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Are at least 10 percent of the people in Country X who are 65 years
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Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  21 Jun 2019, 04:22
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VeritasKarishma wrote:
enigma123 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 percent of the population is 65 year old or older
(2) In country X, of the population 65 year old or older, 20 percent of the men and 10 percent of the women are employed


Question: Of the people who are 65+ yrs old, are at least 10% employed?
So say the population is 100, if 20 are 65+ yrs old, the question is that are at least 10% of them (i.e. 2 people) employed?

(1) In country X, 11.3 percent of the population is 65 year old or older
Doesn't tell us anything about employment. Not sufficient.

(2) In country X, of the population 65 year old or older, 20 percent of the men and 10 percent of the women are employed
So this statement talks about only the population which is 65+ yrs old. It says that of those people, of all the men, 20% are employed and of all the women, 10% are employed. So if you take the population of all 65+ yrs old people, can we guess what the employment rate is? It depends on what percent of 65+ people are men and what percent are women. But is there a range in which it must lie? Yes, the rate of employment of all 65+ people will lie between 10% and 20%. If the entire 65+ population is men, then the rate of employment will be 20%. If the entire 65+ population is women, then the rate of employment will be 10%. In case there is a mix of men and women, the rate of employment will lie between 10% and 20%. It will be the weighted average of 10% and 20%.

Answer (B)

This question, though much easier, is similar to the famous piglet question from GMAT Prep. Check it out here: http://www.veritasprep.com/blog/2014/09 ... difficult/


Hi Karishma, ( VeritasKarishma )
Thank you for the detailed explanation. I do have a doubt though.
The question does NOT state that there are ONLY men and women. Why do we not consider the possibility that men are just 2% of the 65+ year olds and women are 3%. The rest are a third gender. This scenario would prove this statement NOT SUFFICIENT.
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  21 Jun 2019, 11:20
LM 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 percent 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.

Show Spoiler
Attachment:
DS5.PNG


(1) In Country X, 11.3 percent of the population is 65 years old or older.

Doesn't talk about employment - Insufficient

(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.

The average will always lie between 10 O& 20 percent
--> So ,we can definitely say that % employed > 10

Sufficient

Option B

Pls Hit Kudos if you like the solution
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  21 Jun 2019, 19:23
(1) In Country X, 11.3 percent of the population is 65 years old or older.

insufficient, as no info about employment rates


(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 correct
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  23 Jun 2019, 00:06
Bunuel wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

Question: is at least 10% of some particular group of people employed? (Don't let the phrase "of the population 65 year old or older" confuse you, refer to it as to some particular group.)


(1) In Country X, 11.3 percent of the population is 65 years old or older.

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


(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.

20% of the men in this group and 10% of the 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.


Answer: B.


Hi Bunuel ,
The question does NOT state that there are ONLY men and women. Why do we not consider the possibility that men are just 2% of the 65+ year olds and women are 3%. The rest are a third gender. This scenario would prove this statement NOT SUFFICIENT.
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  23 Jun 2019, 01:24
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Karmesh wrote:
Bunuel wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

Question: is at least 10% of some particular group of people employed? (Don't let the phrase "of the population 65 year old or older" confuse you, refer to it as to some particular group.)


(1) In Country X, 11.3 percent of the population is 65 years old or older.

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


(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.

20% of the men in this group and 10% of the 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.


Answer: B.


Hi Bunuel ,
The question does NOT state that there are ONLY men and women. Why do we not consider the possibility that men are just 2% of the 65+ year olds and women are 3%. The rest are a third gender. This scenario would prove this statement NOT SUFFICIENT.


As per GMAT, there are only two genders.
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  24 Jun 2019, 22:50
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Karmesh wrote:

Hi Karishma, ( VeritasKarishma )
Thank you for the detailed explanation. I do have a doubt though.
The question does NOT state that there are ONLY men and women. Why do we not consider the possibility that men are just 2% of the 65+ year olds and women are 3%. The rest are a third gender. This scenario would prove this statement NOT SUFFICIENT.


The concept of a third official gender is not popular enough yet and hence, there are only 2 genders as far as GMAT is concerned. This may change in future but right now, we are safe in assuming 2 genders only.
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  30 Sep 2019, 16:10
LM wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

Let n = a number (65 or older, employed)
Question: n ≥ Total Employed/10 ?

(1) In Country X, 11.3 percent of the population is 65 years old or older.
0.113*Total Population = Total Employed
If (65 or older, NOT employed ) = 0, then yes
But, (65 or older, NOT employed) could also be some big portion of n, say 50%, so then it would be no.
Not sufficient.

(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.
Total Employed = #men + #women
n = #men employed + #women employed
n = 2/10*#men + 1/10*#women
Regardless of actual numbers, n will be more than 10% (take 10 men, 10 women, 3/20 = 15%)
Sufficient.
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Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  07 Oct 2020, 10:27
Note that this question only concerns itself with the population of people who are 65 years old or older. The people who are younger than this age group need not concern us.

We are asked to determine if at least one-tenth of the people in this group are employed.

(1) In Country X, 11.3 percent of the population is 65 years old or older.

We have no information about the employment rates. So this statement is INSUFFICIENT.

(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.

Let the number of men and the women in this group be M and W respectively.

Then, we have:

Number of employed men in this group = 0.2M
Number of employed women in this group = 0.1W

The fraction of men and women who are employed in this group = (0.2M + 0.1W)/(M+W). This fraction must be greater than 1/10.

(0.2M + 0.1W)/(M+W) > 1/10

This reduces to:

M>0

Since we know that M is a positive non-zero quantity, we know that at least 10% of the population of the people who are aged 65 years or older are employed.

Note that this equation is simply a reflection of the concept of "weighted averages". The weighted average will lie somewhere between the two extreme values (here these values are 10% and 20%).
SUFFICIENT

ANSWER: (B)
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  20 Nov 2020, 02:46
Bunuel wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

Question: is at least 10% of some particular group of people employed? (Don't let the phrase "of the population 65 year old or older" confuse you, refer to it as to some particular group.)


(1) In Country X, 11.3 percent of the population is 65 years old or older.

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


(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.

20% of the men in this group and 10% of the 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.


Answer: B.



Is the question not asking 10% of total population?
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  20 Nov 2020, 03:25
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jchaplot wrote:
Bunuel wrote:
Are at least 10 percent of the people in Country X who are 65 years old or older employed?

Question: is at least 10% of some particular group of people employed? (Don't let the phrase "of the population 65 year old or older" confuse you, refer to it as to some particular group.)


(1) In Country X, 11.3 percent of the population is 65 years old or older.

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


(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.

20% of the men in this group and 10% of the 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.


Answer: B.



Is the question not asking 10% of total population?


No. Are at least 10 percent of the people in Country X who are 65 years old or older employed?
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Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  23 Nov 2020, 13:26
LM 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 percent 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.

Show Spoiler
Attachment:
DS5.PNG


(1) 11.3% of the population is 65 years old or older. However, we don't know the percentage of people that are employed. It's possible 0% are employed or 100% are employed. INSUFFICIENT.

(2) Of the population 65 years old or older 20% of men and 10% of women are employed. No matter the ratio of men to women, given 20% men and 10% are employed, we will have greater than 10% employment. This is because the percentage must lie between 10% and 20%. SUFFICIENT.

Answer is B.
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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink] New post  12 Apr 2021, 18:14
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Video solution from Quant Reasoning at 11:45
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

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Re: Are at least 10 percent of the people in Country X who are 65 years [#permalink]
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