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We have 4 groups: Unemployed men, Unemployed women, Employed men, and Employed women. lets call them UM, UW, EM, and EW.

We need to know the value of EW/(EW+UW) We know that: UM+UW+EM+EW=100 EM+EW=64 EM=48

It follows that EW=16

But how do you reach a value for UW?

You can't, but that question is not asked so you don't care!
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

64% of the population are employed. If 48% of the population are males who are employed, what % of the females are employed?

Consider this, and tell me where I make my error:

60 males, 48 of whom are employed 40 females, 16 of whom are employed. This satisfies both conditions, and the answer is 40%

50 males, 48 of whom are employed. 50 females, 16 of whom are employed. This satisfies both conditions, and the answer is 32%

What am I doing wrong?

stoolfi,

I see where you're having the conflict in meanings.

Let me reword the question:
In city X, 64% of the population is employed. If 48% of the total male population is employed, what % of the total female population is employed?

I don't know if I have you banging your head against the wall yet, but I as read your rephrasing:In city X, 64% of the population is employed. If 48% of the total male population is employed, what % of the total female population is employed? I am still hapless.

My conclusion is that the female population must be employed at a rate greater than 64%. Since the male population is less employed (as a percentage) than the total population, then the female population must be more employed (as a percentage) than the total population.

I don't know if I have you banging your head against the wall yet, but I as read your rephrasing:In city X, 64% of the population is employed. If 48% of the total male population is employed, what % of the total female population is employed? I am still hapless.

My conclusion is that the female population must be employed at a rate greater than 64%. Since the male population is less employed (as a percentage) than the total population, then the female population must be more employed (as a percentage) than the total population.

Ok. Here's how I did it, let me know if it makes sense to you.

We know that 48% of the total males are employed, so now have to find the percentage that contributes to 64% employed. That is ratio of employed to total males.
Ratio = 48/100

Find the percentage that this ratio contributes towards total employement.
We get,
64% * Ratio = 64% * 48/100 = 30.72% ..... this is towards the 64% employed

% Total Employed = % Employed Male + % Employed Female
64 = 30.72 + % EF
% EF = 64 - 30.72
% EF = 33.28

And you can round it up or down. I rounded up because I didn't know the exact decimal values because didn't have paper-pen/calculator. I figured it'd be somewhere around 33.5 so might as well round it up.