Need explanation for statistics problem

Expert replies

akpareek: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Sun Feb 14, 2010 8:53 am

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]

Like this post

Source: Beat The GMAT — Problem Solving | Tue Sep 03, 2013 10:09 am

Mission2012: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sun Aug 19, 2012 10:04 pmFollowed by: 2 members; Thanked: 10 times

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?

If you find my post useful -> please click on "Thanks"

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

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/

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review