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

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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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New post 31 Dec 2014, 00:46
Bunuel wrote:
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.

Answer: B.

Also discussed here: gmat-prep-ds-93371.html

I still don't get why B. Assuming there are 100 people in country X and 10 unemployed and over 65 year-old year. So 2 men and 1 woman => 3/10 < 10%. Please explain. 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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New post 16 May 2016, 18:29
I think most people including me, who get the answer as C, read the question stem wrong. I read the question as

- Are at least 10% people in country X, 65 year older & employed. Instead of reading the question as Are at least 10% of people who are older than 65, employed. What a silly mistake!
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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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New post 11 Nov 2016, 08:06
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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.


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

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New post 02 Dec 2016, 19:27
I hope it helps someone

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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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New post 07 Dec 2017, 10:00
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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


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

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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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New post 21 Jan 2018, 23:35
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.


(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
Re: Are at least 10 percent of the people in Country X who are 65 years &nbs [#permalink] 21 Jan 2018, 23:35

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