At a particular company, the average income of managers is $50,000

Question

At a particular company, the average income of managers is $50,000 more than the average of all the employees. The average income of salespeople is $25,000 less than the average of all of the employees. What is the ratio of managers to saleseople?

A) 2:1
B) 3:2
C) 4:3
D) 1:2
E) 1:4

Show Answer

Official Answer

D

A) 2:1
B) 3:2 
C) 4:3 
D) 1:2 
E) 1:4

RJ7X0DefiningMyX · Accepted Answer

Easiest way to take this on is consider the average to be any value, let's take $100,000, for the ease of calculation, now we have the average income of managers = $150,000, and the average income of salespeople to be $75,000

Let the number of managers and salespeople be M and S respectively

Now we have, total sum of the income of managers to be 150000*M and total sum of the income of salespeople to be 75000*S

Simply putting in the formula for average, average of all employees = $100,000 = Total Sum of All Employees / Total No. of Employees

(150000*M + 75000*S) divided by (M + S)

$100,000 = (150000*M + 75000*S) divided by (M + S)

Multiplying both sides by (M+S), we get $100,000*(M+S) = 150000*M + 75000*S

Solving this, we get 25000*S = 50000 * M

And solving further, we get M/S = 1/2 (D)

ScottTargetTestPrep · Answer

We can let n = the average income of all employees, s = the number of salespeople and m = the number of managers, and create the following equation (we assume there are no employees other than managers and salespeople):

n =  /(m + s)

mn + ns = 50,000m + mn + sn - 25,000s

25,000s = 50,000m

25,000/50,000 = m/s

1/2 = m/s

Answer: D

vishalkazone · Answer

M/ S = (Difference of sales person from all avg)/ (Difference of managers from all )
 =25000/50000
1:2
Answer: D

For above here is formula:

Mo2men · Answer

Dear  GMATGuruNY

Can you share your thoughts in solving such problem?

Thanks in advance

GMATGuruNY · Answer

Let the average salary of all the employees = 50,000, implying that the average salary of the managers = 50,000 + 50,000 = 100,000 and that the average salary of the salespeople = 50,000 - 25,000 = 25,000.
To determine the ratio of managers to salespeople, use alligation.

Step 1: Draw a number line, with the averages for the managers and salespeople on the ends and the average for all the employees in the middle: 
M 100,000-------------------50,000------------------25,000 S

Step 2: Calculate the distances between the averages. 
M 100,000----- 50,000 -----50,000----- 25,000 -----25,000 S

Step 3: Determine the ratio in the mixture. 
The ratio of M to S is equal to the RECIPROCAL of the distances in red.
M:S = 25000:50000 = 1:2

D

Palladin · Answer

The question requires us to assume that the managers and the salespeople are the only members of that company.
Shouldn't it be acknowledged in the question?

ishitaz · Answer

Total Employees = Total Managers + Total Salespeople
 E = M + S

Let average of managers be  Ma = Ms / M  where Ms is sum of salaries of Managers,
average of salespeople be  Sa = Ss / S  where Ss is sum of salaries of Salespeople,
average of total employees be  Ea = Es / E  where Es is sum of salaries of All Employees

Given in the question,
Ma = 50,000 + Ea
Sa = Ea - 25,000

Now, from our variables declared
Ms/M = 50,000 + Ea
Ms = M*(50,000 + Ea) ------------------ Equation 1
Ss/S = Ea - 25,000
Ss = S*(Ea - 25,000) -------------------- Equation 2

Average of employees can also be written as,
Ea = (Ms + Ss)/(M + S)

Substitue eqns 1 and 2,

Ea =   / (M + S)

Ea (M + S) =  
Ea (M + S) = 50,000M + Ea*M + Ea*S - 25,000*S
Ea (M + S) = Ea (M + S) + 50,000M - 25,000*S
0 = 50,000M - 25,000*S
50,000*M = 25,000*S
S/M = 25,000/50,000

S/M = 1:2

Hence, Option D
Hope that helps!

Thanks,
Ishita Roy

sambitspm · Answer

I also think the assumption must have been stated here. Without that the calculations could have been something else. As we can see in the screenshot.

ScottTargetTestPrep 
 Palladin

trovo · Answer

where in the Q does it say all number of employees = number of managers + number of salespersons?

anish0953 · Answer

exactly , i was also wondering the same . I thought there were some other employess as well . poorly worded or is it just me

GMATGuruNY · Answer

While it is possible that the company is composed only of managers and salespeople, this condition is not required.

In my earlier solution:
Average salary for managers = 100,000
Average salary for salespeople = 25,000
Average salary for all employees = 50,000
Ratio of managers to salespeople = 1:2

Let the company have 1 manager and 2 salespeople.
Thus:
Total income for the 1 manager = 1(100,000) = 100,000
Total income for the 2 salespeople = 2(25,000) = 50,000

Case 1: 1 manager, 2 salespeople, no other employees
Average salary for all 3 employees =  \frac{150,000}{3} = 50,000

Case 2: 1 manager, 2 salespeople, and 2 other employees, for a total of 5 workers
Since the average salary for all 5 workers must be 50,000, the total income for all 5 workers = 5(50,000) = 250,000
Total income for the 2 other employees = 250,000 - (100,000 + 50,000) = 100,000
Average salary for the 2 other employees =  \frac{100,000}{2} = 50,000

Case 3: 1 manager, 2 salespeople, and 7 other employees, for a total of 10 workers
Since the average salary for all 10 workers must be 50,000, the total income for all 10 workers = 10(50,000) = 500,000
Total income for the 7 other employees = 500,000 - (100,000 + 50,000) = 350,000
Average salary for the 7 other employees =  \frac{350,000}{7} = 50,000

As the cases above illustrate, it is not necessary that the company be composed only of managers and salespeople.
The only requirement is that, if there are other employees, their average salary (50,000 in Cases 2 and 3 above) must be equal to the average salary for the whole company (also 50,000 in the cases above).

vishy001 · Answer

Is it mentioned or implied in the question that number of employees = number of managers + number of sales people as everyone here are solving? What if it is assumed that number of employees include security, IT staff, CEOs etc? Isn't it the rule in gmat quant to not assume anything and only infer from the question? Since it is not clear what constitutes the number of employees, the question falls flat I feel.

Bunuel · Answer

Yes, the question should have specified that the number of employees equals the number of managers plus salespeople. Without this, you'd have to assume there are only those two types of employees to solve it, otherwise, it would be unsolvable.

For example, if there's 1 manager with a salary of 100, 1 salesperson with a salary of 25, and 1 other employee with a salary of 25, the average salary would be (100 + 25 + 25)/3 = 50. In this case, the ratio of managers to salespeople would be 1:1.

Alternatively, if there are 2 managers with salaries of 100 each, 1 salesperson with a salary of 25, and 3 other employees with salaries of 25 each, the average salary would be (2 * 100 + 25 + 3 * 25)/6 = 50. In this scenario, the ratio of managers to salespeople would be 2:1.

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At a particular company, the average income of managers is $50,000

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At a particular company, the average income of managers is $50,000

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