In a demographic study, the population and total income of a

Question

In a demographic study, the population and total income of a certain region were estimated from other data, and both estimates had lower and upper limits. At the time of the estimates, was the per capita income for the region greater than $16500?

1) the lower limit for the estimate of the population was 330,000
2) the lower limit for the estimate of the total income was $5,500,000,000

(1) The lower limit for the estimate of the population was 330,000
(2) The lower limit for the estimate of the total income was $5,500,000,000

GMATinsight · Accepted Answer

Question : Is Income / Total Population > $16,500?

Hint: The question require 
Either, the minimum value of per capita Income which can be calculated by Minimum Income and Maximum Population
Or, the Maximum value of per capita Income which can be calculated by Maximum Income and Minimum Population

Statement 1 : The lower limit for the estimate of the population was 330,000

Neither can we calculate Minimum Per capita Income nor Maximum Per capita Income. Hence,
 NOT SUFFICIENT

Statement 2 : The lower limit for the estimate of the total income was $5,500,000,000

Neither can we calculate Minimum Per capita Income nor Maximum Per capita Income. Hence,
 NOT SUFFICIENT

Combining the Two statements  
Using the Lower limit of both Neither can we calculate Minimum Per capita Income nor Maximum Per capita Income. Hence,
 NOT SUFFICIENT

Answer: option E

scorcho · Answer

The lower limit for income divided by the higher limit for population is the combination that will yield the lowest possible per capita income. You can divide the St 1 by St 2 and get a per capita income number, but it's not the lowest possible value given the available constraints.

If St 1 gave you the highest limit for population, you'd be good to go for C.

gmatnub · Answer

shouldn't statement 1 say 330,000 people instead of $330,000?

If that is the case, it is E

you need to find the worst case scenario number, which is the lower limit of total income divide by the higher limit of total population.

puma · Answer

Why should I divide the lower limit of total income by the higher limit of total population? What's the link between this and per capita income of $16500?

nmohindru · Answer

E) is answer

Least Per capita income = Least total income/ Max population

Since we only have min population we cannot determine whether per capita income was greater then or less than 165000

judokan · Answer

to find the minimum income per captia, we need to lowest limit total income, and highest limit for population. Because we do not have the later. Ans is E

spriya · Answer

This can be calculated with both (1) and (2) =>

LEAST Total popu. = p = 330,000
Least total income = I=$5,500,000,000
Least per capita income=PI= p/I = 5/3 * 10^4 = 1.6667 * 10^4 > 16500 hence the question can be answered using both 
IMO C

spriya · Answer

oops I did silly mistake again

whats the source of these questions ?

zaarathelab · Answer

This is a good question

We need to have sufficient values for the Numerator and the Denominator to determine the Per capita income

Per capita income = Income/Population

Statement 1 -------INSUFFICIENT

We have the value of the estimated lower limit of the population, but have no indication of the Income to evaluate. Hence insufficient

Statement 2------INSUFFICIENT

We have the value of the estimated lower limit of the total income, but no indication of the population. Hence insufficient

Statement 1 and 2,

Since we are only given the estimated lower limit of both, what if either of them is more than the estimate?
Lets see, if the population is higher than the estimate, then we will have a larger denominator and hence per capita income will be less than 16500$. 
If we were given the highest range of the Population, we would have been able to determine it

Hence E

JimGMATAnswers · Answer

The key is that if you divide 5500000000/330000 you get 16,667. While this is higher than the per capita income described, the population (or the denominator) could be higher, making the value of 16,667 potentially lower. As you do not know the upper bound, you can considerate to be infinite, which would lower the value much below 16,500.

NoHalfMeasures · Answer

GMATinsight

So lemme try to understand this. From the question stem we know that the estimated per capita income should lie between -
(LOWER limit for the estimate of the total income/HIGHER limit for the estimate of the population) and (HIGHER limit for the estimate of the total income/LOWER limit for the estimate of the population)

Since st1+st2 give us (LOWER limit for the estimate of the total income/LOWER limit for the estimate of the population) which lies somewhere in the middle we cant answer the question.

So even if the question instead was- was the per capita income for the region LOWER than $17,000? we would not be able to answer it right? Just confirming. Thanks

GMATinsight · Answer

Yes, You are absolutely correct.

if a and b are Greater than zero then

Min value of (a/b) can be calculated when we have minimum value of a and Maximum value of b
Max value of (a/b) can be calculated when we have Maximum value of a and minimum value of b

gmexamtaker1 · Answer

VeritasKarishma   chetan2u  
Hello,
could you please provide some help on this one.
The thing that I want to verify is that even if we were given the Greatest possible income and lowest possible population again we wouldn't be able to answer this question right?
Because in that case we would know the least possible amount but in between there would be many other possibilities.
Eg. let's say that (Max income)/(Max population)= 16.000 then we could give a definite answer
BUT IF (Max income)/(Max population)=17.000 then we would pick E , because those are the max values

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