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555-605 (Medium)|   Math Related|         
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Initially,
In marketing there were 36 people (30% of 120)
and of the remaining people 120-36=84 was divided into 2:1 ratio to Finance and Operations (because: Of the remaining employees, the number in Finance was twice the number in Operations)
So, Finance has 56 people, Operation has 28 people.

Total Lay-Off=28
Let lay off from Finance be X
then from Marketing it will be 2x
and from Operations it will be x/2
so, 3x+x/2=28=> x=28/3.5=8

Members in Finance= 56-8=48
Members in 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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Total Employees = 120

As per given info,
Marketing (M) = 36 , Finance (F) = 56 , Operations(O) = 28

Let the no. of employees laid off from Finance team be x then,
2*x + x + 0.5*x = 28
Solving, x = 8

Finance = 56 - x = 48
Operations = 28 - 0.5*x = 24
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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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Solving as per the provided information the number of staffs in marketing is 36, Finance is 56 , Operations is 28
Therefore the layoff equation is 2x+x+1.5x=4.5x=28 therefore ignore X ratio is 2:1:1.5 since it is not possible to get 1.5 person hence X is 0 implies no layoffs therefore finance staff is 56, operations is 28 staffs
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before lay off

m - 36 | 84 = 2o + o => o = 28; f = 56

after lay off

28 = 2f+f+f/2 => f = 8

headcount post lay off

f = 56 - 8 = 48
0 = 28 - 8/2 = 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 120

30% M= 36
F+O=84
F=2O
3O=84
O=28
F=56

Lay off=28
Let F=2x; then M=2F=4x, O=f/2=X
7x=28
X=4

F=8,O=4,M=16

Remaining F=48,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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X=260, Y=200. Attached picture contains detailed solution
Attachments

IMG_1883.jpg
IMG_1883.jpg [ 1.99 MiB | Viewed 399 times ]

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Total employees = 120
Marketing, m = 30% of 120 = 36

Finance + Operations = f + o = 120 - 36 = 84

f = 2*o
=> o + 2o = 84
=> o = 28

f = 2*28 = 56

Layoffs = 28
m = 2f
o = 0.5f

=> 2f + 0.5f + f = 28
=> f = 8

m = 2*8 = 16
o = .5*8 = 4

Finally,
Finance = 56-8 = 48
Operations = 28-4 = 24
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So total employees at end of the year is 120
Exactly 30% are from marketing = 36 employees
So Finance + operation department = 84 employees

Of the remaining employees, the number in Finance was twice the number in Operations.
Assume Finance department = 2x
And Operations department = X

2x + x = 84
X = 28

Finance department = 56 employees
Operations department = 28 employees.

Since, 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.

Employees lay off in Marketing = 2y
Then Finance = y, and
Operations = 0.5y

So 2y + y + 0.5y = 28
Y = 8

Employees lay off in Marketing = 2y = 16
Then Finance = y = 8
Operations = 0.5y = 4


So for Finance and Operations the number of employees who work in the Finance and Operations departments, respectively, after the layoffs.

Finance = 56-8 = 48 employees
Operations = 28-4 = 24 employees
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At the end of last year
Total Employees - 120
Marketing (M) - 30% of the total Employees = 36
Let Operations (O) be x emlpoyees
Therefore, Finance (F) = 2x employees.
3x = 120-36
x = 28

So,
M = 36
F = 56
O = 28

Now,
At the beginning of the next year
Let F be the employees laid off in Finance department.
Therefore,
2F laid off in M
1/2F laid off in O
Therefore,
2F + F + 1/2F = 28
4F + 2F + F = 56
7F = 56
F = 8

Therefore, remaining employees
F = 56 - 8 = 48
O = 28 - (1/2*8) = 24
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T = 120
M = .3*120=36
Remaining = 84
F=2O
3O=84
O=28
F=56

Let number laid off from O = x
Lay offs
M:F:O
4x: 2x: x
4x+2x+x=28
x=4

Lay offs
M:F:O
16:8:4

Final numbers
M =36-16
F=56-8=48
O=28-4=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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There were 36, 56, and 28 employees in Marketing, Finance, Operations respectively.

If x people were removed from Finance, 2x and x/2 people were removed from Marketing and Operations.

Given that they equal 28, x can be solved for as 8.

It follows that 56 - 8 = 48 people currently work in Finance and 28-4 = 24 in Operations.

Therefore, Finance - 48 and Operations - 24
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Total emp 120
30% in marketing = 36

Remaining emp = 84
Finance = 2x
Operations = x
2x+x = 84
Employees in operations, x = 28
Employees in Finance, 2x = 56
Employees laid off 28
Operations = y
Finance = 2y
Marketing = 4y
y+2y+4y =28
y= 4
Employee laid off from operations = 4
Employees laid off from Finance = 8
Employees laid off from Marketing = 16



Employees left in operation, 28-4 =24
Employees left in Finance, 56-8 =48
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Initially, total = 120.
Marketing department had 30% i.e. 36 people.
Remaining people = 84.

Let people in operations = x. Thus, people in finance = 2x.
2x + x = 84.
x = 28

Hence, Before layoffs:
Marketing: 36
Finance: 56
Operations: 28

Now, 28 people were laid off.
It is given that twice as many were laid off from Marketing as from Finance.
Let people laid off from Finance be y.
Thus, people laid off from Marketing is 2y.

It is also given that half as many were laid off from operations as were from Finance.
Thus, people laid off from operations is y/2.

Now, y + 2y + 0.5y = 28
y = 8.

People left in finance: 56 - y = 48.
People left in operations: 28 - 4 = 24.

Answer:
Finance: 48
Operations: 24
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This question was provided by GMAT Club
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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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We are given:
- Total employees: 120
- Marketing: 30% of 120 = 36
- Remaining (Finance and Operations): 120 - 36 = 84
- Finance is twice Operations: Let O = Operations, then F = 2O
F + O = 84 -> 2O + O = 84 -> 3O = 84 -> O = 28, so F = 56
Initial:
Marketing: 36
Finance: 56
Operations: 28
Layoffs:
Total layoffs: 28
Let layoffs from Finance be L_F.
Then, Marketing layoffs L_M = 2 * L_F
Operations layoffs L_O = (1/2) * L_F
Total layoffs: L_M + L_F + L_O = 2L_F + L_F + 0.5L_F = 3.5L_F = 28
So, L_F = 28 / 3.5 = 8
Then:
L_M = 2 * 8 = 16
L_O = 0.5 * 8 = 4
After layoffs:
Marketing: 36 - 16 = 20
Finance: 56 - 8 = 48
Operations: 28 - 4 = 24
We are asked for Finance and Operations after layoffs: 48 and 24.
So, select 48 for Finance and 24 for Operations.
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Answer
  • Finance: 48
  • Operations: 24


Explanation

Step 1: Find the starting number of employees in each department.

  1. Marketing: 30% of 120 = 36 employees.
  2. Remaining: 120 - 36 = 84 employees for Finance and Operations.
  3. Finance & Operations: The number in Finance was twice the number in Operations. So, we split the 84 employees into three parts (2 for Finance, 1 for Operations).
    • Operations: 84 / 3 = 28 employees.
    • Finance: 28 × 2 = 56 employees.


Step 2: Find how many were laid off from each department.

  1. Total Layoffs: 28 employees.
  2. Let the number of layoffs from Finance be 'x'.
    • Layoffs from Marketing = 2x (twice as many).
    • Layoffs from Operations = x/2 (half as many).
  3. Equation: x + 2x + x/2 = 28.
    • 3.5x = 28
    • x = 8.
  4. Layoffs per department:
    • Finance: x = 8.
    • Operations: x/2 = 4.

Step 3: Calculate the final numbers.

  1. Final Finance: 56 (start) - 8 (laid off) = 48.
  2. Final Operations: 28 (start) - 4 (laid off) = 24.
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Information given:
- Total employees: 120
- 30% in marketing
- Number of employees in finance was twice number in operations
- Total lay-offs 28 employees
- Twice as many laid off from marketing as from finance, and half as many from operations as from finance

Question:
- What is number of employees in finance and operations after the layoffs?

Solution:
- 0.3 * 120 = 36 in marketing
- Remaining: 120 - 36 = 84 in finance & operations
- Finance is twice operations
- Let operations = X, finance = 2x
- 2x + x = 84, so x = 28
- So, finance = 56, operations = 28

- Let finance laid off = F
- Then, marketing laid off = 2F and operations laid off = F/2
- Combine: 3F + F/2 = 28
- 6F/2 + F/2 = 28
- 7F/2 = 28, 7F = 56
- F = 8
- So, finance laid off: 8, finance left: 56 - 8 = 48
- Operations laid off: 8/2 = 4, operations left: 28 - 4 = 24

Answer: Finance = 48, Operations = 24
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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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Correct Answer: 48 Finance and 24 Operations,
As per information,
Marketing - 120*30%= 36
Finance- 2x
operations- x
2x+x= 84
x= 28
So Finance have 56 and operations have 28.
Next Finance layoff= x
Marketing layoff= 2x
operations layoff= x/2
so x+2x+x/2= 28
x=8
Finance layoff= 8
Marketing layoff= 16
operations layoff= 4
Finance 56-8= 48
Operations 28-4= 24
Marketing 36-16=20
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total employees is 120
Marketing is 36
F = 56 & Operations 28
Laid off is 28
F= x , M = 2x & Operations = 0.5x
x is 8
F =8 , M= 16 & O = 4
the number of employees who work in the Finance and Operations departments, respectively, after the layoffs
F= 56-8 ; 48
O = 28-4 ; 24
48, 24 is correct
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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
120*0.3=36 =M
F=2O
84=F+O
F=56
O=28

AFTER m(layoff M) f(layoff F) o(layoff O)
m=2f
o=0.5f
m+o+f=28

3.5 f=28
f=8
o=4
m=16

F-f=56-8=48
O-o=28-4=24
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GMAT Club Olympics 2025 (Day 1): At the end of the year, a company had 30 Jun 2025, 09:45
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From statement one we know, 70% of 120 worked in Operations and finance which is 84.
now from statement two we can calculate, 2* operations (people working in finance) + operations = 84
so people working in operations is 28 and finance is 56.

Now 28 people were laid off.

from the sentence we can calculate people left each department.
let people laid from finance dept be 2f,
then people laid from operations is f and people laid from marketing is 4f
so, 7f = 28
therefore f = 4

so, people working in finance after laid off is, 56 - 8 = 48
and people working in operations after laid off is 28 - 4 = 24
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