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:
- Total : 132
- Ms A: Interviewed - 132; Recommended - 70
- Mr B: Interviewed - 132; Recommended - 86
- 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.