Data Sufficiency

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.

PLEASE EXPLAIN....

dferm 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.

PLEASE EXPLAIN....

(1) No info about employment: insufficient.

(2) if 20% of the old men are employed and 10% of the old women, then even if there's only 5 old men and 100 billion old women, more than 10% of the old people will be employed: sufficient.

(1) is insufficient and (2) is sufficient: choose (b).

This may seem like a stupid question, but in this case, is it possible to assume that there are 0 people over 65? Or is it that the fact of 10% female employment means that there are living people over the age of 65?

YES. If they are asking about a population of 65 years old or older, then there must be some number of this population present in the problem.

Stuart, could you please explain this problem to me ?

Consider Country X's total population is : 100
Population of 65 old and older people is : 10

Then according to 2nd statement:

employed 65 years old and older men : 2
employed 65 years old and older women : 1

So total employed 65 years old and older people : 3 which is 3% of the Country X's total population.

Am I wrong ?

employed 65 years old and older men : 2
employed 65 years old and older women : 1

in this case question asks for "Are at least 10 percent of the people in Country X who are 65 years old or older employed?"

which means that if there are 10 people who are older or old than 65..then is at least 1 of them employed...

From your explanation there are 3...so 30%...

kv_ajay wrote:employed 65 years old and older men : 2
employed 65 years old and older women : 1

in this case question asks for "Are at least 10 percent of the people in Country X who are 65 years old or older employed?"

which means that if there are 10 people who are older or old than 65..then is at least 1 of them employed...

From your explanation there are 3...so 30%...

I couldn't have said it better myself!

Let's say out of a population of 100,10 are 65+.
In those 10,lets consider m=6,w=4.
20/100*6 added with 10/100*4 --16% of 10.

Hence B.

Algebraic solution:

Let X be the number of men over 65 and Y the number of women over 65.

(1)No info about employment: insufficient.

(2) 20%X+ 10%Y are employed
We want to know whether this is bigger than or equals 10%(X+Y)
20/100X+10/100Y>= 10/100(X+Y)
20X+10Y>=10(X+Y)
2X+Y>=X+Y
X>= 0 which is always true

So is it safe to assume that X% of Y and Z% of Y = (X% + Z%) of Y?

Is this some form of the weighted average formula?

pkw209 wrote:So is it safe to assume that X% of Y and Z% of Y = (X% + Z%) of Y?

Is this some form of the weighted average formula?

Hi,

it's just simple addition.

2z + 7z = 9z

.2z + .7z = .9z

20%z + 70%z = 90%z

Stuart, thanks for your patience:)

Can I assume this as a general rule: If the percentages I have at hand like here (20 and 10%) are equal or greater than the percentage I am being asked about (10%) then the result is always greater than the 10% no matter what the question is?

Thanks

Thouraya wrote:Stuart, thanks for your patience:)

Can I assume this as a general rule: If the percentages I have at hand like here (20 and 10%) are equal or greater than the percentage I am being asked about (10%) then the result is always greater than the 10% no matter what the question is?

Thanks

Definitely - if we're looking at a weighted average (i.e. the average of at least 2 groups with different internal averages), the overall average has to be greater than that of the group with the lowest average.

I'm not clear about 1 thing here... Does the question mean 10% of the total population who are employed or (10% of the population who are aged 65+ and employed) ?
Can u pl explain?

Stuart Kovinsky wrote:

dferm 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.

PLEASE EXPLAIN....

(1) No info about employment: insufficient.

(2) if 20% of the old men are employed and 10% of the old women, then even if there's only 5 old men and 100 billion old women, more than 10% of the old people will be employed: sufficient.

(1) is insufficient and (2) is sufficient: choose (b).

Statement 1 is very clear coming to Statement (2)

The least number of employed men >=65 years will be 1. similarly least number of employed women >=65 years will be 1. As u cannot have decimals for the number of men and women . now you have a total of 2 people atleast who are >=65 and employed..Lets calculate the total number of men and women...
Total men = 5 as 20% of it is 1 person
Total women = 10 as 10% of it is 1 person
Total people >=65 = 15
Therefore least % of people >=65 and employed is = (2/15)*100 = 40/3 > 10%....so SUFFICIENT...
Hope its clear...if there is any other easy kindly tell...thanks.....