Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving

Question: Paracelsus University has two kinds of professors, academic professors and professional professors. At Paracelsus University, 60% of the professors are academic professors and 70% of the professors are tenured. If 90% of the professors at Paracelsus University are academic professors or tenured or both, then what percent of the professional professors there are tenured?

1. 25
2. 37.5
3. 50
4. 62.5
5. 75

“Paracelsus University has two kinds of professors, academic professors and professional professors. At Paracelsus University, 60% of the professors are academic?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1:

Tenured professor = 70
Academic professor = 60
If 90% of the professors at Paracelsus University are academic professors or tenured or both then the professional non-tenured = 10

Correct option: E

Approach Solution 2:

100 professors
60 are academic, 40 are 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

\(\frac{30}{40}=\frac{3}{4}\)=75%

Correct option: E

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