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Bunuel
At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
Show more

Before layoffs
Marketing = \(\frac{30}{100} * 120 = 36\)
Finance + Operations = F + O = 2O + O = 120 - 36 = 84 -> O = 28
Finance = 56

Layoffs = 28 = \(L_f + L_o + L_m = L_f + 0.5L_f + 2L_f = 3.5L_f\)
\(L_f = 8\)
\(L_o = 4\)

After Layoffs
Finance = 48
Operations = 24
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Total employees= 120
Marketing- 0.30*120=36
Employees remaining=84
Finance= 2 op
o+2o=84
no. of emp in operations=28
no. of employees in Finance= 56

Layoffs
Let x be the no of employees laid off from Finance, x/2 from operations and 2x from Marketing

x+2x+x/2=28
x=8
So, total emp in Finance after layoffs= 56-8=48
and total no. of emp. in Operations after layoffs= 28-4=24
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Initial:
Marketing = 30% of 120 = 36
Remaining 84 split in 2:1 ratio → Finance = 56, Operations = 28

Layoffs:
Ratio of layoffs: Marketing : Finance : Operations = 2 : 1 : 0.5
Multiply all by 2 to eliminate the fraction → 4 : 2 : 1
Total parts = 4 + 2 + 1 = 7 parts
Total layoffs = 28 → each part = 4

So layoffs:
Marketing = 4×4 = 16
Finance = 2×4 = 8
Operations = 1×4 = 4

After layoffs:
Finance = 56 − 8 = 48
Operations = 28 − 4 = 24
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M = 36 (120*30/100)
Finance and Operations are 120-36=84
F = 2*O
2*O + O = 3*O = 84 -> O = 28
F = 2*O = 56

2l+l+0.5l=3.5l=28 -> l = 8
Layoffs M = 16
Layoffs F = 8
Layoffs O = 4

F - Layoffs F = 56 - 8 = 48
O - Layoffs O = 28 - 4 = 24

The right answers are Finance = 48 and Operations = 24
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Finance = 48 | Operations = 24

How to get those numbers
  1. Start-of-year head-count
    • Total employees = 120
    • Marketing = 30 % of 120 = 36
    • Remaining for Finance + Operations = 120 − 36 = 84
    Let Operations = O
    Finance is twice Operations, so Finance = 2O
    O+2O=84 ⟹ 3O=84 ⟹ O=28, Finance=56
  2. Lay-offs
    Let laid-off Finance staff = f.
    • Marketing lay-offs = 2f
    • Operations lay-offs = 1/2f
    Total lay-offs = 28:
    f+2f+1/2f=28⟹3.5f=28⟹f=8
    So
    • Finance lay-offs = 8
    • Marketing lay-offs = 16
    • Operations lay-offs = 4
  3. After lay-offs
    • Finance: 56−8=48
    • Operations: 28−4=24
Hence the only consistent choices are 48 for Finance and 24 for Operations.
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Total employees = 120

Marketing is 30 percent of 120, so 0.3 times 120 equals 36

Remaining employees = 120 minus 36 equals 84

Finance is twice Operations, so Finance = 2x, Operations = x
2x plus x = 84
3x = 84
x = 28
So Finance = 56, Operations = 28

Now layoffs:
Let number laid off from Finance be f
Then from Marketing: 2f
From Operations: 0.5f
Total layoffs: f plus 2f plus 0.5f = 3.5f
3.5f = 28
f = 8
Marketing layoffs = 16
Finance layoffs = 8
Operations layoffs = 4

After layoffs:
Finance = 56 minus 8 = 48
Operations = 28 minus 4 = 24

Answer: Finance = 48, Operations = 24
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Ans: Finance = 48 and Operations = 24

At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Lets do the calculation:
Total of 120 employee : of this 30% marketing = 36
of the remaining 84, Finance has twice as many as operations, so F = 56 (84/3 * 2) and Operations = 28 (84/3)
M = 36 , F = 56, and O = 28

Now coems the layoff of 28 people
for layoff M = 2F and O = F/2
2F + F + F/2 = 28 ==> F = 8

Remaining employees after the layoff
Marketing = 36- 2F = 36 - 2* 8 =36- 16 = 20
Finnace = 56 - F = 56 - 8 = 48
Operations = 28 - F/2 = 28 - 8/2 = 24
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
Show more

Total staff = 120.

Step 1 – initial head-count by department
• Marketing = 30 % of 120 = 36
• Let O = Operations, F = Finance.
Given F = 2O and F + O = 120 − 36 = 84
⇒ 3O = 84 ⇒ O = 28, F = 56.

Step 2 – layoffs
Let f = number laid off from Finance.
• Marketing layoffs = 2f
• Operations layoffs = f/2
Total layoffs = f + 2f + f/2 = 28
\(3.5f = 28 \;\Longrightarrow\; f = 8.\)
⇒ Marketing layoffs = 16, Operations layoffs = 4.

Step 3 – remaining employees
\(\\
\begin{aligned}\\
\text{Finance} &= 56 - 8 = 48,\\\\
\text{Operations} &= 28 - 4 = 24.\\
\end{aligned}\\
\)

Thus 48 in Finance and 24 in Operations after the layoffs.
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Quote:
At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

[color=#0f3850]• Exactly 30% of these employees were in the Marketing department.[/color]
[color=#0f3850]• Of the remaining employees, the number in Finance was twice the number in Operations.[/color]

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
[color=#000000]Finance[/color][color=#000000]Operations[/color]
[color=#000000]12[/color]
[color=#000000]24[/color]
[color=#000000]28[/color]
[color=#000000]32[/color]
[color=#000000]48[/color]
[color=#000000]56[/color]
Show more
Ans : Marketing = 30% of 120 = 36
Rest = 84
Finance + Oper = 84

given : Finance= 2(Operations)

Hence Operations = 28
Finance= 56

Now, 4a + 2a +a = 28 ( a = people who have been laid off)
a=4

Therefore after lay offs

marketing = 36- 4a= 36-14 = 20
operations = 28-a = 24
finance = 56-2a = 48
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Initially, Marketing= 30% of 120 = 36.
Remaining = 84.
Let 'x' be from Operations then Finance would be '2x'.
x+2x=84.
x=28.
Operations = 28, Finance = 56.

Now Layoffs, Let Finance be 2x, the Marketing would be 4x and opeartions would be x
2x+4x+x=28
7x=28
x=4.
Therefore layoffs from finance = 8, marketing=16, Operations=4.

After layoffs people left, Finance=48 and Operations= 24
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Quote:
At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
Finance Operations
12
24
28
32
48
56
Show more

Ans : Marketing = 30% of 120 = 36
Rest = 84
Finance + Oper = 84
given : Finance= 2(Operations)
Hence Operations = 28
Finance= 56
Now, 4a + 2a +a = 28 ( a = people who have been laid off)
a=4
Therefore after lay offs

marketing = 36- 4a= 36-14 = 20
operations = 28-a = 24
finance = 56-2a = 48
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the number of employees in marketing, finance, operations before layoffs=36,56,28respectively.

as per the question let the number of employees got laid off from the finance be x then from marketing and operations it will be 2x, x/2.

x+2x+x/2=28
solving we get x=8

the no of employees in finance and operations after lay off is 48(56-8), 24(28-4).
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Total = 120

M = 30% * 120 = 36

120 -36 = 84

F = 2O
F + O = 84

On solving - F = 56, O = 28

During Layoff => M = 2x, F = x, O=x/2

2x + x + x/2 = 28

x = 8

F = 56 - 8 = 48
O = 28 - 4 = 24
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
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Total 120 employees

Marketing: 30% of 120 = 36,
Finance: 2/3 of remaining = 56,
Operations: 1/3 of remaining = 28.

If layoff is x in Operations then 2x in Finance and 4x in Marketing, Hence total layoff is 7x which is equal to 28, x = 4

Remaining employees after layoff
Finance: 56 - 8 = 48,
Operations: 28 - 4 = 24.
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Total employees = 120

Employees are in Marketing, Finance, and Operations

⸻

🔹 Step 1: Find number of employees in each department before layoffs

“Exactly 30% of these employees were in the Marketing department”

\text{Marketing} = 30\% \text{ of } 120 = 0.3 \times 120 = 36

So remaining employees (Finance + Operations):

120 - 36 = 84

“Of the remaining employees, the number in Finance was twice the number in Operations”

Let’s say Operations = x
Then Finance = 2x

So:
x + 2x = 84 \Rightarrow 3x = 84 \Rightarrow x = 28

✅ Before layoffs:
• Marketing = 36
• Operations = 28
• Finance = 56

⸻

🔹 Step 2: Apply the layoffs

“The company decided to lay off 28 employees in total”

“Twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance”

Let the number laid off from Finance = x

Then:
• Marketing: 2x
• Operations: x/2

Total layoffs:
x + 2x + \frac{x}{2} = 28
\Rightarrow 3x + \frac{x}{2} = 28
\Rightarrow \frac{6x + x}{2} = 28
\Rightarrow \frac{7x}{2} = 28
\Rightarrow 7x = 56
\Rightarrow x = 8

✅ Layoffs:
• Finance: 8
• Marketing: 16
• Operations: 4

⸻

🔹 Step 3: Final count after layoffs
• Finance: 56 - 8 = 48
• Operations: 28 - 4 = 24
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No. of employees in Marketing = 120*30% = 36
Remaining Employees = 120-36 = 84
Let, No. of employees in Operations = x
& No. of employees in Finance = 2x
2x+x = 84
3x = 84
x = 28 (Operations ), 2x = 56 (Finance)

Now,
Let
Layoff in Finance = y, Marketing = 2y and Operations = y/2

Given that, y+2y+y/2 = 28
Solving, we get, y = 8

Hence no. of employees remaining in Finance after Layoff = 56 - y = 48
No. of Employees remaining in Operations after Layoff = 28-y/2 = 24

Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
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Total Employees = 120

Marketing department = 30% of 120 = 36
Assuming the number in ops = x, then the number in finance = 2x and given the total number of employees we have the following equation

x + 2x + 36 = 120
x = 28
so,
Finance department = 56
Operations department = 28

Assuming no. of people laid off in finance = 2y, then people laid off in Marketing = 4y, then people laid off in Operations = y
and we know that
y + 2y + 4y = 28
y = 4

Answering the question
Number of employees who work in the Finance after layoffs = 56 - 2y = 48
Number of employees who work in the Operations after layoffs = 28 - y = 24
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Total Employees = 120

Marketing department = 30% of 120 = 36
Assuming the number in ops = x, then the number in finance = 2x and given the total number of employees we have the following equation

x + 2x + 36 = 120
x = 28
so,
Finance department = 56
Operations department = 28

Assuming no. of people laid off in finance = 2y, then people laid off in Marketing = 4y, then people laid off in Operations = y
and we know that
y + 2y + 4y = 28
y = 4

Answering the question
Number of employees who work in the Finance after layoffs = 56 - 2y = 48
Number of employees who work in the Operations after layoffs = 28 - y = 24
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



At the end of the year, a company had exactly 120 employees working in three departments: Marketing, Finance, and Operations, with each employee working in exactly one of the three departments.

• Exactly 30% of these employees were in the Marketing department.
• Of the remaining employees, the number in Finance was twice the number in Operations.

At the beginning of the next year, the company decided to lay off a total of 28 employees from these three departments, with twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance.

Select for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs. Make only two selections, one in each column.
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Year end employees = 120
Marketing department employees = 30% of 120 = 36
Now Finance = 2 * Operations

Then F = 2O

=> F + O + 36 = 120
=> F + O = 120 - 36 = 84
=> 2O + O = 84
=> 3O = 84
=> O = 28
=> F = 2O = 56

Hence F = 56, O = 28 and M = 36


Now Layoff Scenario

Let's say
Finance lay offs = f
Operations lay offs = o
Marketing lay offs = m

=> f + o + m = 28 ----- (a)

Now m = 2f
and o = f/2 => 2o = f
now m = 2f = 2 * 2o = 4o

Hence we have equation (a) as
2o + o + 4o = 28
=> 7o = 28
=> o = 4
Hence f = 2o = 2*4 = 8
m = 4o = 4*4 = 16

IMHO
Finance after Layoff = 56 - 8 = 48
Operations after layoff = 28 - 4 = 24
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