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

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

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Updated on: 21 Jan 2018, 22:45
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Difficulty:

55% (hard)

Question Stats:

56% (01:19) correct 44% (01:45) wrong based on 1910 sessions

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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.

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Originally posted by LM on 27 Apr 2010, 09:03.
Last edited by Bunuel on 21 Jan 2018, 22:45, edited 2 times in total.
Renamed the topic and edited the question.
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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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17 Jan 2012, 07:42
71
71
enigma123 wrote:
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

Any idea how to solve this please?

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

(2) 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.

Also discussed here: gmat-prep-ds-93371.html
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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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04 Nov 2011, 11:23
21
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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
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##### General Discussion
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Are at least 10 percent of the people in Country X who are 65 years  [#permalink]

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27 Apr 2010, 10:38
11
14
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.

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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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28 Apr 2010, 07:50
Bunuel 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.

No info about employment. 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.

No matter how many men and women are in this group (>65), more than 10% will be employed (the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages). Sufficient.

Can you please explain this by an example?
The weighted average of 2 individual averages (10% and 20%) must lie between these individual averages
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Are at least 10 percent of the people in Country X who are 65 years  [#permalink]

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28 Apr 2010, 09:40
5
8
LM wrote:
Bunuel 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.

No info about employment. 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.

No matter how many men and women are in this group (>65), more than 10% will be employed (the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages). Sufficient.

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

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  [#permalink]

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10 May 2010, 20:37
Bunuel wrote:
LM wrote:
Bunuel 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.

No info about employment. 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.

No matter how many men and women are in this group (>65), more than 10% will be employed (the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages). Sufficient.

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

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%.

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

$$Weighted-average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}=\frac{2*10+10*100}{(10+100)}\approx{9.27.1%<10%}$$
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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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11 May 2010, 02:22
4
3
LM wrote:
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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Re: Are at least 10 percent of the people in Country X who are 65 years  [#permalink]

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11 May 2010, 11:20
1
Bunuel wrote:
LM wrote:
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.

You are AWESOME....If I could some favor for all this unconditional help....I would be glad.
Thanks a lot.
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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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04 Nov 2011, 11:39
3
3
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
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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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04 Nov 2011, 11:42
1
1
Should be B:
Stat 1: doesnt help by itself as it does not give information about employment.

Stat 2: says that at least 10% of man and woman above 65 years of age are employed, which is sufficient to answer the questions being asked. Assuming that Country X has only man and woman.
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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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24 Jan 2012, 23:42
2
1
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
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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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27 Jan 2012, 00:00
4
1
(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.

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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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28 Jul 2013, 01:49
9
1
(1) insuff

(2) 20/100 M + 10/100F >= 10/100(M+F) ? Yes, because 20M + 10F >=10M +10F --> 20M>=10M
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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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25 Nov 2014, 05:54
Quote:
Stat 2: says that at least 10% of man and woman above 65 years of age are employed, which is sufficient to answer the questions being asked. Assuming that Country X has only man and woman.

AND... Assuming that Country X has at least 1 man!
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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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28 Nov 2014, 00:18
4
3
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%.

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/
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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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26 Dec 2014, 11:36
the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages

Can someone explain the above please..
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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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27 Dec 2014, 02:42
LUC999 wrote:
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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Re: Are at least 10 percent of the people in Country X who are 65 years  [#permalink]

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28 Dec 2014, 03:49
1
statement 1 is definately not sufficient. Now statement 2 states that 20% M and 10% W are employed... Now if We rephrase the question mathematically we are being asked whether atleast 0.1(M+W) is employed. Here we are taking the total male pop 65 or above as M and total female pop 65 or above as W. Now 2nd statement gives us the info that 0.2M +0.1F is employed Now 0.2M+0.1F is definately more than 0.1(M+F) so sufficient. Hope this explanation helps.
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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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28 Dec 2014, 20:55
1
LUC999 wrote:
the weighted average of 2 individual averages (10% and 20%) must lie between these individual averages

Can someone explain the above please..

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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Re: Are at least 10 percent of the people in Country X who are 65 years &nbs [#permalink] 28 Dec 2014, 20:55

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