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Generalizations about aggregate percentage - GMATPrep

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Generalizations about aggregate percentage - GMATPrep

by barrelbowl » Sat Dec 17, 2011 8:48 am
Hey guys this may be a dumb question, but it is pertaining to the following question from GMAT prep.

Are at least 10% of people 65 and older employed?

A) 11.3% of the population is 65 or older
B) Of those 65 and older, 20% of the men and 10% of the women are employed.

[spoiler]OA: B[/spoiler]

I chose B, but I was wondering because the question is asking if AT LEAST 10% of the people 65+ are employed...

..could we have generalized that as long as the splits (men/women employed) are each greater than 10% then the aggregate sample will be greater than 10%? In other words is there a 'percentage threshold' about making generalizations about a population, from a split up sample?
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by GmatMathPro » Sat Dec 17, 2011 9:57 am
barrelbowl wrote: ..could we have generalized that as long as the splits (men/women employed) are each greater than 10% then the aggregate sample will be greater than 10%? In other words is there a 'percentage threshold' about making generalizations about a population, from a split up sample?
Yes, the overall percentage must lie between 10% and 20%. You can see this by thinking about it in terms of extremes. If every single person over 65 were a woman, then the overall percentage would also be 10%. Adding the men, who work at a rate of 20% clearly would not make the overall percentage go down, so the overall percentage must be greater than 10%. From the other side, if every single person were a man, then the overall percentage would be exactly 20%. Adding the women, who work at a rate of 10% clearly would not make the overall percentage go up, so the overall percentage must be less than 20%. The phrasing of the question implies that there are at least some men and at least some women, so the overall percentage must be somewhere between 10% and 20%. If we had needed to find the exact overall percentage we would need to know the exact ratio of men to women. If the number of men and women were equal, the overall percentage would be right in the middle: 15%. If there are more men then women, it would be closer to the men's percentage, 20%, and if there are more women than men, it would be closer to the women's percentage, 10%. If you want to learn more about this type of approach, try searching for "weighted averages" on the forum or on google.
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by barrelbowl » Sat Dec 17, 2011 12:20 pm
Thanks! I should have recognized it as a weighted average.. the explanation was very useful.
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by [email protected] » Sat Feb 18, 2012 5:55 am
good tricky but I would say that a good chiki sum!!!
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