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24 Jan 2025, 09:13
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p: 9
q: 7
A tech startup has recently expanded its team to 32 employees, focusing on two main areas: artificial intelligence (AI) and cybersecurity. Here's the team composition:
• 75% of the employees work in AI, while the remaining 25% work in cybersecurity. There is no overlap between these departments.
• In the cybersecurity team, the ratio of employees with a master's degree to those without is 3:5.
• In the AI team, the ratio of employees with a master's degree to those without is 5:3.
If the ratio of employees with a master's degree to those without is \(p\) to \(q\), select for p the possible value of \(p\), and select for q the possible value of \(q\) that would be jointly consistent with the given information. Make only two selections, one in each column.
• 75% of the employees work in AI, while the remaining 25% work in cybersecurity. There is no overlap between these departments.
• In the cybersecurity team, the ratio of employees with a master's degree to those without is 3:5.
• In the AI team, the ratio of employees with a master's degree to those without is 5:3.
If the ratio of employees with a master's degree to those without is \(p\) to \(q\), select for p the possible value of \(p\), and select for q the possible value of \(q\) that would be jointly consistent with the given information. Make only two selections, one in each column.
| p | q | |
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 11 |
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Official Answer
p: 9
q: 7
24 Jan 2025, 09:13
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Official Solution:
Total employees: 32
• AI employees: 75% of 32 = 24
• Cybersecurity employees: 25% of 32 = 8
Cybersecurity team:
• For every 3 employees with a master's degree, there are 5 without.
• With 8 employees, this splits into 3 with master's and 5 without.
AI team:
• The ratio of employees with a master's degree to those without is 5:3.
• With 24 employees, this splits into 15 with master's and 9 without.
Company total:
• Employees with a master's degree: 3 (cybersecurity) + 15 (AI) = 18
• Employees without a master's degree: 5 (cybersecurity) + 9 (AI) = 14
The overall ratio of employees with a master's degree to those without is 18:14, which reduces to 9:7.
Correct answer:
p "9"
q "7"
Bunuel
Total employees: 32
• AI employees: 75% of 32 = 24
• Cybersecurity employees: 25% of 32 = 8
Cybersecurity team:
• For every 3 employees with a master's degree, there are 5 without.
• With 8 employees, this splits into 3 with master's and 5 without.
AI team:
• The ratio of employees with a master's degree to those without is 5:3.
• With 24 employees, this splits into 15 with master's and 9 without.
Company total:
• Employees with a master's degree: 3 (cybersecurity) + 15 (AI) = 18
• Employees without a master's degree: 5 (cybersecurity) + 9 (AI) = 14
The overall ratio of employees with a master's degree to those without is 18:14, which reduces to 9:7.
Correct answer:
p "9"
q "7"
18 Sep 2025, 10:35
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I don’t quite agree with the solution. I think answer is wrong here mainly due to the fact that MAsters to non masters is given to be 3:5 for AI and 5:3 for Cs respectively
