DS Query

[MI3]

Q. Are at least 10 percent of the people in Country X who are 65 year 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

I chose the answer as C, based on the fact that when we combine the two statements, we know that 30% of the 11.3% of the total population would be employed, and this would be < 10% of the overall population. Is my reasonining sound?

[Tani]

The answer is B.

You are only looking at the people over 65 so you don't worry about the rest of the population. The first statement is no help.

Looking at B, if everyone over 65 was female, 10% of the over 65 population would be employed. If even a few are male, more than 10% would be employed. B is sufficient.

Your reasoning is incorrect. Assume there are 100 men and 100 women over 65 in this country. 20% of the men would be 20 people and 10 % of the women would be 10 people. The total employed would be 30 people, which is 15% of the 200 total, not 30%. The most over 65 that could be employed would be 20% if the population were all male. You could never reach 30% employed.

[manpsingh87]

Q. Are at least 10 percent of the people in Country X who are 65 year 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

I chose the answer as C, based on the fact that when we combine the two statements, we know that 30% of the 11.3% of the total population would be employed, and this would be < 10% of the overall population. Is my reasonining sound?

1) it states 11.3 percent of the population is 65 year old or older; but it didn't provide any data on their employment, hence 1 alone is not sufficient to answer the question.

2) let population of country x which is 65 years old or older be 100;
now if this 100 people are all male than no. of employed persons=20; which is greater than 10%;
now if this 100 people are all female than no. of employed persons=10; which is 10 %;
now if its mixed, i.e. made up of both male and female, assume no. of males to be 20 and females be 80;
therefore no. of employed men=4; and no. of employed women =8; and total no. of employed persons is 12; which is greater than 12 %;

we will see that for mix case, i.e. when population is made up of both male and female, percentage of employed people will always lie between 10 and 20 %; hence answer should be B

[sourabh33]

IMO B

Let total population of Country x = P
Let total population of 65+ = O
Let no of employed 65+ = E
We need to find weather E>= 0.10 O

Statement 1

This talks about relationship between P & O i.e O = 0.113P
No info available on E, therefore insufficient

Statement 2

This talks directly about the people 65+ employed
Let Male population 65+ = M
Let Female Population 65+ = F
Now M+F = O
And, 0.2 M + 0.1 F = E
Now E/O =
(0.1M + 0.1F + 0.1M)/M+F
0.1O +0.1M

Now we can clearly see that e>= 0.10 O therefore statement 2 is sufficient