Problem Solving

At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured or both, then what percent of the men are tenured?

a) 25.0
b) 37.5
c) 50.0
d) 62.5
e) 75

I created a table for this

Assume there are 100 professors



+---+---+---+-----+
| | M | W | Tot |
+---+---+---+-----+
| T |30 | | 70 |
+---+---+---+-----+
| N |10 | | 30 |
+---+---+---+-----+
|Tot|40 | 60|-----|
+---+---+---+-----+

From the information in the question, I know that 60% are women so there are 60 women and 40 men. 90% are women,tenured or both. So 10% are men who are not tenured. So there are 10 non-tenured men.

Therefore 30 tenured men.

30/40 = 75%

IMO E (75%)

I also assumed 100 professors, 60 of whom are women and 40 men.

90 professors are either women or tenured or both.
Since I have a total of 60 women this leaves us with 90-60=30 who are tenured but not women, ergo tenured men.
Since we have a total of 40 men and 30 are tenured, there must be 10 who are not.
Therefore: 30/40=3/4=75%

imo 75%

Nice work! The official answer is E.

Here's a link to a video explanation that gives an overview of the "double matrix" technique: GMAT

Text explanation: