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555-605 (Medium)|   Math Related|         
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M = 0.3*120 = 36
Let total employees working in Ops (before layoff) = x
So, F = 2x

2x+x = 84 (120-36)
x= 28
2x = 56

Layoff:
People laid-off from M = 2*laid-off from Finance (F)
also, People laid-off from O = 1/2*laid-off from Finance (F)

2F+F+1/2F = 28 => F =8, M = 16, O = 4

Remaining employees after layoff in:

Finance = 56-8 = 48
Operations = 28-4 = 24
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Initially:
  • Marketing: 120 * 0.3 = 36 people
  • Out of remaining 120-36 = 84 people,
    • If Ops had x people, Finance had 2x people <=> 3x = 84; x = 28
    • Thus, Ops had 28 people, Finance had 56 people

Out of laid-off 28 people:
  • Finance got a layoff of y people, then
  • Marketing = 2y
  • Ops = 0.5y
Total layoffs = 28 = y + 2y + 0.5y = 3.5y <=> y = 8
Thus, Finance had a layoff of 8 people, Ops had 4.

Finance after layoff = 56 - 8 = 48 people
Ops after layoff = 28 - 4 = 24 people
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Finance = 32
Operations = 24

120 (employees) = M (marketing) + F (finance) + O (operations)
120 (30%) = M (marketing) = 40 employees

120 total - 40 marketing = 80 employees for F and O

F = 2(O) (Finance is twice operations)

Layoffs.
M= 2F
O= 2F

Layoff O + M + F = 28
F=14
M=7
O=7

What number for O+7 and F+14 makes it so that sum is 80 and 2(O)=F

I am a little lost at this point but the closest I can math is
Operations of 24
Finance of 32

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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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M = 30% of 120 = 36
F+O = 84
F = 2*84/3 = 56
O = 84/3 = 28

Total layoffs = 4x(M) + 2x(F) + x(O) = 7x = 28 -> x = 4

16(M), 8(F), 4(O)

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

Finance = 48 and Operations = 24
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Total employees in 3 depts = 120
Marketing = 30% = 36
Of the rest, Finance = 2*Operations. Hence, Finance = 56 and Operations = 28.

Layoffs:
Total layoffs = 28
Marketing layoffs = 2*Finance layoffs
Operations layoffs = 0.5*Finance layoffs
Hence, adding it all up, Finance layoffs = 8, Marketing layoffs = 16, and Operations layoffs = 4.

Final Answer:
Current number of employees in Finance = 56 - 8 = 48
Current number of employees in Operations = 28 - 4 = 24
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Initially, Marketing was 36, Finance 56 (2x Operations) and Operations 28. 120 minus 36 from Marketing, resulting in 84 which, divided by 3, results in 56 from Finance and 28 from Operations. The text says that to divide 28 employees on lay-off: 2 (M) : 1 (F) : 1/2 (O) or 4 (M) : 2 (F) : 1 (O). So, when we divide 28 by 7, we find 16 (M), 8 (F) and 4 (O). Remaining employees in Finance: 56 - 8 = 48 and in Operations: 28 - 4 = 24.
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M =36
F = 2x
O = x

2x+x = 120-36 = 84
x= 84/3 = 28
People working in Finance (F) = 28x2= 56
People working in Operation (o) = 28

People laid off
M= 4y
F= 2y
O= y

4y+2y+y = 28
y= 4

People working in finance = 56- 8 = 48
People working in ops = 28 - 4 = 24
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Number of employees before layoff :


Marketing: (30/100) *120 = 36
Finance: (70/100)*(2/3)*120 = 56
Operation: (70/100)*(1/3)*120 = 28

The layoffs were 28 total, with the ratio of 2 : 1 : 1/2 or for easy calculation 4:2:1

Marketing: (4/7) *28 = 16
Finance: (2/7) *28 = 8
Operation: (1/7) *28 = 4
So the new number of employees is:

Marketing: 36-16=20
Finance: 56-8=48
Operation: 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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should be 48 and 24 for finance and ops respectively
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Initially there were 120 employees, of whom 30% (36) worked in Marketing and the remaining 84 split into Operations (28) and Finance (56) in a 1:2 ratio. The company laid off a total of 28 people such that twice as many were let go from Marketing as from Finance and half as many from Operations as from Finance, yielding 16 layoffs in Marketing, 8 in Finance, and 4 in Operations. After these reductions, Finance has 56 − 8 = 48 employees and Operations has 28 − 4 = 24 employees.

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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[color=#e82a1f]Answer: Finance = 48, Operation: 24 [/color]

  • Exactly 30% of these employees were in the Marketing department => Employees of Marketing = 120 x 30% = 36
==> Finance + Operation employees = 120 - 36 = 84
  • Of the remaining employees, the number in Finance (F) was twice the number in Operations (O) => Finance employees = 2x Operation employees
==> Finance employees = 2/3*84 = 56; Operation employees = 84-56= 28

  • Total employees being laid off from each department next year: 28 = Marketing (O) + Finance (F) + Operation (O);
  • M = 2F; O = (1/2)F
=> 2 F + F + (1/2)F = (7/2)F = 28
=> F = 28*(2/7)= 8 ==> Number of people working in Finance after the layoffs: 56 - 8 = 48
=> O = 4 ==> Number of people working in Operation after the layoffs: 28 - 4 = 24
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Initial: Finance = 56, Operations = 28, Marketing = 36
Layoffs:
x = number of layoffs in Finance
28 = 2x + x + x/2 --> x = 8

After layoffs:
F = 56 - 8 = 48
O = 28 - 4 = 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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End of the year:

Total \(=120\)

Marketing, \(M=0.3*120=36\)

\(Finance+Operations = F+O=84\)

\(2x+x=3x=84; x=28\)

\(F=56\) & \(O=28\)

Beginning of next year:

Total laid off \(=28\)

laid off from respective departments, \(f, m, o\)

\(f+m+o=28\)

\(f=l, m=2l, o=\frac{l}{2}\)

\(l+2l+\frac{l}{2}=28\)

\(l=8\)

\(f=8, m=16, o=4\)

Finance after layoffs \(=56-8=48\)
Operations after layoffs \(=28-4=24\)

Finance: 48
Operations: 24
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Marketing = 0.3*120 = 36
Finance + Operations = 120-36 = 84
Finance = 84/3 * 2 = 56
Operations = 84/3 = 28

Layoffs = 2x(Marketing) + x(Finance) + 0.5x(Operations) = 3.5x = 28 -> x = 8

16(Marketing), 8(Finance), 4(Operations)

Finance = 56 - 8 = 48
Operations = 28 - 4 = 24

Answers: Finance = 48 and Operations = 24
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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.
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48 = F, 24=O
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Let \(M\), \(F \) and \(O\) be the number of employees in Marketing, finance, and operation respectively.

Given, \(F = 2O\)

now, consider \(m\), \(f \) and \(o \) as the number of people laid off from each department

Given, \(m=2f\) and \(o=\frac{1}{2}f\)
therefore, \(m=2f=4o\)
we are also given, \(m+f+o=28\)
solving both gives as \(f=8\) and \(o=4\)

Now using \(f=8\), \(o=4\) and \(F = 2O\) we can find out from the option the number that fits.
I started from the bottom with \(F-8=56 \) as \(F>O\) and thus got \(O=32\), therefore 32-4=28 would be the folks left over in operations.
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First get the number of people working in marketing which is 30 percent of 120 : 30

This means 84 people work in Finance and Operations Combines with a ratio of 2 : 1

to get the number of people working in operations we use ratio equivalence (1: 3 as x: 84 ) we get 28 for operations and likewise 56 for finance.

to get the number of people layed off, we create a ratio matrix

M : F : O
1 : 2 :
:0.5 : 1
--> 1 : 2 : 4

with total ratios of 7x = 28 (x = 4)
This means 4 person were layed of from Marrketing, 8 from finance and 16 from Operations
This implies the number of people left of lay offs were (M : 32, F: 48, O : 12)

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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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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since every employee work in exactly 1 dept:
M+F+O =120
M=0.3*120
let employees in ops be 'x'
x+2x = 120-36 ==> x=28 (employees in Ops)
Employees in Finance = 2x= 56

Post Layoff (M:F:O):
2y+y+y/2 = 28 ==> y=8

Finance = 56-y = 48
Ops = 28 - y/2 = 24
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Before layoffs:
Marketing 36 (30% of 120)
Finance + Operations = 120-36=84
Finance 2/3 * 84 = 56
Operations 1/3 * 84 = 28

After layoffs:
2a+a+a/2=7a/2=28 -> a=8

Finance = 56 - a = 48
Operations = 28 - a/2 = 24

Correct answers are Finance = 48 and Operations = 24
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total=120
marketing 30% of 120=36
remaining (F+O)= 120-36=84
F= 2*operation= 56
O= 28
layoff=28
layoff from Finance= F
M= 2F
o=0.5F
T=2f+f+0.5f=3.5f=28, F=8
mkt laid off=16
F=8
Operations=4
employee after layoff
F=56-8=48
o= 28-4=24
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