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In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:
I. The number of students who passed in English was 20 less than those who did not pass in English.
II. The number of students who passed in more than one subject was 90.
III. Of the students who had passed in English, 35 did not pass in Science.
IV. 45 students had passed in both Mathematics and Science.
V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.
VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.
VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.
 
Q. How many students have passed in both Mathematics and English but not in Science?
Correct answer is '10'. Can you explain this answer?
Most Upvoted Answer
In Rosemary school, which had 200 students in Class X, the results in ...
From the diagram shown in the solution of the first question of the set, we find that 10 students passed in both Mathematics and English but not in Science.
Answer: 10
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In Rosemary school, which had 200 students in Class X, the results in ...
Given information:
- Total number of students in Class X = 200
- There are 3 papers - Mathematics, Science, and English
- Number of students who passed in more than one subject = 90
- Number of students who passed in both Mathematics and Science = 45
- Number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.
- Number of students who had passed in all the three subjects = half of the number of students who did not pass in any of the three subjects.

To find: Number of students who have passed in both Mathematics and English but not in Science.

HTML bold tag: Solution

Solution:
Let the number of students who passed in Mathematics, Science, and English be M, S, and E respectively. Let the number of students who did not pass in Mathematics, Science, and English be m, s, and e respectively.

From given information II, we have:
- Number of students who passed in more than one subject = 90
- Let x be the number of students who passed in all three subjects.
- Therefore, number of students who passed in exactly two subjects = 90 - x

From given information IV, we have:
- Number of students who passed in both Mathematics and Science = 45

From given information V, we have:
- Number of students who passed in Science and exactly one other paper = 60
- Let y be the number of students who passed in Science and also in Mathematics.
- Therefore, number of students who passed in Science and English only = 60 - y

From given information VI, we have:
- Number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.
- Therefore, S - y - 45 = 2(M - y)

From given information I, we have:
- The number of students who passed in English was 20 less than those who did not pass in English.
- Therefore, E = e - 20

From given information VII, we have:
- Number of students who had passed in all the three subjects = (1/2)(m + s + e - x)

Using the above information, we can form the following equations:
- M + m + y + 45 + x = 200 (total number of students)
- S + s + y + 45 + x = 200 (total number of students)
- E + e + y + 60 - y = 200 (total number of students)
- S - y - 45 = 2(M - y) (from VI)
- E = e - 20 (from I)
- x = (1/2)(m + s + e - x) (from VII)

Simplifying the equations, we get:
- M + m + y + x = 155
- S + s + y + x = 155
- E + e + 60 = 200
- S - M - y = 45
- E = e - 20
- x = (1/2)(200 - m - s - e + x)

Substituting E = e - 20 in the third equation, we get:
- M + m + y + x = 155
- S + s + y + x = 155
- 2E + 40 + 60
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In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer?
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In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer?.
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The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer? has been provided alongside types of In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In Rosemary school, which had 200 students in Class X, the results in the recent examinations, which had three papers in the area of Mathematics, Science and English were as follows:I. The number of students who passed in English was 20 less than those who did not pass in English.II. The number of students who passed in more than one subject was 90.III. Of the students who had passed in English, 35 did not pass in Science.IV. 45 students had passed in both Mathematics and Science.V. Of the students who had passed in Science, 60 students had passed in exactly one other paper as well.VI. The number of students who had passed only in Science was twice that of the number who had passed only in Mathematics.VII. Further, the number of students who had passed in all the three subjects was half of the number of students who did not pass in any of the three subjects.Q. How many students have passed in both Mathematics and English but not in Science?Correct answer is '10'. Can you explain this answer? tests, examples and also practice CAT tests.
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