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Need explanation for statistics problem

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by akpareek » Tue Sep 03, 2013 10:09 am
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 $16,500 ?

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

A. Statement (1) ALONE is sufficient but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) alone is not sufficient.
C. BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statement (1) and (2) TOGETHER are NOT sufficient. [/color][/size]
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by Mission2012 » Tue Sep 03, 2013 10:40 am
akpareek wrote: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 $16,500 ?

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

A. Statement (1) ALONE is sufficient but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient but statement (1) alone is not sufficient.
C. BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statement (1) and (2) TOGETHER are NOT sufficient. [/color][/size]
E

For estimating lower limit of per capita income , we need lower limit of salary and higher limit of population. None of the option provides us with higher limit of population. What is the OA?
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by [email protected] » Tue Sep 03, 2013 12:35 pm
Hi akpareek,

Mission2012 explains the proper reasoning for why we can't calculate an answer to this question. Here's the physical reason why:

The question asks if the per capita income was > $16,500?

We would need:

(Income) / (total population) to answer this question.

Fact 1 estimates the population, but doesn't tell us the income.
Fact 2 estimates the income, but doesn't tell us the population.

Combined, we only have the lower limit of each item. If either one is significantly higher than its lower limit, then the answer to the question will change.

Thus, the Final Answer is E

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by Mike@Magoosh » Tue Sep 03, 2013 4:22 pm
akpareek wrote: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 $16,500?

1) the lower limit for the estimate of the population was 330,000 people.
2) the lower limit for the estimate of the total income was $5,500,000,000
Dear akpareek,
I'll just add my two cent, noting that Rich already did a good job with this.

Obviously, the individual statements are woefully insignificant, because we need a ratio. The real question is: what happens when we combine them?

The prompt question, in essence, wants us to look at the minimum, the lower limit of the ratio:

per capita income = (total income)/(population)

To make a fraction as small as possible, we have to make the numerator as small as possible, and the denominator as big as possible.
Statement #2 makes the numerator as small as possible, but Statement #1 makes the denominator as small as possible, and we want it to be as big as possible. thus, we don't have enough information. Answer = [spoiler](E)[/spoiler]

Really, this question is not about statistics, but just about fundamental fraction properties. Here are some blogs you may find relevant:
https://magoosh.com/gmat/2012/comparing- ... -the-gmat/
https://magoosh.com/gmat/2012/fractions-on-the-gmat/
https://magoosh.com/gmat/2012/gmat-math- ... -decimals/
https://magoosh.com/gmat/2012/gmat-short ... nominator/

I hope this helps. Let me know if you have any further questions.

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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