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At a certain university, all employees can be categorized as either pr

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At a certain university, all employees can be categorized as either professors or administrators, and the average professor earns $18,000 more than the average administrator. How much less does the average administrator earn than the average employee at the university?

(1) The average salary of a professor is $88,000.

(2) There are twice as many administrators as professors.
[Reveal] Spoiler: OA

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Re: At a certain university, all employees can be categorized as either pr [#permalink]

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New post 18 May 2017, 11:35
Bunuel wrote:
At a certain university, all employees can be categorized as either professors or administrators, and the average professor earns $18,000 more than the average administrator. How much less does the average administrator earn than the average employee at the university?

(1) The average salary of a professor is $88,000.

(2) There are twice as many administrators as professors.


Analyzing question stem -

Let there be "x" professors & "y" administrators. Also let the average salary of administrator be "a"
So average salary of professor = a+18,000
This implies average salary of ALL the employees will be = {(a+18,000)*x+a*y} / (x+y)____[i.e. total salary of all employees upon total number of employees]
As the question asks us to find out the difference between administrator's average salary and average salary of all employees

= {(a+18,000)*x+a*y}/(x+y) - a = (ax+ay+18000x - ax+ay) / (x+y)
Or, 18000x / (x+y) -----------------(Eq.1)

So we only need relation between number of professors and number of administrators.

Statement 1: Provides no info about number of profs & number of admin. Hence Insufficient

Statement 2: Directly provides the relation between no. of profs. & no. of admin. Hence sufficient. (you can substitute the value in eq.1 to get the exact value but for DS it is not required)

Hence Option B

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Re: At a certain university, all employees can be categorized as either pr [#permalink]

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New post 19 May 2017, 14:11
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Let:

Average Salary of an Administrator = $A
Average Salary of an Professor = $A + 18000

Number of Administrators = M
Number of Professors = N


Average Salary of all Employees (Administrators + Professors)

= [MA + N(A+1800)]/(M+N)

How much less does the average administrator earn than the average employee at the university

= [MA + N(A+1800)]/(M+N) - A

= (MA + NA + 18000N - MA - NA)/(M+N)

= (18000N)/(M+N)

To Solve this we would need

Number of Administrator and Professors

Statement 1:The average salary of a professor is $88,000.

This statement does not give the information we need. Hence is insufficient.

Statement 2:There are twice as many administrators as professors.

This means => M = 2N

Substituting in the above equation

= (18000N)/(M+N) = 18000N/(2N+N) = 18000N/3N = 6000

This statement is sufficient.

Answer is B

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Re: At a certain university, all employees can be categorized as either pr [#permalink]

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New post 19 May 2017, 22:58
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Statement 1. Average salary of a professor is 88000, that of administrator becomes 88000-18000 = 70000.
Let number of Administrators be A, number of professors be P.

Average salary per employee = (70000*A + 880000*P)/(A+P)
This cant be found unless we either know the values of A & P or the ratio A:P.
So Insufficient.

Statement 2. Ratio of Administrators (A) and Professors (P) is 2:1. Let A = 2s, P = 1s.
Let Average salary of an administrator be x, that of professor becomes (x+18000).

Net average salary per employee = [x*2s + (x+18000)*1s]/[2s+1s] = x+6000.
While average salary per Administrator = x
Their difference = x + 6000 - x = 6000. So Sufficient.

Hence answer should be B

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Re: At a certain university, all employees can be categorized as either pr [#permalink]

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New post 20 May 2017, 04:58
Bunuel wrote:
At a certain university, all employees can be categorized as either professors or administrators, and the average professor earns $18,000 more than the average administrator. How much less does the average administrator earn than the average employee at the university?

(1) The average salary of a professor is $88,000.

(2) There are twice as many administrators as professors.


Administrator average pay = $x
Professor's average pay = $(x+18000)

Question: AVerage of employee pay - x = ?

P.S. To answer the question we need average of all employees and to calculate avergae of all employees we need ration of number of Administrators to the number of Professors

Statement 1: The average salary of a professor is $88,000.
NOT SUFFICIENT

Statement 2: There are twice as many administrators as professors.
We get the ratio of Administrators to the Professors
SUFFICIENT

Answer: option B
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Re: At a certain university, all employees can be categorized as either pr [#permalink]

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New post 10 Aug 2017, 02:54
Bunuel wrote:
At a certain university, all employees can be categorized as either professors or administrators, and the average professor earns $18,000 more than the average administrator. How much less does the average administrator earn than the average employee at the university?

(1) The average salary of a professor is $88,000.

(2) There are twice as many administrators as professors.


Given : All employees can be categorized as either professors or administrators
P = A +18000
Let P,A,E be the avergae salaries of Professors, Administrators and Employees.

DS: E - A = ?

Statement 1 : P = 88000
A = 70000
But we don't know the numbers of professors and administrators. So we can't find the avergae salary of the total number of employees.

NOT SUFFICIENT

Statement 2 : Let p, a , e be the number of professors, administrators and employees.

So, e = a + p
also a = 2p

Now average salary of employees E = (a*A + p*(A+18000))/(a+p) = (2p*A + p*(A+18000) )/(2p+p) = (3A + 18000)/ 3 = A+ 6000
So E- A = 6000

SUFFICIENT

Answer B
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Re: At a certain university, all employees can be categorized as either pr   [#permalink] 10 Aug 2017, 02:54
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