Data Sufficiency

Are at least 10% of the people in country X who are 65 years old or older employed ?

(1) in country X, 11.3% of the population is 65 years old or older
(2) in country X, of the population 65 years old or older, 20% men and 10% women are employed.

Please provide answer explanation. OA to follow after a couple of threads.
Thanks.

IMO it is b

let the population of 65 or older be M+W

total employed .2M + .1W

now putting values will show it is always greater than 10%

I know its not a good method but i am stuck there

Lets assume that there are 1000 people

statement 1:

it says that 11.3% of the population is 65 years old or older..
So there are 113 people who are 65 years old or older

But the question is asking us to find whether at least 10% of the people who are 65 years or older employed...This question doesn't tell us anything about employment..So this statement is insufficient

statement 2:

This statement says that of the population 65 years old or older, 20% men and 10% women are employed.

Unemployed male=20/100 *113=23 (approx)
Unemployed female=10/100*113=11(approx)

Unemployed people(male+female)=34

Insufficient

Combining both the statements we have 34/113=30%

30% of the people who are 65 years or older are unemployed...So 70% of the people who are 65 years or older are employed

So it is shown that at least 10% of the people in country X who are 65 years old or older employed

Hence the ans should be C...

I am not sure about the method I have used...Please do let me know if I am wrong..What is the source of this question & whats the OA?

OA is B and the source of the question is gmat PREP #1

cubicle_bound_misfit: Sorry but i still do not get the logic you used. Can you please elaborate further ?

Okay..I think what cubicle was trying to explain was this

Let M be the no of males and F be the no of females.
Let M+F represent people who are 65 years or older

As per statement 2


20% of the men are employed
10% of the women are employed

so the total number of employed persons is 0.2M+0.1F

Now we have to determine the percentage of people who are 65 years or older and employed
((0.2M+0.1F)/(M+F))*100
=0.1(2M+F)/(M+F)

Let M=50 and F=25
0.1(100+25)/75=16.67%

Let M=25 and F=50
0.1(50+50)/75=13.33%

So it is observed that for any value of M or F the percentage is at least 10%...


hence the ans is B

It would be nice if you could post in the subject if it is a GMAT prep question.

It is a GMAT prep question...

Raju,
I couldnt get the solution. First M+F = Whole population then how u arrived on .2M+.1F. It would have been correct if M+F represent population of ppl 65 yrs and above.
and if u take it as 65 yrs and above.then
.2M+.1F/M+f...how it can represnt whole population
...



U have to calculate..Ppl 65 yrs above AND employed or
ppl 65yrs above OR employed..
Pls elaborate it furthur.

I have clearly mentioned in my previous post that M+F represents the people who are 65 years or older...

In the second statement it is mentioned that In country X, of the population 65 years old or older, 20% men and 10% women are employed.

So Employed persons who are 65 years or older is represented by 20%M+10%W
0.2M+0.1W

we are asked to calculate to the percentage of people who are 65 years or older and employed which is nothing but
((0.2M+0.1F)/(M+F))*100
=0.1(2M+F)/(M+F)


Hope this helps...

Another easier way to do this:

Are at least 10% of the people in country X who are 65 years old or older employed ?

(1) in country X, 11.3% of the population is 65 years old or older - misses the point of employment , thus insufficent

(2) in country X, of the population 65 years old or older, 20% men and 10% women are employed.

20% of Men + 10% of women are employed..... 20/100 M + 10/100 w = 0.2M + 0.1F

So, the question asks if 10% of all persons at or over 65 employed?...which can be algebraically written as ................10/100(M + W) = 0.1(M + W) = 0.1M + 0.1W?

Therefore , 0.2M+0.1W > 0.1M + 0.1W and so B is the correct answer

The question asks do at least 10% of people older than 65 or older work?

(1) says nothing about employment. Insufficient.

(2) Because there can be only men or women in the population of those that are 65 or older, (2) tells us that 30% of those that are 65 or older are employed. Sufficient.

I assume you got mixed up because the question stem said "who are 65 or older" and you forgot about it or you missed that (2) specifically states that, "of the population 65 years or older", meaning the group of 65+ people.

Not a whole lot to think about as long as you pay attention to details. If you're doing any algebra on this you're doing way more work than you should be.