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# Are at least 10 percent of the people in Country X who are

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Are at least 10 percent of the people in Country X who are [#permalink]  22 Jan 2009, 09:22
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Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In Country X, 11.3% of the population is 65 years old or older
(2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.
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Re: Stats [#permalink]  22 Jan 2009, 09:56
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study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

Clearly statement 1 is not suffcieint

statmnt 2:

10% W and 20% M. Even we don't the no of Men and Women it is clear that
employment must be between 10 and 20
Sufficient.
B.
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Re: Stats [#permalink]  22 Jan 2009, 10:07
x2suresh wrote:
study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

Clearly statement 1 is not suffcieint

statmnt 2:

10% W and 20% M. Even we don't the no of Men and Women it is clear that
employment must be between 10 and 20
Sufficient.
B.

can u explain how the employment will be between 10 and 20 percent
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Re: Stats [#permalink]  22 Jan 2009, 10:45
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ALD wrote:
x2suresh wrote:
study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

Clearly statement 1 is not suffcieint

statmnt 2:

10% W and 20% M. Even we don't the no of Men and Women it is clear that
employment must be between 10 and 20
Sufficient.
B.

can u explain how the employment will be between 10 and 20 percent

its not employment of total country people.. its employment of people who are 65 years old or older is between 10 and 20

Question:Are at least 10 percent of the people in Country X who are 65 years old or older employed?
rewrite the question

Is employment atleast 10 percent of people who are 65 year old or older?

From 65+ group 10% W employed and 20% M employed.
W = no of women
M = no of men

employment(65+group) = 10*W/(M+W) + 20*M/(M+W) = weighted averge.
If all are women . M=0 and employment =10 (Minimum value)
if all are men W=0 and employment = 20
For any other ratio. it should be between 10 and 20.
So employment is alwasy >=10
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Re: Stats [#permalink]  23 Jan 2009, 05:36
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

x2suresh, i couldn't really understand your logic.

St B: If country X has 200 people. 65+ are 20 of the 200 people. Of the 20 , 10 are male and 10 female. Then the number employed will be 20% of 10 and 10% of 10 which is equal to 3.
3 is not anywhere close to 10% of 200.

On the other hand If country X has 200 people. 65+ are 150 of the 200 people. Of the 150 , 100 are male and 50 female. Then the number employed will be 20% of 100 and 10% of 50 which is equal to 25, which is over 10% of 200.
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Re: Stats [#permalink]  23 Jan 2009, 06:53
study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

x2suresh, i couldn't really understand your logic.

St B: If country X has 200 people. 65+ are 20 of the 200 people. Of the 20 , 10 are male and 10 female. Then the number employed will be 20% of 10 and 10% of 10 which is equal to 3.
3 is not anywhere close to 10% of 200.

On the other hand If country X has 200 people. 65+ are 150 of the 200 people. Of the 150 , 100 are male and 50 female. Then the number employed will be 20% of 100 and 10% of 50 which is equal to 25, which is over 10% of 200.

I agree that quesiton is poorly worded.

Are at least 10 percent of the people in Country X who are 65 years old or older employed?

are atleast 10% of people who are 65+ .. are employed ?

are atleast 10% of 20(people who are 65+) are employed?
3 people are employer.. 3/20*100=15% >10%

I hope you got it.

What is the source of this question.
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Re: Stats [#permalink]  23 Jan 2009, 09:14
B shld be the ans
The main point in this question is that it asks the percentage of 65+ age grp who are employed. So we need not know the total no of ppl .
statement 1 is insufficient.Its not telling anything abt employement. so A and D are out
St 2: suppose 65+ age grp ppl are 100 in no. Then out of these 20 men and 10 women are employed. That means employed %age ppl in this category is 30%. Hence suff

study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

1. In Country X, 11.3% of the population is 65 years old or older
2. In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.
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Re: Stats [#permalink]  26 Nov 2009, 04:23
ritula wrote:
B shld be the ans
The main point in this question is that it asks the percentage of 65+ age grp who are employed. So we need not know the total no of ppl .
statement 1 is insufficient.Its not telling anything abt employement. so A and D are out
St 2: suppose 65+ age grp ppl are 100 in no. Then out of these 20 men and 10 women are employed. That means employed %age ppl in this category is 30%. Hence suff

study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

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

B is indeed the answer. However, it is important to point out that we do not know the ratio of Men/Women above age 65. For example, if 65+ group have 100 ppl and all are women, we would only have 10 employed. Since the question asked at least 10, it is sufficient. I would just like to point out that people need to consider the absolute "minimum" since we are not given men/women ratio of the group.

Another point is that, you cannot simply added 10% and 20% to get the total employed to be 30%. The total have to be between 10% and 20%....

I am not sure if this is reading too much into the question
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Re: Stats [#permalink]  26 Nov 2009, 19:21
ritula wrote:
B shld be the ans
The main point in this question is that it asks the percentage of 65+ age grp who are employed. So we need not know the total no of ppl .
statement 1 is insufficient.Its not telling anything abt employement. so A and D are out
St 2: suppose 65+ age grp ppl are 100 in no. Then out of these 20 men and 10 women are employed. That means employed %age ppl in this category is 30%. Hence suff

The red part is not correct.
Men + Women = 100, you can say 20% of men is 20 just in case women = 0.
Similarly, Women = 10 only when Men=0.
So employ 65+ cann't be 10+20=30. Instead, it is between 10-20.
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Re: Stats [#permalink]  27 Nov 2009, 13:27
yes i think ritula was just a bit confused

assuming a 50/50 Man/woman split youd have 10 men employed and 5 women employed = 15% employment for this age group

range must be 10-20% inclusive. immediately i considered an all women population even though technically ridiculous
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Re: Stats [#permalink]  30 Jul 2010, 23:57
Discussions are always the main source of accurate information and to ensure a comfortable results, you can get immediate and reliable information, which will definitely help you in every area of your concern.
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Re: Stats [#permalink]  11 Sep 2010, 11:56
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study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In Country X, 11.3% of the population is 65 years old or older
(2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.

Question: is at least 10% of some particular group of people employed?

(1) This particular group composes 11.3% of total population. Clearly insufficient, as no info about employment rates in this group.

(2) 10% of men in this group and 20% of women in this group are employed. No matter how many men and women are in this group, more than 10% will be employed. This is because the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages, so percent of employed people in this group is between 10% and 20%. Sufficient.

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Re: Stats [#permalink]  10 Mar 2011, 22:37
got it wrong but thanks for the explanation
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  18 Apr 2012, 18:01
Wow... the wording on this question is very tough. For the longest time i thought it was asking for 10% of the entire population. Thanks for the clarification.
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  30 May 2012, 08:14
Statement 1: Insufficient, there is no info on employed and the question asks about the employed.

Statement 2: If it's intuitively not clear, draw a tree diagram. from x emerges two branches: 65 years or older people and less than 65. we are not concerned about the second branch. of the first branch of 65 years or older, they can be either men or women. from men, we can draw two branches, one for the employed, one for unemployed. we do the same for the women. we are told that the employed category % for men is 20%, for women 10%. at this point, forget everything and think: if of all the grandmas, 10% are employed and of all the grandpas 20% are employed, then at least 10% of these grandparents are employed. It should make sense for at least two reasons: 1. there is no "third" sex as far as i know. 2. Uncle Sam's social security system is bankrupt making retirement a dream for many.
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  02 Jul 2012, 16:37
I set out the equation ...(10%*F + 20%*M)/ (F + M) ? >= 10%, where F and M represent the number of females and males in the older than or equal to 65 group. I then subbed in the lowest numbers 1 and 1 for both female and male (potentially you can also use 0), and the result was 15%. Since this is greater than 10%, statement B is sufficient.
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  23 Jul 2013, 23:47
The person has tagged this question as overlapping sets. I seem to face the same problem How can you tell the difference between an overlapping set and weighted average problem? They seem to be worded very similarly.

Statement 2 equation is

$$\frac{10% F + 20% M}{F + M}> = \frac{10}{100}$$
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  23 Aug 2014, 11:31
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  30 Aug 2014, 10:53
Bunuel wrote:
study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In Country X, 11.3% of the population is 65 years old or older
(2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.

Question: is at least 10% of some particular group of people employed?

(1) This particular group composes 11.3% of total population. Clearly insufficient, as no info about employment rates in this group.

(2) 10% of men in this group and 20% of women in this group are employed. No matter how many men and women are in this group, more than 10% will be employed. This is because the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages, so percent of employed people in this group is between 10% and 20%. Sufficient.

Hi Bunuel,

Question regarding your explanation of Stm2.

It says that 10% of m over 65 and 20 % of w over 65 are employed. How does this translate into 10% of over 65 being employed? If it's a weighted average problem, then don't we need to know the number of m/f over 65 to prove sufficiency?
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Re: Are at least 10 percent of the people in Country X who are [#permalink]  31 Aug 2014, 23:53
Expert's post
russ9 wrote:
Bunuel wrote:
study wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In Country X, 11.3% of the population is 65 years old or older
(2) In Country X, of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.

Question: is at least 10% of some particular group of people employed?

(1) This particular group composes 11.3% of total population. Clearly insufficient, as no info about employment rates in this group.

(2) 10% of men in this group and 20% of women in this group are employed. No matter how many men and women are in this group, more than 10% will be employed. This is because the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages, so percent of employed people in this group is between 10% and 20%. Sufficient.

Hi Bunuel,

Question regarding your explanation of Stm2.

It says that 10% of m over 65 and 20 % of w over 65 are employed. How does this translate into 10% of over 65 being employed? If it's a weighted average problem, then don't we need to know the number of m/f over 65 to prove sufficiency?

Let me ask you a question: the average height of girls in a class is 1.5 meters and the average height of boys in the class is 1.6 meters. Can the average height of all students there be less than 1.5 meters or more than 1.6 meters?
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Re: Are at least 10 percent of the people in Country X who are   [#permalink] 31 Aug 2014, 23:53

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