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Are at least 10 percent of the people in Country X who are 65 years 21 Jun 2019, 05:22
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VeritasKarishma
enigma123
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/09 ... difficult/
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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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Are at least 10 percent of the people in Country X who are 65 years 24 Jun 2019, 23:50
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Karmesh


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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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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Are at least 10 percent of the people in Country X who are 65 years 12 Apr 2021, 19:14
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Video solution from Quant Reasoning at 11:45
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Are at least 10 percent of the people in Country X who are 65 years 19 Jun 2021, 04:41
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In country X, out of all the people who are at least 65 years old, are at least 10 percent of them employed?

From statement I alone, 11.3 percent of the total population of Country X is at least 65 years old.
This is not sufficient to say how many of them are employed.

Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, out of all the people in country X who are at least 60 years old, 20 percent of the men and 10 percent of the women are employed.

This means a minimum of 10 percent of people in this age group are definitely employed. Statement II alone is sufficient to answer the question with a YES. Answer options C and E can be eliminated.

The correct answer option is B.

Hope that helps!
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Are at least 10 percent of the people in Country X who are 65 years 07 Aug 2021, 10:02
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Total no of people in country is not known.Then how it is concluded that 10% of people (who are 65 or older) employed?
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Are at least 10 percent of the people in Country X who are 65 years 13 Aug 2021, 22:00
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LM
Are at least 10 percent of the people in Country X who are 65 years old or older employed?
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(1) In Country X, 11.3 percent of the population is 65 years old or older.
We cannot conclusively decide on the same since we have no information on the employability

(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 ys assume there are 10 people then 2 men and 1 women are employed either we will yield greater than 10 percent
we cannot assume a population to be lowe than this since it will not involve in whole numbers and people cannot be fractions
Therefore clearly sufficient
Hence IMO B
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Are at least 10 percent of the people in Country X who are 65 years 17 Aug 2021, 11:54
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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 percent of the population is 65 years old or older.


Statement 1 says about the percent population of 65 years old or older. No information regarding their employment. So clearly 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.

In 65 years old or older group, there will be both men and women. Its given that 20 % men are employed and 10 % percent women are employed. That means by applying the basic concept of weighted average , we can say that at least 10 percent of people in the group are employed. Hence sufficient .Hence sufficient.

Option B is the answer.

Example: Assume there are 60 men and 40 women in the group. So total 100 people.
20 percent of men are employed i.e 20 % of 60 = 12.
10 percent of women are employed i.e 10 % of 60 = 6.

Total percent of people employed in the group \(= \frac{(12+6)}{100}*100\) = 18 %

As per the weighted average concept, Percent of people employed in the group should lie between 10 % and 20 % i.e. min of 10 % guaranteed.


Thanks,
Clifin J Francis,
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Are at least 10 percent of the people in Country X who are 65 years 28 Oct 2021, 05:23
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VeritasKarishma
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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 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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/09 ... difficult/
Show more

I understood the part saying that if we assume the entire population is male, then the average will be 20%, and same with the women's percentage. But when we mix the population and we dont know how many men and women are there, then how can I be sure that 10% of men (idk how many) and 20% of females is going to be in between 10 and 20?
How can I be sure of that in a logical way? Could you please explain that part in detail pls?

Bunuel VeritasKarishma @scotttragettestprep
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Are at least 10 percent of the people in Country X who are 65 years 28 Oct 2021, 21:14
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VeritasKarishma
enigma123
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/09 ... difficult/

I understood the part saying that if we assume the entire population is male, then the average will be 20%, and same with the women's percentage. But when we mix the population and we dont know how many men and women are there, then how can I be sure that 10% of men (idk how many) and 20% of females is going to be in between 10 and 20?
How can I be sure of that in a logical way? Could you please explain that part in detail pls?

Bunuel VeritasKarishma @scotttragettestprep
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Chitra657

Think of it this way:
You have a 100 boys weighing 50 kgs each and 100 girls weighing 70 kgs each.

Now you pick some of these kids. You don't know how many boys and how many girls. What can their average weight be?

If we pick only boys, their average weight will be 50 kgs (since each is 50 kgs).
If we pick only girls, their average weight will be 70 kgs (since each is 70 kgs).
Now what happens if we pick some boys and some girls? What will the average weight of the kids be? It will depend on how many boys and how many girls we pick. But one thing we can be sure of - the average will lie somewhere between 50 kgs and 70 kgs. Can the average be say 10 kgs? No. When each person is either 50 kgs or 70 kgs, how can the average be 10 kgs? Similarly, can the average be 90 kgs? No. Again, when each person is either 50 kgs or 70 kgs, how can the average be 90 kgs? You need at least one person to be much more than 90 kgs to get the average to 90.
The average will always lie between 50 and 70 kgs.

Similarly, considering the 65+ yrs old people, if 10% women and 20% men are employed, we can say that total percentage of people employed will lie between 10% and 20%.
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Are at least 10 percent of the people in Country X who are 65 years 21 Nov 2021, 11:59
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VeritasKarishma
enigma123
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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/09 ... difficult/
Show more

I have one doubt - I got why avg percentage will lie in between 10 to 20 %. But that percentage is of the people who are age of 65 or higher. How can we compare this with total population? Question is asking about total population. Please clarify .
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Are at least 10 percent of the people in Country X who are 65 years 22 Nov 2021, 22:46
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While I think that Bunuel's method (weighted average) is preferred, I used extreme extents.

Say there are 100 people, so 20% men = 20 and 10% women = 10. Total of 30/100, or 30% sufficient.
Say there are only 10 people. So 20% men = 2, 10% women = 1. Total of 3/10, or 30%, sufficient.

We can test more cases if not feeling comfortable, but we can see that if 2 extents provide the same percentage, then some principal here stays constant or unchanged if you will - no matter what.

Option B.
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Are at least 10 percent of the people in Country X who are 65 years 28 Dec 2023, 06:03
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LM
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
Show more

Edit: \frac{AD}{BCE}

From St 1. we have only the population of the country not the number of people employed; Not sufficient
St. 2: Consider this information as a sum of averages, we know that if we have two numbers (1,10) their average would always be greater than one no matter how many times you take one in the counting like 1+1+1+1+1+10 divided by 6 will be greater than 1.
With the same concept no matter the population of male and female we know that the percentage of population of employed 65 or + would be greater than 10%
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Are at least 10 percent of the people in Country X who are 65 years 27 May 2025, 10:30
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this is how algebraically i understood why B

F + M = Total
atleast 10 % so, 0.1F+0.1M
given : 0.2M+0.1F so thats more than required or atleast required
so hence B is sufficient

LM
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
Show more
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Are at least 10 percent of the people in Country X who are 65 years 29 May 2025, 04:25
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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 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.

This question focuses on those who are 65+ in age. And whether 10%+ of this group are employed or not.

Statement (1) is not sufficient by itself; it only gives us percentage info about this group in terms of the total population and doesn't tell us any info regarding employment.

Statement (2) is sufficient. Whether you're a man or a woman, the employment figure is 10%+. Therefore, we know the percentage of those employed in this group has to be at least 10%.
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Are at least 10 percent of the people in Country X who are 65 years 18 Nov 2025, 00:54
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Are at least 10 percent of the people in Country X WHO are 65 years or older employed?

We need to find within the group that is 65 or 65+.
02999


I have one doubt - I got why avg percentage will lie in between 10 to 20 %. But that percentage is of the people who are age of 65 or higher. How can we compare this with total population? Question is asking about total population. Please clarify .
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