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From a group of 61 students, each student appears for at least one of the 3 papers i.e. GATE, ESE or SSC. Out of the students appearing for SSC, the number of students appearing for ONLY SSC is equal to the number of students who also appear for GATE. The number of students who appear for only GATE is 3 more than the number of students who appear for all 3; number of students who appear for ESE alone is higher than the previous number by 5. If 32 students appear for ESE and 36 students appear for exactly ONE exam, then the number of students appearing for all 3 exams are ______.
  • a)
    6
  • b)
    4
  • c)
    3
  • d)
    2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
From a group of 61 students, each student appears for at least one of...
Base on the diagram and information available,
c = f + g ...(i)
a + b + c = 36
⇒ d + e + f + g = 61 – 36 = 25 ...(ii)
a + b + c = 36
⇒ g + 3 + g + 8 + c = 36
⇒ 2g + c = 25 = 3g + f ...(iii)
∵ b + d + e + g = 32
⇒ g + 8 + d + e + g = 32
⇒ d + e + g + g = 24
⇒d + e + f + g + g = 24 + f = 25 + g
⇒ f = g + 1
∵ 3g + f = 25
⇒ 4g = 24
∴ g = 6
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Most Upvoted Answer
From a group of 61 students, each student appears for at least one of...
Given information:
- Total number of students = 61
- Number of students appearing for SSC only = Number of students appearing for GATE
- Number of students appearing for GATE only = Number of students appearing for all 3 exams + 3
- Number of students appearing for ESE only = Number of students appearing for all 3 exams + 5
- Number of students appearing for ESE = 32
- Number of students appearing for exactly one exam = 36

To find:
- Number of students appearing for all 3 exams

Solution:
Let's assume the number of students appearing for all 3 exams as x.

Number of students appearing for SSC only = Number of students appearing for GATE
Number of students appearing for GATE only = x + 3
Number of students appearing for ESE only = x + 5
Number of students appearing for exactly one exam = 36

Total number of students = Number of students appearing for SSC only + Number of students appearing for GATE only + Number of students appearing for ESE only + Number of students appearing for all 3 exams

61 = Number of students appearing for GATE + (x + 3) + (x + 5) + x

Simplifying the equation:

61 = 3x + 8

3x = 61 - 8

3x = 53

x = 53/3

x ≈ 17.67

Since the number of students cannot be in decimal, we take the nearest whole number.

x = 18

Therefore, the number of students appearing for all 3 exams is 18. Answer: (a) 6
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From a group of 61 students, each student appears for at least one of the 3 papers i.e. GATE, ESE or SSC. Out of the students appearing for SSC, the number of students appearing for ONLY SSC is equal to the number of students who also appear for GATE. The number of students who appear for only GATE is 3 more than the number of students who appear for all 3; number of students who appear for ESE alone is higher than the previous number by 5. If 32 students appear for ESE and 36 students appear for exactly ONE exam, then the number of students appearing for all 3 exams are ______.a)6b)4c)3d)2Correct answer is option 'A'. Can you explain this answer?
Question Description
From a group of 61 students, each student appears for at least one of the 3 papers i.e. GATE, ESE or SSC. Out of the students appearing for SSC, the number of students appearing for ONLY SSC is equal to the number of students who also appear for GATE. The number of students who appear for only GATE is 3 more than the number of students who appear for all 3; number of students who appear for ESE alone is higher than the previous number by 5. If 32 students appear for ESE and 36 students appear for exactly ONE exam, then the number of students appearing for all 3 exams are ______.a)6b)4c)3d)2Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about From a group of 61 students, each student appears for at least one of the 3 papers i.e. GATE, ESE or SSC. Out of the students appearing for SSC, the number of students appearing for ONLY SSC is equal to the number of students who also appear for GATE. The number of students who appear for only GATE is 3 more than the number of students who appear for all 3; number of students who appear for ESE alone is higher than the previous number by 5. If 32 students appear for ESE and 36 students appear for exactly ONE exam, then the number of students appearing for all 3 exams are ______.a)6b)4c)3d)2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a group of 61 students, each student appears for at least one of the 3 papers i.e. GATE, ESE or SSC. Out of the students appearing for SSC, the number of students appearing for ONLY SSC is equal to the number of students who also appear for GATE. The number of students who appear for only GATE is 3 more than the number of students who appear for all 3; number of students who appear for ESE alone is higher than the previous number by 5. If 32 students appear for ESE and 36 students appear for exactly ONE exam, then the number of students appearing for all 3 exams are ______.a)6b)4c)3d)2Correct answer is option 'A'. Can you explain this answer?.
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