Are at least 10 percent of the people in Country X who are 65 years

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.
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Statement (2) is weighted average example. \(Weighted-average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}\).

Weighted average always will be between two individual weights, weight 1 and weight 2.

Example:
Let's say there are 10 men (value 1) and 100 (value 2) women in this group (>65).
20% of men are employed --> 2 men are employed (individual average - weight 1);
10% of women are employed --> 10 women are employed (individual average - weight 2);

% of population employed (>65):

\(Weighted-average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}=\frac{2+10}{110}\approx{10.1%>10%}\).
For any numbers of men and women weighted average will be between 10% and 20%.
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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.
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(St. # 1) is alluring. But it doesn't tell about the employment rate of that that specific demographic group. Insufficient.

(St. # 2) At the first glance, the statement seems insufficient. But, if you look at it critically (possibly, once again) you will see this: Even if there is no MAN in the in that specific demographic group, 10% WOMEN are employed i.e. 10% of that population is employed. And, if any MAN is added to that group, the rate will be more than 10%. Sufficient.

So, the answer is B.

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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Can you please explain this by an example?
The weighted average of 2 individual averages (10% and 20%) must lie between these individual averages

Sorry if I am not correct... shouldn't your equation be....

\(Weighted-average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}=\frac{2*10+10*100}{(10+100)}\approx{9.27.1%<10%}\)

No it's not correct.

20%=0.2 and 10%=0.1, so in nominator you'd have \(0.2*10+0.1*100=2+10=12\) --> \(\frac{12}{110}\approx{0.109}=10.9%\)

There is another mistake in your calculations: 1020/110=~9.27, which in percents equals to \(9.27=9.27*100=927%\) not 9.27% (you transformed number into percent incorrectly).

To explain the concept better:
Consider a class with \(x\) boys (value_1) and \(y\) girls (value_2). The average height of boys is 1.70m (weight_1) and the average height of girls is 1.6 (weight_2). What is the average height of all students in the class?

Now no matter what \(x\) and \(y\) are, weighted average can not be less that the height of girls and can not be more than the height of boys.

Which means:
Weighted average always will be between two individual weights.

Hope it helps.
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You are AWESOME....If I could some favor for all this unconditional help....I would be glad.
Thanks a lot.

S1 - 11.3% provided, but not sure about how many are employed - insufficient
S2 - Out of all 65 yrs or older, 20% Men and 10% Women are employed, but overall how many are there 65 yrs or older? - insufficient
Together - 11.3 from S1 given, 30% from S2 are employed 65yrs or older (M + W). So, 30% of 11.3 < 10% - sufficient
Answer: C

we have been asked "from the group of people who are >=65 yrs" ; are 11.3% employed

statement 1
11.3 percent of total population is >=65; still nothing is given about how many people out of these are employed; insufficient

statement 2
of the people who are >=65, 20% men and 10% women are employed
now assuming 100 people out of which 50 are >=65 yrs
out of these 50 say 30 are men & 20 are women
i.e. 6 men & 2 women are employed =8 (employed) out of 50 (of the group >=65)
which is 16% > 11.3%
for any assumed value we will have the % greater than 11.3; sufficient

hence B

(1) insuff

(2) 20/100 M + 10/100F >= 10/100(M+F) ? Yes, because 20M + 10F >=10M +10F --> 20M>=10M

the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages

Can someone explain the above please..

Let me ask you a question if the average height of boys in a class is 1.8 meters and the average height of girls is 1.7 meters, could the average weight of all the pupils be less than 1.7 or more than 1.8?
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Check out the explanation of this concept here:
on-a-partly-cloudy-day-derek-decides-to-walk-back-from-work-147050.html#p1192637

Average of two quantities will always lie between the two.
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We need to determine whether at least 10 percent of the people in Country X who are 65 years old or older are employed. Let’s refer to the population of those who are 65 years old or older in Country X as the “older population.”

Statement One Alone:

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

Knowing the percentage of the population in Country X who are 65 years old or older doesn’t give us enough information to determine the percentage of the older population who are employed. For example, it could be the case that 5% of the older population are employed or it could be the case that 35% of them are employed. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

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

Of the older population, if 20% of the men and 10% of the women are employed, then it must be true that the overall employment percentage is between 10 and 20 percent. Anytime there is a group of people or objects divided into two subgroups, if x percent of one subgroup satisfies a criterion and y percent of the other subgroup satisfies the same criterion, then the percentage of the whole group satisfying this criterion is some number between x and y percent. Since the percentage of the older population who are employed is between 10 and 20 percent, then at least 10 percent of them are employed. Statement two alone is sufficient.

Answer: B
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I hope it helps someone

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Posted from my mobile device

Let's use the term seniors, to refer to those who are 65 years old or older.

Target question: Are at least 10 percent of Country X's seniors employed?

Statement 1: In Country X, 11.3 percent of the population is 65 years old or older.
Okay, so we know that a certain percent of the population are seniors, but we aren't told anything about their employment rates.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Among Country X's seniors, 20 percent of the men and 10 percent of the women are employed
To get a feel for what this tells us, let's examine the two EXTREMES:
Extreme #1 - among the seniors, there are ZERO women. This means all of the seniors are men, which means 20% of the seniors are employed
Extreme #2 - among the seniors, there are ZERO men. This means all of the seniors are women, which means 10% of the seniors are employed
Now that we have examined the extremes, we have a range of values that represent the employment rate among Country X's seniors.
We can conclude: 10% < senior employment rate < 20%
In other words, at least 10 percent of Country X's seniors are employed
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

RELATED VIDEO - WEIGHTED AVERAGES

(1) Just gives us 65 yrs or old population as a percentage of total population. We dont know total population, so cant say about 65 yrs or old population. Also there is no data about the percentage of people out of this 65 yrs or old population that are employed. So not sufficient.

(2) We don't know how many of the 65 yrs or older people are men, and how many of them are women. But one interesting thing about this data is that no matter how many women are there in this group, 10% of them are employed and no matter how many men there are in this group, 20% of them are employed. By the concept of weighted average, the total percentage of people employed in this group would be between 10% and 20%, hence definitely we can say that 'at least 10% of people are employed'.
So this is sufficient to answer the question with a YES.

Hence B answer