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Women and Tenured Professors

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Women and Tenured Professors [#permalink] New post 14 Nov 2009, 08:33
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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 question from magoosh, i guess a Sub-600 level question.
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Re: Women and Tenured Professors [#permalink] New post 14 Nov 2009, 19:46
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ctrlaltdel 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?

A question from magoosh, i guess a Sub-600 level question.
Any Shortcut?


answer is 75%

total women = 60%
total men = 40%

total tenured = 70% (both men and women)

therefore, women tenured + women professors + men tenured = 90%

men tenured = 30%
but question wants to know the percent of men that are tenured
30%/40% = 75%
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Re: Women and Tenured Professors [#permalink] New post 14 Nov 2009, 20:49
Quote:
therefore, women tenured + women professors + men tenured = 90%

men tenured = 30%


Not clear with the above part of the explanation??
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Re: Women and Tenured Professors [#permalink] New post 14 Nov 2009, 21:29
abhi758 wrote:
Quote:
therefore, women tenured + women professors + men tenured = 90%

men tenured = 30%


Not clear with the above part of the explanation??


well there are four options:

women tenured-men tenured
women not tenured-men not tenured

they are asking for professors that are women, tenured or both
that means that they want everyone except men not tenured
but women make up 60% (both tenured and not tenured) that leaves 30% tenured men professors
90%-60%
men tenured = 30%
women tenured = 40%
total tenured = 70%
women not tenured = 30%
total women = 60%
total men = 40%

and if you wanted to calculate men-not tenured = 10%
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Re: Women and Tenured Professors [#permalink] New post 14 Nov 2009, 21:44
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another way to think about it:

they are asking for professors who are women, tenured or both

Total women = 60%
Total tenured = 70%
Total both = 130%

But adding both means we are double-counting women-tenured
130-90 = 40% are women tenured or the number being double-counted
That leaves 30% men tenured
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Re: Women and Tenured Professors [#permalink] New post 15 Nov 2009, 02:04
Kudos for both the methods. :)
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Re: Women and Tenured Professors [#permalink] New post 15 Nov 2009, 04:15
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With problems like this were you are comparing two qualities, I think a simple table would be the easiest way to solve:

It was also easier to assume that there was a total of 10 people in the university. This is easier to deal with than percentages for me:

---------------------WOMEN----------MEN
TENURED---------------A---------------B--------7
NOT TENURED----------C---------------D--------3
-----------------------6----------------4-------10

Since 90% of the professors are women or tenured or both, this means that A+B+C = 9

So D = 10-(A+B+C) = 1, which means B is equal to (4-1) = 3.

Since we want the percentage of men tenured, it would be B/(B+D) or 3/4 = 75%
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Re: Women and Tenured Professors [#permalink] New post 15 Nov 2009, 05:13
Quote:
A question from magoosh, i guess a Sub-600 level question.


Its not a very difficult question I agree, but is it really below level 600?

I wonder if there is anyway to truly determine the level of a question.
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Re: Women and Tenured Professors [#permalink] New post 15 Nov 2009, 05:38
Of all the questions i solved in Magoosh, this is one of the 3 questions which went wrong.
And i personally feel magoosh has sub 600 or upto 650 level not more than that.

Others please comment....
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Re: Women and Tenured Professors [#permalink] New post 15 Nov 2009, 10:49
I really can't see this problem being higher than a 600/650 level question.

There really arn't more than three steps to solving this problem (three very straightforward steps).
Re: Women and Tenured Professors   [#permalink] 15 Nov 2009, 10:49
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