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555-605 (Medium)|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 23 Dec 2024, 23:01
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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.




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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 23 Dec 2024, 23:28
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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.
Show more

Total Employees = 32
75% work in AI = 24
25% work in CS = 8
[No Overlap]

AI = Master's : No Master's = 5:3
CS = Master's : No Master's = 3:5

Total (32)Artificial IntelligenceCyber Security
Master's Degree153
No Master's Degree95

Ratio of Employees w/ Master's vs w/o Master's = p : q
p = 15+3 = 18
q = 9+5 = 14

p/q = 18/14 = 9/7

p = 9 & q = 7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 23 Dec 2024, 23:38
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T=32

AI=0.75*32=24
Master=15, Non master=9


CY=0.25*32=8
Master=3, Non Master=5

p=15+3=18
q=9+5=14

p/q=18/14=9/7


Answer 9 & 7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 23 Dec 2024, 23:53
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Masters in cybersecurity =3
Masters in AI = 5*3=15

Thus total masters =18

Total non masters = 32-18=14

Ratio of masters: non masters = 18:14 =9:7
P=9, q=7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 00:31
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I would say p=9 and q=7

There are 32 employees, 24 (15 with a master) in the AI department and 8 (3 with a master) in the cyber department
Total employee with a master = 18 = p
Total employee without a master = 32-18=14 = q
p/q = 18/14 = 9/7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 01:04
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Answer is p = 9 and q = 7

0.75 * 32 = 24 in AI
0.25 * 32 = 8 in cybersecurity
3:5 in cybersecurity = 3 with and 5 without
5:3 in AI = 15 with and 9 without
Total = 18 with and 14 without = 18:14 = 9:7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 01:05
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Quote:
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.

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Employees in AI= 3/4*32=24
Employees in Cybersec= 8

Employees with master degrees in AI= 3/8*24=9
Employees without master degrees in AI= 15

Employees with master degrees in Cybersec= 5/8*8=5
Employees without master degrees in Cybersec= 3/8*8=3


Employees with master's degree= 14 (p)
Employees without masters degree= 18 (q)

Ratio= 7:9

Answer= 7,9 IMO
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 01:19
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Hi All,

No of AI employees = 24,

No of Cyber security emps= 8

People with masters in cyber security= 8*(3/8)=3 then withuout masters will be 5.

People with masters in in Ai = 24*(5/8)=15 then without masters will be 9.

There fore total people with masters 15+3 and without 5+9

hence ratio of p:q will be 18:14--> 9:7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 02:16
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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.
Show more
Step 1: Calculate the number of employees in AI and cybersecurity
The total number of employees is 32. Given that:
  • 75% work in AI: 0.75×32=24 employees.
  • 25% work in cybersecurity: 0.25×32=8 employees.
Step 2: Determine master's degree ratios in each department
  • In cybersecurity, the ratio of employees with a master's degree to those without is 3:5, so the total of 8 employees can be divided as:
    With master’s: 3 and without master’s: 5
  • In AI, the ratio of employees with a master's degree to those without is 5:3, so the 24 employees can be divided as:
    With master’s: 15 and without master’s: 9
Step 3: Combine the totals
  • Total employees with a master's degree: 3+15=18
  • Total employees without a master's degree: 5+9=14
The overall ratio of employees with a master's degree to those without is:
Master’s:Non-Master’s=18:14=9:7

Step 4: Select values for p and q
From the result 9:7, the possible values are:
  • p=9
  • q=7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 02:40
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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.
Show more

AI = 3/4 * 32 = 24
CS = 1/4 * 32 = 8

CS
* Masters = 3/8 * 8 = 3
* Non Masters = 8 - 3 = 5

AI
* Masters = 5/8 * 24 = 15
* Non Masters = 24 - 15 = 9

Total Masters = 15 + 3 = 18
Total Non Masters = 9 + 5 = 14

p : q = 18 : 14 = 9 : 7

p = 9
q = 7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 03:22
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Total 32
75% AI = 24

25% CS = 8
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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.
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 03:23
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We can breakdown the given info as follows:

GivenWith a master's Without a master's Total
Artificial Intelligence15924
Cyber Security358
Total181432

Based upon the given info ,
P (employees with a master's degree) / Q (employees without a master's degree) = 18/14 => 9/7

So , p= 9 and q=7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 05:00
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Total Employees:
  • Total: 32 employees
Team Breakdown:
  1. AI Team:
    • 75% of 32: 0.75 × 32 = 24 employees
    • Ratio (Masters: Without): 5:3
      • Masters: 5/8 × 24 = 15 employees
      • Without Masters: 38 × 24 = 9 employees
  2. Cybersecurity Team:
    • 25% of 32: 0.25 × 32 = 8 employees
    • Ratio (Masters: Without): 3:5
      • Masters: 38 × 8 = 3 employees
      • Without Masters: 58 × 8 = 5 employees
Total Across Both Teams:
  • Masters Degrees: 15 (AI) + 3 (Cybersecurity) = 18 employees
  • Without Masters Degrees: 9 (AI) + 5 (Cybersecurity) = 14 employees
Overall Ratio (Masters: Without):
  • Ratio: 18:14
  • Simplified: Divide both numbers by 2 → 9:7

Final Answer:
  • p = 9
  • q = 7
Selections:
pq
97
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 05:40
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Total employees = 32
AI = 75% of 32 = 24
Cybersecurity (CS) = 8

Master’s degree to without in CS = 3:5
That means, 3 with master’s degree and 5 without.

Master’s degree to without in AI = 5:3 = 5x:3x
8x=24
X=3

Therefore, 15 with degree and 9 without.

Total with master’s degree = 15+3 =18
Total without master’s degree = 9+5=14

18/14
9/7

FINAL ANSWER - 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.

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.
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 05:46
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Let the number of employees in Cybersecurity with Masters and without Masters be a & b
Let the number of employees in AI with Masters and without Masters be c & d.

We have the following matrix:

AICyberTotal
Mastersca
non Mastersdb
24832

So c + d =24; a + b = 8 (1)

We also have a/b = 3/5, c/d = 5/3. (2)

From (1) and (2), we have a = 3, b = 5, c = 15, d = 9.

So p/q = 18/14 = 9/7.
Answer: p = 9. q = 7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 05:57
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total 32
AI=24 (15 master, 9 no master)
C=8 (3 master, 5 no master)

p/q=(15+3)/(9+5)=18/14=9/7

p=9 and q=7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 06:03
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Bunuel
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.
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Given : Total = 32
75% in AI and 25% in CC so A = 24 , C =8
In C = 8 --> Cm : Cw :: 3 : 5 that means ==> Cm = 3 , Cw = 5
In A = 24 --> Am : Aw :: 5 : 3 ==> Am =15 , Aw = 9

p/q = Masters/Withoout = Am + Cm / Ao + Co
= 18 /14 = 9/7
p=9
q = 7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 06:08
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32 employees
In AI 75% of 32 = 24 employees
master/no master = 5/3 = 15/9

In cybersecurity 25% of 32 = 8 employees
master/no master = 3/5

p/q=18/14=9/7

Answers p=9, q=7
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 06:21
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From the given information, we get
Employees in AI = 32 * 3/4 = 24
Employees in Cybersecurity = 32 * 1/4 = 8

Masters in AI = 5/8 * 24 = 15
No Masters in AI = 3/8 * 24 = 9

Masters in Cybersecurity = 3/8 * 8 = 3
No Masters in Cybersecurity = 5/8 * 8 = 5

Hence, Masters to No 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.

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.
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12 Days of Christmas GMAT Competition - Day 6: A tech startup has 24 Dec 2024, 06:38
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IMO
• For p: 9
• For q: 7

Step-by-Step Solution:
1. Calculate the number of employees in each department:
• Total employees: 32
• Employees in AI: 0.75×32=24
• Employees in cybersecurity: 0.25×32=8
2. Determine the number of employees with and without a master's degree in each department:
Cybersecurity:
• Ratio of employees with a master's degree to those without is 3:5.
• Let x be the number of employees with a master's degree in cybersecurity.
• Then, the number of employees without a master's degree in cybersecurity is 5/3x.
• Total employees in cybersecurity: x+5/3x=8
• Solving for x: X=3
• Employees with a master's degree in cybersecurity: 3
• Employees without a master's degree in cybersecurity: 8−3=5
AI:
• Ratio of employees with a master's degree to those without is 5:3.
• Let yy be the number of employees with a master's degree in AI.
• Then, the number of employees without a master's degree in AI is 3/5.
• Total employees in AI: y+3/5y=24
• Solving for y: y=15
• Employees with a master's degree in AI: 15
• Employees without a master's degree in AI: 24−15=9
3. Calculate the overall ratio of employees with a master's degree to those without:
• Total employees with a master's degree: 3+15=18
• Total employees without a master's degree: 5+9=14
• Ratio of employees with a master's degree to those without: 18:14
• Simplify the ratio:18/14=9/7
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