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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 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)
    4
  • b)
    2
  • c)
    6
  • d)
    8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted 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
Free Test
Community Answer
From a group of 61 students, each student appears for at least one of...
Given information:
- Total number of students = 61
- Each student appears for at least one of the 3 papers (GATE, ESE, SSC)
- Number of students appearing for SSC = Number of students appearing for ONLY SSC
- Number of students appearing for ONLY SSC = Number of students appearing for GATE
- Number of students appearing for ONLY GATE = Number of students appearing for all 3 papers + 3
- Number of students appearing for ONLY ESE = Number of students appearing for all 3 papers + 5
- Number of students appearing for ESE = 32
- Number of students appearing for exactly ONE exam = 36

Let's solve the problem step by step:

Step 1:
Let's assume the number of students appearing for all 3 exams is 'x'.

Step 2:
Number of students appearing for ONLY SSC = Number of students appearing for SSC = x (Given)
Number of students appearing for ONLY GATE = Number of students appearing for GATE = x (Given)
Number of students appearing for ONLY ESE = Number of students appearing for ESE - Number of students appearing for all 3 papers = 32 - x (Given)

Step 3:
Number of students appearing for exactly ONE paper = Number of students appearing for ONLY SSC + Number of students appearing for ONLY GATE + Number of students appearing for ONLY ESE
36 = x + x + (32 - x)
36 = 2x + 32 - x
36 - 32 = x
4 = x

Therefore, the number of students appearing for all 3 exams is 4.

Hence, the correct answer is option 'C' (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 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)4b)2c)6d)8Correct answer is option 'C'. Can you explain this answer?
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