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555-605 Level|   Math Related|         
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Initial split of employees:

M - 30% of 120, or 36 employees.
From the remaining 84 employees, there is a 2:1 ratio for F:O. Thus, 3x=84, giving you x=28.
F - 2*28 = 56 employees.
O - 28 employees.

The layoff ratio when you take Finance as x is -
M : F : O
2y : y : 0.5y

adding up to find 3.5y = 28, so y = 8.

Final split of employees:

F - 56-8=48 employees.
O - 28-4=24 employees.
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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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\(120\) employees in three departments. Marketing (\(M\)), Finance (\(F\)) and Operations (\(O\)).

Exactly \(30\)% of these employees were in the Marketing department -> \(M = \frac{30}{100}*120 = 36\)
Remaining employees -> \(M+F+O = 120\) -> \(36+F+O = 120\) -> \(F+O = 84\)
Of the remaining employees, the number in Finance was twice the number in Operations -> \(F = 2O\)

\(F+O = 84\)
\(2O+O = 84\)
\(O=28\) and \(F=56\)

Company decided to lay off a total of 28 employees from the three departments -> \(L_M + L_F + L_O = 28\)
Twice as many laid off from Marketing as from Finance -> \(L_M = 2L_F\)
Half as many laid off from Operations as from Finance -> \(L_O = \frac{L_F}{2}\)

\(2L_F + L_F + \frac{L_F}{2} = 28\)
\(L_F = 8\) and \(L_O = 4\)

\(F_n = 56-L_F = 56-8 = 48\)
\(O_n = 28 -L_O = 28-4 = 24\)
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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 Employes – 120.

30% of 120 = 36 -> Marketing , Operations + Finance = 120-36= 84
Operations = x, Finance = 2x è 3x = 84 -> x=28
Employes in each Department = M=36, F=56, O=28:

Let’s consider Employees laid off in Operations =y, Finance = 2y and Marketing = 4y;
Total employes laid off = 7y = 28-> y=4:

Employees after layoff in Finance = 56-8=48;
Operations = 28-4 = 24
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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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I'm taking quite long time for TPA, how do I reduce my timing without dip in accuracy?
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Finance = 48, Operation = 24
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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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Before lay off
Number of employees in Marketing M = 0.3*120 =36
Number of employees remainig is 120 - 36 = 84 (let us define F as the number of employees in finance and O the number in operation).
We know that O + F = 84 ---> O + 2O = 84 ---> O = 28 and F = 56

Number of employees laid off
x is the number for finance. We know that x (finance) + 2x (marketing) + 0.5x (operations) = 28
We find x = 8 (finance employees laid off) ; 2x = 16 (marketing employees laid off) ; 0.5x = 4 (operations employees laid off).

After lay off
Pay attention, we are asking the number of remaining employees in Finance and Operations. We have to make substraction :
Fr = 56 - 8 = 48
Or = 28 - 4 = 24
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Finance 48 (56 - 8)
Operations 24 (28 - 4)
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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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The company has 120 employees.
30% in Marketing → 36 people
84 in Finance and Operations.
We're told Finance has twice as many as Operations. Therefore, Operations = 28, Finance = 56
They lay off 28 people total with this ratio: Marketing : Finance : Operations = 2 : 1 : 0.5
Let layoffs from Finance = 8, then Marketing = 16, Operations = 4
After layoffs: Finance = 56 − 8 = 48 and Operations = 28 − 4 = 24

My answer is
Finance: 48
Operations: 24
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I just made a table for easier solving:
MarketingFinanceOperationsTotal
Initial30% x 120 = 362xx120
Lay off4y2yy28
Final

First equation: 36 + 3x = 120 => x = 28
Second equation: 7y = 28 => y = 4

After lay off, the amount of people working in finance is 2x - 2y = 2x28 - 2x4 = 48
working in Operations is x - y = 28 - 4 = 24
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Step 1: Total employees = 120
30% were in Marketing.
That means:
Marketing = 30% of 120 = 36 employees
Remaining employees = 120 - 36 = 84 employees
Now we’re told:
Quote:
Of the remaining, the number in Finance was twice the number in Operations.
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Let’s call the number in Operations = x, so Finance = 2x
Then:
x + 2x = 84
3x = 84
x = 28 → Operations
Finance = 2 × 28 = 56
So initial department breakdown:
  • Marketing: 36
  • Finance: 56
  • Operations: 28
[hr]
Step 2: Layoffs
Total layoffs = 28
We’re told:
  • Twice as many laid off from Marketing as from Finance
  • Half as many laid off from Operations as from Finance
Let’s say number laid off from Finance = f
Then:
  • Marketing layoffs = 2f
  • Operations layoffs = f/2
  • Total layoffs = f + 2f + f/2 = 3f + f/2 = (6f + f)/2 = 7f/2
Set that equal to 28:
7f/2 = 28
Multiply both sides by 2:
7f = 56
f = 8
So:
  • Finance layoffs = 8
  • Marketing layoffs = 16
  • Operations layoffs = 4
[hr]
Step 3: Find number of employees after layoffs
  • Finance: 56 - 8 = 48
  • Operations: 28 - 4 = 24
[hr]
Final Answer:
Finance = 48
Operations = 24

Bunuel
 


This question was provided by GMAT Club
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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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Finance 48, Operations 24. 30% of 120 is 36, remaining: 84, now finance is twice operations in this remaining , let both be x and 2x resp. ...solving this you get 28 and 56, going further reading the text, stem says " twice as many laid off from Marketing as from Finance, and half as many from Operations as from Finance." let these in tems of y now. add on now , to get y and equate it to 28. you will get y. since we just need finance and operations , finally subtract the obtained value from 56 and 28
Bunuel
 


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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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Abhishek_Relan
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Total employees : 120
Let no. of people in marketing = M
Let no. of people in finance = F
Let no. of people in operations = P

30% of the total employees are in marketing department = 30% of 120 = 36
Remaining employees : 84 = F + P

As per question : F = 2P ----- (1)
That's why 2P + P = 84
P = 28 and after putting value of "P" in (1)
F = 56

Let no. of people those were laid off in marketing = M'
Let no. of people those were laid off in finance = F'
Let no. of people those were laid off in operations = P'

M' + F' + P' = 28 ----- (2)

Again as per question : M' = 2F' and P' = F'/2

Putting above conditions in (2)

2F' + F' + ( F'/2 ) = 28
7F' = 56
F' = 8

That's why M' = 16 and P' = 4

Employees left after lay off :
Marketing= 36 - 16 = 20
Finance = 56 - 8 = 48
Operations = 28 - 4 = 24

Bunuel
 


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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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Bunuel
 


This question was provided by GMAT Club
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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 Employees=120.
Number of employees in:
Marketing(M)= 30%of 120=36
Remaining=84
Finance(F)= 2x
Operations (O)=x
Therefore, 2x+x=84.
=> x=28
Thus we have,

M= 36
F= 56 (2*28)
O= 28

Total number of employees to be laid off = 28.
Let the number of employees to be laid off from Finance be k.
Thus, according to the information,
The number of employees laid off from Marketing will be 2k, and the number laid off from Operations will be k/2.

=> 2k+k+k/2=28.
On solving, we get k=8.

Number of employees who work after layoffs:
In Finance, 56-8= 48.
In Operations, 28- (8/2) =24.

Ans:
Finance:48
Operations:24
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Total = 120

Marketing= 30% of 120 = 120* 30/100 = 12*3 = 36
Remaining employees = 120 - 36 = 84

"Of the remaining employees, the number in Finance was twice the number in Operations" ->

Finance = (2/3)*84 = 56
Operations = (1/3)*84 = 28

"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" ->

4x + 2x + x = 28 -> x = 4

Finance after lay off = 56 - 2x = 56 - 8 = 48
Operations after lay off = 28 - x = 28 - 4 = 24

Hope this helps.
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F= 48 and O=24

Initial there were 36 in M, 56 in F and 28 in 0

then 2y(M) +y (F)+ 1/2y (O) = 28 which gives y=8 therefore F= 48 and O = 24
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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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Let's focus on Finance and Operations,
70% of 120 is 84 (50% is 60, and 20% is 24).
Employees in operations would be 84/3, which is 28, and in Finance is 56.

The total laid off is 28.
Number of employees laid off ratio, Dept wise - 4:2:1 (Marketing:Finance:Operations), which leaves us with the number of employees laid off in Operations is 4 (28/7 * 1), and in Finance is 8 (28/7 * 2).
So total left in Finance is 48 and in Operations is 24.
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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
30% of 120 = 36
Remaining employees = 120−36=84

Let Operations = x, then Finance = 2x

=> x+2x = 84
=> x = 28

Operations = 28
Finance = 56

Now,
Total layoffs = 28
We know that,
Twice as many laid off from Marketing as from Finance
Half as many laid off from Operations as from Finance

So,
Let Finance layoffs = y
Marketting layoffs = 2y
Operations layoffs = y/2

Total layoff => y+2y+ (y/2)=28
=> y = 8

Therefore,
Finance = 8
Marketting = 16
Operations = 4

Final employee count after layoff
Finance = 56 - 8 = 48
Operations = 28- 4 = 24
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total = 120 employees
Marketing = 0.3×120=36
So remaining = 120−36=84
120−36=84 employees in Finance + Operations.

Finance = twice the number in Operations
Let Operations = x, so Finance = 2x
Then:

x+2x=84⇒3x=84⇒x=28
Operations = 28, Finance = 56
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DyutiB
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GMAT Club Olympics 2025 (Day 1): At the end of the year, a company had 01 Jul 2025, 06:54
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The question clearly states that these sets are not overlapped.

So we have, M = 36, F+O = 84
F = 2*O, So F = 56, O = 28

For layoffs, M = 2F, O = F/2, M+F+O = 28, So 7F = 56, F = 8, O = 4

So after layoffs, F = 48, O = 24.
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GMAT Club Olympics 2025 (Day 1): At the end of the year, a company had 01 Jul 2025, 07:08
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Step 1: Finding the number of employees in M, F and O at the end of the year

employees in Marketing \( = 0.3 * 120 = 36 \)
let employees in Operations be \(x\), then employees in Finance is \(2x\)
\(2x + x = 0.7 * 120 = 84 \)
From this we get \(x\) = 56, and \(2x\) = 28 >> employees in Operations are 56, and employees in Finance are 28


Step 2: Finding number of people laid off

Let the number of people laid off at Finance be \(y\)
Then those in Marketing laid off = twice as many = \(2y\)
those in Operations laid off = half as many = \(0.5y \)

\(\\
>> 2y + y+ 0.y = 28\\
>> y = 4 \\
\\
\)

For Finance, people after layoffs = 56- 4 = 48
For Operations, people after layoffs = 28 - 4= 24
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