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12 Nov 2024, 03:46
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Both A and B: 37
Rejected: 45
A candidate applying for a research program must undergo up to three interview cycles. The first interview is conducted by A, followed by B, and, if necessary, by C. A candidate is selected as soon as exactly two interviewers provide a recommendation. For example, if both A and B recommend a candidate, the candidate is selected and does not proceed to an interview with C. C interviews only those candidates recommended by exactly one of A or B.
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
| Both A and B | Rejected | |
| 13 | ||
| 37 | ||
| 44 | ||
| 45 | ||
| 50 | ||
| 82 |
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Official Answer
Both A and B: 37
Rejected: 45
12 Nov 2024, 03:46
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Official Solution:
Denoting the candidates recommended by both A and B as "Both," the number of candidates recommended by only A is 70 - Both, and the number of candidates recommended by only B is 86 - Both. Since C interviewed 82 candidates, and C only interviews those recommended by exactly one of A or B, we have (70 - Both) + (86 - Both) = 82, which gives Both = 37.
Therefore, both A and B recommended 37 candidates, and since C (together with A or B) recommended 50 candidates, the total number of candidates selected for the program is 37 + 50 = 87. Thus, the number of candidates not selected for the program is 132 - 87 = 45.
Correct answer:
Both A and B "37"
Rejected "45"
Bunuel
Denoting the candidates recommended by both A and B as "Both," the number of candidates recommended by only A is 70 - Both, and the number of candidates recommended by only B is 86 - Both. Since C interviewed 82 candidates, and C only interviews those recommended by exactly one of A or B, we have (70 - Both) + (86 - Both) = 82, which gives Both = 37.
Therefore, both A and B recommended 37 candidates, and since C (together with A or B) recommended 50 candidates, the total number of candidates selected for the program is 37 + 50 = 87. Thus, the number of candidates not selected for the program is 132 - 87 = 45.
Correct answer:
Both A and B "37"
Rejected "45"
27 Dec 2024, 02:51
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
