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In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.
There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.
The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.
It was further known that the number of prospective candidates that this institute had was less than 40.
Which of the following can be the number of candidates in this institute?
  • a)
    25
  • b)
    27
  • c)
    37
  • d)
    All of the above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In the placement season of a leading management institute, all the ava...
In case 1, the range of number of candidates can be from 24 (24 + 0) to 29 (24 + 5) 
In case 2, the number of candidates can be from 36 (36 + 0) to 39 (since the number of prospective candidates that the institute had was less than 40)
Hence, option 4.
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In the placement season of a leading management institute, all the ava...

Analysis:

Given Information:
- All candidates got at least one job.
- Industries: Infrastructure, Services, and Consultancy.
- 15 candidates got placed in exactly one industry.
- Number of candidates placed in all three industries ≤ 5.
- Number of candidates placed in at least two industries, one of which is Services, > those placed in Infrastructure or Consultancy.
- Number of candidates not placed in Services = Number not placed in Consultancy ≠ Number not placed in Infrastructure.
- Candidates placed in Services & Consultancy = Candidates in Infrastructure & Services + 1 = Candidates in Infrastructure & Consultancy - 1.
- Candidates placed only in Infrastructure = Candidates in Services & Consultancy, but not in Infrastructure.

Solution:
- Let the number of candidates be x.
- The maximum number of candidates who got placed in all three industries = 5.
- The minimum number of candidates placed in only one industry = 15.
- The number of candidates not placed in Services = Number not placed in Consultancy = x - (15 + 5) = x - 20.
- Number not placed in Infrastructure = x - (15 + 5) = x - 20.
- From the given conditions, the number of candidates placed in at least two industries, one being Services, must be greater than those placed in Infrastructure or Consultancy. Hence, the maximum number of candidates placed in Services = 5 + 15 = 20.
- From the condition that the number of candidates placed in both Services and Consultancy is 1 more than those in Infrastructure and Services, we can deduce that the number of candidates placed in Services and Consultancy = 9.
- Therefore, x - 20 = 9. Solving this, we get x = 29, which is less than 40.

Therefore, the possible number of candidates in the institute can be 25, 27, or 29, which are all less than 40. Hence, the correct answer is option D) All of the above.
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In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.It was further known that the number of prospective candidates that this institute had was less than 40.If there were a maximum of 35 candidates in the institute then which of the following statements is/are definitely true?

Group QuestionAnswer the following question based on the information given below.In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.It was further known that the number of prospective candidates that this institute had was less than 40.What was the maximum possible number of placements that were offeredto the candidates in this institute?

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In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.It was further known that the number of prospective candidates that this institute had was less than 40.Which of the following can be the number of candidates in this institute?a)25b)27c)37d)All of the aboveCorrect answer is option 'D'. Can you explain this answer?
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