Paracelsus University has two kinds of professors, academic professors

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100 professors
60 are academic, 40 professional
70 tenured, 30 not tenured

90 are Academic, or tenured, or both
90 = A + T - ANT
ANT = Academic and Tenured = 40

70 total Tenured - 40 Academic and Tenured = 30 professional tenured

40 professional - 30 professional = 10 professional

the trick here is to recognize what the question is asking.
It wants the subset percentage of the professionals who are tenured

total professionals = 40
total professionals tenured = 30

30/40 = 3/4 = 75%

Dont we get negative equation here?

90/100x = 60/100x +70/100x + y
Here both value (y) = -40/100x
How can the value be negative? Where am I going wrong?

Bunuel - Can you help ?

­
There are 4 categories of profs here:
1) Academic + Tenured
2) Academic + Not tenured
3) Professional + Tenured
4) Professional + Not tenured

We are given that (1) + (2) + (3) = 90% (Academic or tenured or both)
=> Professional + Not tenured = 10%

Because 60% of profs are Academic, 40% are professional. So, now we have the following ->

- Total Professional profs: 40% of total number of profs
- Professional + Not tenured = 10% of total number of profs
=> Professional + Tenured = 40-10 = 30% of total number of profs

What percent of the professional professors there are tenured?
30/40 = 75%. Choice E.
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Harsha
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