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Idea of overlapping sets

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Idea of overlapping sets

by lkcr » Tue May 22, 2012 12:34 am
Is at least 10% of the population in Country X who are 65yrs old or older employed?

1. In country X, 11.3% of the population is 65yrs old or older
2. In country X, of the population 65yrs old or older, 20% of the men and 10% of the women are employed.

Ideas / Suggestions / Answers?

I initially thought E, since even combined I cannot tell from statement 2 the % of men to the % of women in the subset of 65yrs old or older but the question source says B.....
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by Anurag@Gurome » Tue May 22, 2012 12:36 am
lkcr wrote:Is at least 10% of the population in Country X who are 65yrs old or older employed?

1. In country X, 11.3% of the population is 65yrs old or older
2. In country X, of the population 65yrs old or older, 20% of the men and 10% of the women are employed.
(1) There is no information of the people employed. So, (1) is NOT SUFFICIENT.

(2) Now, the problem can be viewed as an weighted average problem.
20% of the men + 10% of women are employed. Although the number of men and women are not known, but the employment should be greater than 10% and less than 20%. So, (2) is SUFFICIENT.

The correct answer is B.
Last edited by Anurag@Gurome on Sun Mar 03, 2013 7:20 am, edited 1 time in total.
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by aneesh.kg » Tue May 22, 2012 12:57 am
lkcr wrote:Is at least 10% of the population in Country X who are 65yrs old or older employed?

1. In country X, 11.3% of the population is 65yrs old or older
2. In country X, of the population 65yrs old or older, 20% of the men and 10% of the women are employed.

Ideas / Suggestions / Answers?

I initially thought E, since even combined I cannot tell from statement 2 the % of men to the % of women in the subset of 65yrs old or older but the question source says B.....
Let the number of Males and Females who are 65 years or older be M and F respectively.

Since your doubt is about Statement(2), lets go to it first.

Statement(2):
Number of people employed in this age group= 20% of M + 10% of F
% of people employed in this age group = (20% of (M/(M + F)) + 10% of (F/(M + F))

This is a classic weighted mean concept.
If the values of two groups are 20% and 10%, then the average of the two groups taken together always be between 10 and 20.

So, in this case the percentage of people 65 years or older employed will vary lie between 10% and 20%. The exact value will depend on the values of M and F, but that's none of our concerns in this problem.

This statement is SUFFICIENT

Statement(1) is clearly INSUFFICIENT

[spoiler](B)[/spoiler] is correct.
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by GmatKiss » Tue May 22, 2012 2:26 am
This question tests understanding of the language than understanding of maths :)
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