 20.
- The number of students studying H and P, but not E, can be calculated as follows:
- The total number of students studying H is x + 20 (students studying H and E, but not P).
- The number of students studying H and P is x (students studying all three) + 20 (students studying H and E, but not P) - 74 (total students) = x + 20 - 74.
- Since the number of students studying H is equal to the number of students studying E, we can equate the calculations for H and E:
- x + 20 = x + 20 - 74
- Simplifying the equation, we get 0 = -74
- This implies that the given information is not consistent, and there is no unique solution.
Step 3: Conclusion
The given information is contradictory, and there is no unique solution for the number of students studying H. Therefore, we cannot determine the exact number of students studying H based on the given information.
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Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer?
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Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer?.
Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H isCorrect answer is '52'. Can you explain this answer?.
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