12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes 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.

GMAT Club's Official Explanation: 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.

Total employees = 32 Employees (A + C = 32) In AI = 75% of 32 =24 In Cybersecurity=8 Given in AI : master's degree to those without is 5:3 5x+3x=24 x=3 With master's in AI=15 , without in AI=9 Given in Cybersecurity : master's degree to those without is 3:5. 3y+5y=8 y=1 With master's in C=3 , without in C=5 => p/q=(15+3)/(9+5)=9/7

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. Artificial Intelligence (AI) Cybersecuity Total With a master's degree 5/8*24 = 15 3 15+3 = 18 Without a master's degree 3/8*24 = 9 5 9+5 = 14 Total 75%*32 = 24 25%*32= 8 32 The ratio of employees with a master's degree to those without = 18:14 = 9:7 = p:q 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 9 7

AI C 24 8 M 15 3 18 W 9 5 14 P:q = 18:14 = 9:7

AI CS 75% of 32 = 24 25% of 32 = 8 M/~m=5/3=15/9 M/~m=3/5 Clearly Total M/ Total ~m = (15+3)/(9+5) = 18/14 = 9/7 And Hence (p,q) = (9,7)

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Bunuel

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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.

Total employees = 32

AI employees = (3/4)*32 = 24
Cybersecurity employees = (1/4)*32 = 8

AI with masters = (5/8)*24 = 15
AI without masters = (3/8)*24 = 9

Cybersecurity with masters = (3/8)*8 = 3
Cybersecurity without masters = (5/8)*8 = 5

Total masters = 18
Total without masters = 14

Masters/Without masters = p/q = 18/14 = 9/7

p = 9 and q = 7

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23 Dec 2024, 09:37

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Employees in AI = 3/4*32 = 24. Ratio of those with master to those without is 5:3 which implies number of masters = 15, without = 9
Employees in Cyber = 1/4*32 = 8. Ratio of those with master to those without is 3:5 which implies number of masters = 3, without = 5

Total masters = 18
Total Non-masters = 14
Ratio = 18/14 = 9/7 =p/q

Hence answer is P:Q is 9:7

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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.

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23 Dec 2024, 09:41

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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.

	Artificial Intelligence (AI)	Cybersecuity	Total
With a master's degree	5/8*24 = 15	3	15+3 = 18
Without a master's degree	3/8*24 = 9	5	9+5 = 14
Total	75%*32 = 24	25%*32= 8	32

The ratio of employees with a master's degree to those without = 18:14 = 9:7 = p:q
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
9	7

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23 Dec 2024, 09:46

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This was Pretty straightforward.
Total employees = 32
Employees in AI = 24 (15 with masters, 9 without masters)
Employees in Cybersecurity = 8 (3 with masters, 5 without masters)
Total ratio of employees with a master's degree to those without is 18:14 = 9:7

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23 Dec 2024, 09:49

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	AI	C
	24	8
M	15	3	18
W	9	5	14

P:q = 18:14 = 9:7

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23 Dec 2024, 09:51

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Given total 32 employees
75% (24 employees) work in AI and remaining 25% (8 employees) work in cs

CS the ratio of M to W (master to without masters) is 3:5 ==> 3 employees and 5 employees

AI the ratio is 5:3 which means 15 employees with masters and 9 without masters

So p/q is 18/14 ==> 9/7

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23 Dec 2024, 09:54

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The ratio of employees with a master's degree to those without is 18:14, which simplifies to 9:7.

Thus, the correct selections are:

p = 9
q = 7

Ans 9,7

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AI: 75% of 32 = 24
CS: 25% of 32 = 8

Master to non-master in CS = 3:5 => CSm = 3, CSn = 5
Master to non-master in AI = 5:3 => AIm = 15, AIn = 9

(AIm+CSm)/(CSn+AIn) = p/q
p/q = 9/7

Answer: (9, 7)

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AI	CS
75% of 32 = 24	25% of 32 = 8
M/~m=5/3=15/9	M/~m=3/5

Clearly
Total M/ Total ~m = (15+3)/(9+5) = 18/14 = 9/7

And Hence (p,q) = (9,7)

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Out of 32 people, 75% of them are in the AI department (75% of 32 =24) & the remaining (8) are in cyber security

There is no overlap between the two branches, hence on proceeding further

In AI,
No of masters to non masters degrees are in the 5:3 ratio which means there are 8x=24 if we assume masters & non masters degrees to be 5x & 3x respectively.

X=3
Hence masters degree there are 15 people & non masters there are 9 in the AI department

When it comes to Cybersecurity, ratio of masters to non masters is 3:5 hence there are 8y=8 if we assume masters & non masters degrees to be 3y & 5y respectively.
Y=1
Hence masters degree there are 3 people & non masters there are 5 in the Cybersecurity department

Hence the ratio of total masters to non masters degree across both departments is (15+3)/(9+5)=18/14

On simplification this comes out to be 9/7

Here p/q denotes ratio of masters to non masters degree, hence the answer is

P=9
Q=7

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AI = 3/4 * 32 = 24
Masters = 5/8 * 24 = 15
Non Masters = 9

CS = 8
Masters = 3
Non Masters = 5

Master / Non Masters = 15 + 3/ 9 + 5 = 18/14= 9/7

p = 9, q = 7

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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.

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Bunuel

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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.

the number of employees in each department:
AI team: 75% of 32 employees = 0.75 * 32 = 24 employees
Cybersecurity team: 25% of 32 employees = 0.25 * 32 = 8 employees
the number of employees with and without a master's degree in each department:
Cybersecurity Team
Ratio of employees with master's to those without: 3:5
Total parts: 3 + 5 = 8 parts
Employees with master's: (3/8) * 8 = 3 employees
Employees without master's: (5/8) * 8 = 5 employees
AI Team:
Ratio of employees with master's to those without: 5:3
Total parts: 5 + 3 = 8 parts
Employees with master's: (5/8) * 24 = 15 employees
Employees without master's: (3/8) * 24 = 9 employees
the total number of employees with and without a master's degree in the entire company:
Employees with master's: 3 (Cybersecurity) + 15 (AI) = 18 employees
Employees without master's: 5 (Cybersecurity) + 9 (AI) = 14 employees
the overall ratio of employees with a master's degree to those without:
Ratio: 18:14
Simplify the ratio: 9:7
values for p and q are:
p: 9
q: 7

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Bunuel

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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.

Number of people in AI = 3/4 * 32 = 24
in masters = 3/8 * 24 = 9
in non-masters = 5/8 * 24 = 15
Number of people in cybersecurity = 1/4 * 32 = 8
in masters = 5
in non-masters = 3
Total masters = 14
Total non-masters = 18

14:18 => 7:9

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23 Dec 2024, 10:17

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Total employees = 32;
employees from cybersecurity = 32*0.25 = 8;
employees from AI= 32*0.75 = 24;

From cybersecurity -> 3 holds a master degree and 5 doesn't hold;
From AI -> 15 holds a master degree and 9 doesn't hold; (5:3 ratio)
p:q = (15+3):(5+9) = 18:14 = 9:7;
p - Option D
q - Option B

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23 Dec 2024, 10:34

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Total employees = 32

AI department,
Employees = 75% i.e. 24
Ratio of employees with master’s degree to non master’s degree (p:q) = 5:3

Employees with master’s degree = 15 and without master’s degree = 9

Cybersecurity department,

Employees = 25% i.e. 8
Ratio of employees with master’s degree to non master’s degree (p:q) = 3:5

Employees with master’s degree = 3 and without master’s degree = 5

Total employees with master's degree (p) = 15+3 =18

Total employees without master's degree (q) = 9+5=14

p:q = 18:14 or 9:7

The answer is,
P= 9 and q = 7

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23 Dec 2024, 10:36

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IMO, p=9, q=7

TOTAL: 32
AI 75% team => AI team = 3/4*32=24 people
Cyber team = 32-24 = 8 people

In team AI, master/non-master = 5/3
=> Master = 5/8*24 =15 people
Non-Master = 24 -15=9 people

In team Cyber, master/non-master=3/5
=> Master = 3/8*8=3 people
Non-master = 8-3=5 people

Total master = 15+3=18 people =p
Total non-master = 9+5=14 people=q
=> p/q = 18/14 = 9/7
=> p=9, q=7

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23 Dec 2024, 10:49

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In TPA questions its always better to form a strategy first before solving. Well this is a detail bulky question.

The stem tells us that;

A tech startup has recently expanded its team to 32 employees
focusing on two main areas: artificial intelligence (AI) and cybersecurity
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.
the ratio of employees with a master's degree to those without is p to q

And we have to select;