Are at least 10 percent of the people in country X who are 6

[Guest]

Are at least 10 percent of the people in country X who are 65 yrs old or older employed?
1) in country X, 11.3 percent of population is 65 yrs old or older
2)in country X, of the population 65 yrs old or older , 20 percent of the men and 10 percent of the women are employed


Source: Gmatprep 1 ...DS

ANS:-B

Please explain

[Guest]

RON, anyone can you please reply to this question. Need help on the above

have my exam scheduled next week

[Saurav]

Statement 1 - gives percent of people in the age group, but there is no mention of employment figures. Not sufficient

Statement 2 - it gives the percent of men (20%) and women (10%) over 65 years AND who are employed. The total number of men and women in this age group is not given. let us assume it is denoted by M and W. hence the total figure is

( 20 % of M + 10 % of W )
------------------------------
( M + W )

this gives a weighted average whose value will always be greater than 10 and less than 20.

So infact M and W is not required to answer teh solution.

[RonPurewal]

Statement 1 - gives percent of people in the age group, but there is no mention of employment figures. Not sufficient

Statement 2 - it gives the percent of men (20%) and women (10%) over 65 years AND who are employed. The total number of men and women in this age group is not given. let us assume it is denoted by M and W. hence the total figure is

( 20 % of M + 10 % of W )
------------------------------
( M + W )

this gives a weighted average whose value will always be greater than 10 and less than 20.

So infact M and W is not required to answer teh solution.

this is a good write-up.

notice the following more general lessons that may be drawn here:

(1)
if you have "so-and-so-many-% of X are Y", this serves only to elucidate the relationship between X and Y. here, those two quantities are the total population of the country ("X") and the total of all 65+ year olds ("Y").
the problem statement is asking you for a percentage OF the 65+ year olds, so this statement is completely useless (it doesn't fragment the 65+ year old population at all in any way).
insufficient.
very insufficient, if i may say so.

(2)
if you like classifying problems, you can recognize this as part of a weighted average setup.

facts:

* the weighted average MUST lie somewhere from 10% (which would be the "average" if everyone 65+ years old were female) to 20% (which would be the "average" if everyone in that demographic were male). note that this fact is sufficient to answer the problem, since all the possibilities are at least 10%.
this should also be intuitive: you can't have an overall percentage that's less than that of any component! think how absurd it would be if, say, 40% of men and 55% of women voted for some presidential candidate, but that candidate only captured 30% of the overall vote. that's clearly impossible (unless there are other voters besides men and women, like, say, robots).

* you can't determine the weighted average, because you don't know the relative numbers of men and women in the 65+ population. you'd need that ratio to determine the weighted average, though you don't need the actual numbers. the higher the ratio of men to women, the closer the number is to 20%.

this statement is sufficient.

the post above contains a fine explication of the algebraic approach, if that's your style.

[Deepak_J_Shah]

hmnn - still confused (Statement 2)
I read this solution online on beatthegmat.com

Statement 1 - gives percent of people in the age group, but there is no mention of employment figures. Not sufficient
1000 * 11.3% =
113 people who are 65 yrs or older (men+women, unemployed+employed)
Note: neither does it say that these are men or women i.e., 113 are combination of men+women.

(the remaining, 1000-113 = 887 are 65 yrs or younger. Could be men/women-employed/unemployed)

Statement 2 -
NEED TO DRILL THIS FURTHER WITH NUMBERS - IF IT CAN BE DONE.
Que 1: Can we say 20%+10%=30% (of say 113) employed and 70% (of 113) unemployed? I believe the answer is NO (cause need to weigh it or something) - could someone please explain this further.

Que 2:
Can we say this?

>=65 Employed Unemployed TOTAL
Men 20%
Women 10%
TOTAL 30% 70% 113


>=65 Employed Unemployed TOTAL
Men 23
Women 11
TOTAL 34 113-34=79 113

% of employed = 34/113 = 30% - but that is outside the boundary of 10-20 so this cannot be right!!
If someone could explain what is wrong here.

It would be nice if the xls grid (MGMAT way) could be completely filled with unknowns that cannot be determined and elaborate on the entire distribution regardless of its need i.e., for this particular question.

que 3:
Can we always conclude that if M=20% and Women = 10%
then the weighted average value will always be greater than 10 and less than 20?

Thank you in advance
Deepak_J_Shah@yahoo.com

[RonPurewal]

Que 1: Can we say 20%+10%=30% (of say 113) employed and 70% (of 113) unemployed?

dear sweet god, no.

if you're in doubt about something like this, just check REALLY EASY cases.
for instance, let's say that everyone is employed, i.e., 100% of the men and 100% of the women. according to the same logic, then, 200% of everyone must be employed.
um, no.

Que 2:
Can we say this?

>=65 Employed Unemployed TOTAL
Men 20%
Women 10%
TOTAL 30% 70% 113


>=65 Employed Unemployed TOTAL
Men 23
Women 11
TOTAL 34 113-34=79 113

% of employed = 34/113 = 30% - but that is outside the boundary of 10-20 so this cannot be right!!
If someone could explain what is wrong here.

where do i start?

* you can't add the 20% and the 10%. that's preposterous; if you don't understand why, see the easy example above.
if x% of this component and y% of that component are (whatever quality), then the overall % of the combined population that is (whatever quality) must be between x% and y%.

analogy: think how crazy it would be if you could make a drink that was 50% alcohol by pouring together drinks that were 10%, 15%, and 25% alcohol. the high school kids would be going crazy.

It would be nice if the xls grid (MGMAT way) could be completely filled with unknowns that cannot be determined and elaborate on the entire distribution regardless of its need i.e., for this particular question.

i have no idea what this means. in fact, it doesn't even look like a question.

if it's a question, could you please ask it in clearer terms?
thanks.

que 3:
Can we always conclude that if M=20% and Women = 10%
then the weighted average value will always be greater than 10 and less than 20?

if you mean that 20% OF the men and 10% OF the women are (whatever quality), then, yes.

if you mean something else, which you certainly could ("men = 20%" and "women = 10%" are, to say the least, highly ambiguous), then maybe not.

[sprparvathy]

Hi,

I had some trouble intepreting st. 2 (though, I had the weighted avg. scenario in mind):

I read st. 2 as follows:

The 20% men and 10% women are not to be considered on the total 100% of the population, but on the fraction of the population whose age is > 65.

(the statement reads: Of the population 65 yrs old or older, 20 percent of men...)

In that case, we need to know this fraction of population > 65 to see if the total employed population with age > 65 constitutes more than 10 percent of the total population.


(if we take this interpretation along with statement 1, then, it means that this 20% men and 10% women is actually a fraction of 11.3%.)


I hope I'm making it clear.

Why can't the statement be interpreted in this manner?

[akhp77]

One quick approach

Assume M = Men, W = Women

Statement 2 is sufficient because of the following reason
20M/100 + 10W/100 = 10M/100 + 10M/100 + 10W/100
= 10M/100 + 10(M+W)/100 > 10(M+W)/100
So, 20% of men and 10% of women is always greater than 10% of men and women

Statement 1 does not talk about employment
So it is insufficient

[mschwrtz]

sprparvathy, you understood S2 correctly, but you misunderstood the question.

"Are at least 10 percent of the people in country X who are 65 yrs old or older employed?" means "Of the people 65 years or older in country X, are at least 10% employed?" You seem to take it to mean "Are at least 10% of the people in country x both 65 or older and employed?"

The clause "who are 65 yrs old or older" is a relative clause. It restricts the group we consider the whole for the purposes of this percent question. This very issue comes up in the occasional difficult overlapping sets questions. If I say that 60% of my good-looking students are smart, that doesn't mean that 60% of my students are good-looking and smart. Maybe I have 100 students, and 5 of those are good-looking, and 3 of those 5 are also smart.

Full disclosure: in real life, all my students are good-looking and smart.

[ayush.sharma]

Yep I got B as well.
Let X be the population of men and women who are at or above 65 years.
X= A + B.
Where A is men over or at 65
B is women over or at 65.

The questions asks wether at-least 10/100 ( A+B) are employed.
From 2 we know :
20/100 (A) + 10/100 (B) are employed.
So now the question being asked is wether 20/100 (A)+ 10/100(B) amounts to atleast 10/100 (A+B).

Since A and B are positive integers you will see that 30 % of the population of 65 years or over is employed - which is greather than the 10% and hence the answer is sufficient.

[RonPurewal]

Since A and B are positive integers you will see that 30 % of the population of 65 years or over is employed - which is greather than the 10% and hence the answer is sufficient.

whoa, no. you got lucky in this case -- you have the correct multiple-choice answer, just by coincidence -- but the "30%" part here is horribly incorrect.

just to recap, you're saying that 10% of the men and 20% of the women, taken together, represent 30% of the total population.
* first, this can't be true. if you had 20% of each, that would be 20% of the total population -- so this must be less than 20% of the total population.
* second, think of what would happen if you had 75% of the men and 75% of the women. (the way you're reasoning here, that would be 150% of the population!)

in general, this is a weighted average situation. if you have P% of the men and Q% of the women -- written as decimals, e.g., P = 0.10 if it's 10% -- then that's [(Pm + Qw)/(m + w) x 100]% of everyone.

[divudu.v]

Can we do this same problem using Overlapping sets by any chance? As soon as I read the problem while taking exam, I assumed that this problem should deal with overlapping sets and went ahead to draw the grid. But after reading stmt 2, I was bit thrown off as I didnt know how that can be accommodated in the grid.Is there a way I can differentiate an overlapping set problem from a weighted average problem?

[jlucero]

Can we do this same problem using Overlapping sets by any chance? As soon as I read the problem while taking exam, I assumed that this problem should deal with overlapping sets and went ahead to draw the grid. But after reading stmt 2, I was bit thrown off as I didnt know how that can be accommodated in the grid.Is there a way I can differentiate an overlapping set problem from a weighted average problem?

You could if you used a 3-way overlapping set matrix (which we don't teach b/c it's too tricky to ever be useful on the GMAT). You could start with the a normal matrix, and then divide each box in half to represent men or women. You could then algebraically prove the equation.

However, the bigger takeaway is to learn to give up on your matrix and notice that the second statement introduces a different style of information. As many other commenters have shown, there's a far easier way of solving this problem.

[AbhishekL802]

I need to work on these styles of questions to improve my score. Which would be the right strategy guide to review this concept - fractions/decimals/percentages guide or the algebra guide from Manhattan Prep?

[esledge]

Hi Abishek, this is a good question, and the answer depends on what you mean by "these styles of questions."

At first, I thought this was an Overlapping Sets question, because of the implication that the population can be split by two different categorizations: by age (at least 65 years old or under 65) and by employment status (employed or not). If that's the type you want to practice, work on Overlapping Sets in the Word Problems section, specifically focusing on the Double Set Matrix.

However, this question really ends up being about Weighted Averages, which is also discussed in the Word Problems section. In Statement (2), the population is split by yet a third category: gender (men or women), and the necessary insight is that the Weighted Average employment rate for the whole 65 years old or older group is thus somewhere between 10% and 20%.

Finally, there's a little bit of Percents in this problem, which would be found in the Fractions, Decimals, and Percents section, but it's not really the focus of this problem.