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12 Nov 2024, 04:17
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A university conducts a written examination and an interview to admit students to a research program. A student is selected only if the student scores more than \(x\%\) in both the written examination and the interview, and has at least \(z\) years of work experience, where \(x\) and \(z\) are integers. The written examination is scored out of 100 marks, and the interview is scored out of 50 marks, with each score being an integer.
Based on the selection criteria and the information provided, determine whether each of the following students would be selected. Select Yes if the student would be selected. Otherwise, select No.
| Yes | No | |
| Amol: Written – 72; Interview – 35; Experience – 3 years | ||
| Brent: Written – 80; Interview – 35; Experience – 2 years | ||
| Donald: Written – 90; Interview – 45; Experience – 4 years |
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Official Answer
Amol: Written – 72; Interview – 35; Experience – 3 years: Yes
Brent: Written – 80; Interview – 35; Experience – 2 years: No
Donald: Written – 90; Interview – 45; Experience – 4 years: Yes
14 Nov 2024, 11:41
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Official Solution:
Amit (written 70, interview 40, experience 3 years) was selected with a written score of 70%. Shukla (written 72, interview 35, experience 4 years) was selected with an interview score of 35, which is exactly 70% of the 50-mark interview. So, scoring 70% is sufficient in both the written examination and the interview.
On the other hand, Reetu (written 69, interview 38, experience 10 years) — who had more than 70% in the interview and more experience than Amit — was obviously rejected because of her written score of 69%. This makes it clear that 69% is not sufficient. Thus, \(x = 69\%\), meaning a candidate must score more than 69% in both components.
Priya (written 75 (75%), interview 35 (70%), experience 2 years) met the score thresholds for \(x = 69\%\), but had only 2 years of work experience and was rejected. Amit, with 3 years of experience, was selected. So it’s clear that \(z = 3\), and a candidate must have at least 3 years of work experience to be eligible.
So, \(x = 69\%\) and \(z = 3\).
• Amol: Written 72 > 69%; Interview 35 > 69%; Experience 3 years ≥ 3 → meets all thresholds → Selected
• Brent: Written 80 > 69%; Interview 35 > 69%; Experience 2 years < 3 → fails experience → Rejected
• Donald: Written 90 > 69%; Interview 45 > 69%; Experience 4 years ≥ 3 → meets all thresholds → Selected
Correct answer:
Amol: Written – 72; Interview – 35; Experience – 3 years "Yes"
Brent: Written – 80; Interview – 35; Experience – 2 years "No"
Donald: Written – 90; Interview – 45; Experience – 4 years "Yes"
Bunuel
Amit (written 70, interview 40, experience 3 years) was selected with a written score of 70%. Shukla (written 72, interview 35, experience 4 years) was selected with an interview score of 35, which is exactly 70% of the 50-mark interview. So, scoring 70% is sufficient in both the written examination and the interview.
On the other hand, Reetu (written 69, interview 38, experience 10 years) — who had more than 70% in the interview and more experience than Amit — was obviously rejected because of her written score of 69%. This makes it clear that 69% is not sufficient. Thus, \(x = 69\%\), meaning a candidate must score more than 69% in both components.
Priya (written 75 (75%), interview 35 (70%), experience 2 years) met the score thresholds for \(x = 69\%\), but had only 2 years of work experience and was rejected. Amit, with 3 years of experience, was selected. So it’s clear that \(z = 3\), and a candidate must have at least 3 years of work experience to be eligible.
So, \(x = 69\%\) and \(z = 3\).
• Amol: Written 72 > 69%; Interview 35 > 69%; Experience 3 years ≥ 3 → meets all thresholds → Selected
• Brent: Written 80 > 69%; Interview 35 > 69%; Experience 2 years < 3 → fails experience → Rejected
• Donald: Written 90 > 69%; Interview 45 > 69%; Experience 4 years ≥ 3 → meets all thresholds → Selected
Correct answer:
Amol: Written – 72; Interview – 35; Experience – 3 years "Yes"
Brent: Written – 80; Interview – 35; Experience – 2 years "No"
Donald: Written – 90; Interview – 45; Experience – 4 years "Yes"
