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­A person applying for a research program has to undergo three cycles

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chetan2u
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­A person applying for a research program has to undergo three cycles [#permalink] New post   08 Feb 2024, 05:16
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95% (hard)

Question Stats:

26% (03:55) correct 74% (03:41) wrong based on 77 sessions
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Data Insights (DI) Butler 2024 [ Date: 08-Feb-2023] 


­A person applying for a research program has to undergo three cycles of interviews. First by Ms A, then by Mr B and finally by Ms C. A person is selected the moment that person is recommended by two of the interviewers. That is, a person recommended by both A and B is not interviewed by C. C interviews a person only when the person has been recommended by exactly one of Ms A or Mr B.
132 people applied for the research program out of which C interviewed 82. The number of people recommended by Ms A, Mr B and Ms C are 70, 86 and 50 respectively.

Based on the information above, select for Selected the number of people recommended by both Ms A and Mr B, and select for Rejected the total number of people out of 132 people not selected for the research program..­­
Selected Rejected
13
37
44
45
50
82
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Selected: 37 Rejected: 45
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Re: ­A person applying for a research program has to undergo three cycles [#permalink] New post   08 Feb 2024, 05:25
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Re: ­A person applying for a research program has to undergo three cycles [#permalink] New post   09 Feb 2024, 06:24
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chetan2u wrote:
­A person applying for a research program has to undergo three cycles of interviews. First by Ms A, then by Mr B and finally by Ms C. A person is selected the moment that person is recommended by two of the interviewers. That is, a person recommended by both A and B is not interviewed by C. C interviews a person only when the person has been recommended by exactly one of Ms A or Mr B.
132 people applied for the research program out of which C interviewed 82. The number of people recommended by Ms A, Mr B and Ms C are 70, 86 and 50 respectively.

Based on the information above, select for Selected the number of people recommended by both Ms A and Mr B, and select for Rejected the total number of people out of 132 people not selected for the research program..­

The question is 700+ level, and you are likely to see questions on actuals testing the logic used here.

­Data known to us:
  1.  Total : 132
  2. Ms A: Interviewed - 132; Recommended - 70
  3. Mr B: Interviewed - 132; Recommended - 86
  4. Ms C: Interviewed - 82; Recommended - 50


Let S be number of students recommended by both A and B, so Only A = 70-S and Only B = 86-S.

Selected:
The number of student interviewed by C should be those who were recommended by exactly one of A and B.
=> \(70-S+86-S = 82 ..........S = \frac{74}{2} = 37\) 
The correct answer is B
Thus, out of 50 not interviewed by C, 37 are selected(R by both) and 13 are rejected(rejected by both)

Rejected:
(a) Rejected by both A and B(not interviewed by C) = 13
(b) Recommended by exactly one of A or B but rejected by C = 82-50 = 32
Total = 13+32 = 45 
The correct answer is 45.­­­
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Re: ­A person applying for a research program has to undergo three cycles [#permalink] New post   09 Feb 2024, 22:56
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But when we add the selected and rejected we should be getting a total of 132 right?
45+37 = 82

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Re: ­A person applying for a research program has to undergo three cycles [#permalink] New post   09 Feb 2024, 23:36
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37 is the selected candidates without getting interviewed by C. They have been recommended by both A and B.
Add to it 50 recommended by C(this lot was recommended by one of A or B and required positive recommendation from C)
Total selected = 37+50 = 87
Rejected = 45

Total : 87+45 = 132
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Re: ­A person applying for a research program has to undergo three cycles [#permalink]
09 Feb 2024, 23:36
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