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?

75

Appreciate your help!

Assuming 100 professors are in university, 60 are women so 40 are men. 70 are tenured so 30 are not tenured. Now 90 professors are women, tenured or both. So number of professors both women and tenured are 70+60-90=40. So number of men tenured are 70-40=30.

Please let me know if the answer is correct

venmic wrote: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?

75

Appreciate your help!

Well, Since its given, 90% of the people are either women/tenured or both, that leaves us with 10% of men who are not tenured( the only possible case not covered). We also know 40% of profs are men (given 60% are women).

Therefore, % of men tenured = Total % of men - % of men not tenured.

=40-10.
% of tenured men (considering total inclusive of women) = 30%.

But the question asks us to find this as a percentage of men only

so 30 of the 40 men are tenured, which is nothing but 75%.
Hope you got it,

venmic wrote: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?

75

Appreciate your help!