This is a problem from GMAT FOCUS. Test #1. Not sure if anyone has taken GMAT Focus but i found the questions to be significantly harder than the OG.

Here is one below:

[Deleted because this is a banned source. Any PAID product from GMAC is not allowed to be reproduced online.]


It would seem to me that the lower limit would be 16,666 so C should be the answer. I thought this is one of those questions, where when you do the math you realize you don't need the upper limit since we already have the lower limit, which is greater than 16,5000 already. But the answer is E.

hmmm...i agree with you on that answer c. i'm confused....

i would think the answer is unanswerable without the upper limits and therefore the information provide is incomplete.

Please remember to follow the posting guidelines... the subject should be the first few words of the question. Thanks.

Each statement alone is clearly not enough... we are trying to determine if income/population > 16,500 so we need to have values for the numerator and the denominator. So it's either C or E.

(1&2) Suppose we start with the fraction $5.5B/330K. This is greater than $16,500. However, the given values are both lower limits. If we increase the numerator while keeping the denominator constant, income per capita will certainly increase. If, instead, we increase the denominator, the income per capita will decrease. A slightly larger value for the population would bring it down below $16,500. Not knowing what the upper limit for the population is what makes it insufficient.

Answer is E.

Rey

I am still having difficulty understanding why it is not sufficient to have only the lower limits for both the population and total income. Since the population & income estimates have upper and lower limits, is the question asking for all possible per capita incomes? Why is it possible to have the numerator be the lower limit and the demoninator be the upper limit? Is this a similar approach to looking for extreme values?

Taken together, the two statements tell us that the per capita income is

((5.5)(10^9) + x) /((3.3)(10^5) + y) , where x and y are at least 0. This could be any real number greater than 0. If y=0, the answer is yes, but if x=0 and y is a large number, the answer could well be no.

The question is asking a yes/no question: whether the income is greater than $16,500. If we can answer "yes, always" or "no, always," then the info is sufficient. If we answer "sometimes it's greater and sometimes it's lower," then the info is not sufficient. So if we can show that, in one instance, it is greater, and in another, it's not, then we know the info is not sufficient.

per capita income = total income / total number of people

Start with the two given lower limit numbers. These are the lower limits for total income and for total number of people, but putting them together does NOT necessarily equal the lower limit for per capita income.

Let's use slightly easier numbers to illustrate.
lower limit on total income = $100
lower limit on total number of people = 20

If we use these two numbers, we get a per capita income of 100/20 = $5. But $5 is NOT the lower limit for the per capita income figure.

Let's say we have the same amount of income, $100, but we have 50 people. Now the per capita income is $100/50 = $2. What is we have $100 in total income and 500 people? $100/500 = $0.20. Keep increasing the number of people and you can make the per capita income really small.

Now, let's say we have $1,000 in income but still only 20 people. Now the per capita income is $1,000/20 = $50. Keep increasing the income and you can make the per capita income really large.

So without any more info, we don't have sufficient info to say the per capita income figure is above or below some set amount, because we can create pretty much any figure we want, depending upon what we choose for our two inputs.

Basically, I can create any number I want

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

This seems to be one of Ron's "C TRAP" questions. The way i would look at this is that you need to have the following fraction to answer the question:

(Upper limit of numerator)/(Lower limit of denominator)

This should "maximize" your error on the low side of the estimate

That's a good way to look at it. Thanks!

_________________
Ben Ku
Instructor
ManhattanGMAT

Tom:
in order to get the more conservative estimate for per capita income...you would want to minimize numerator and maximize denominator. i.e. min income / max pop
and since, the question only gives us min for both, info is insufficient.
can an MGMAT instructor pls confirm?

we are actually barred from using GMAT FOCUS as a source on this forum; that is a paid product from gmac, so it's not fair use if the problems are reproduced here in full.

normally this would be grounds for immediate deletion of the post, but i do notice that this post is old enough that it may perhaps pre-date this decision. i'll check, but be aware that this entire post will be deleted if it is not older than the original decision to bar GMAT FOCUS as a source.

The problem was posted before we officially made the announcement, but we do still have to delete it, as GMAC has made clear that any paid problem is not allowed to be reproduced online. I've left the discussion of the problem, though, because we can technically discuss the problem as long as we don't put it in here. (Which does make it kind of hard to discuss the problem...)

sudaif, I think that was what tom was saying: we WOULD need to know what he typed in order to answer... but we don't. That's why he called it a "C TRAP" answer - because it's one of those things that might look good unless you really know for sure what you need in order to answer.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT