#24 - Ditrama is a federation made up of three autonomous

[Administrator]

Complete Question Explanation

Must Be True—Numbers and Percentages. The correct answer choice is (E)

The situation in Ditrama is as follows:

     Under the federal revenue‑sharing plan, each region receives a share of federal revenues
     equal to the share of the total population of Ditrama residing in that region, as shown by a
     yearly population survey.

     Last year, the percentage of federal revenues Korva received for its share decreased
     somewhat even though the population survey on which the revenue‑sharing was based
     showed that Korva’s population had increased.

If the total population of Korva increased but at the same time they experienced a decrease in
revenue allocation, the only possible solution is that the total population of Ditrama increased by
more than the Korva increase. Thus, you must seek an answer that indicates that the total population
increased more than Korva’s population increased. But be careful: this question is one of high
difficulty because the test makers do not make it easy to spot the correct answer.

Answer choice (A): Either Mitro or Guadar could have a smaller number of residents than Korva.

Answer choice (B): This answer is impossible to prove because we do not have information about
the population growth of Korva in the years prior to the last one.

Answer choice (C): This is the most popular wrong answer choice. The key error is the claim that
“Mitro and Guadar each increased by a percentage that exceeded” Korva’s increase. Although
it must be true that at least one exceeded Korva’s increase, it does not have to be true that both
exceeded Korva, as shown by the following example:

Capture.PNG

In the example above, only one of the other regions had a population increase that exceeded Korva;
the other did not. Hence this answer choice is incorrect. Note also that this example disproves answer
choice (A) as well.

Answer choice (D): As shown by the previous example, this answer is incorrect.

Answer choice (E): This is the correct answer. From the stimulus we know that Korva had a
population increase, but a revenue drop. So, the total population of Ditrama must have increased
by more than Korva’s increase, and for this to happen, at least one other region must have had an
increase in population that exceeded Korva’s.

Note that the scenario in answer choice (C) would force answer choice (E) to be correct, and based
on the Uniqueness Rule of Answer Choices, answer (C) is incorrect for that reason alone.

[jiyounglee]

Hello powerscore,

I am having difficulty with this must #% question.

So, let's assume

Population for

Korva: 100
Mitro: 100
Guadar: 100

Then, each region receive 1/3 (33%) of federal revenue.
When federal revenue is $100 in total, each region receive $33.

From the stimulus,

Last year, the percentage of federal revenues Korva received for its share decreased somewhat even though the population survey on which the revenue-sharing was based showed that Korva's population had increased

Then,

let's assume
population in Korva was increased by 10% and its share decreased by 10%

This means population in Korva: 110 and federal revenue it receives is 23% (meaning $23)

How did this happen?

If population for Mitro or Guadar or both increased, then federal revenue for Korva would decrease.

I have chose C over E

Why is E a better answer?

Also, do you have any other example to understand this easier?

Or During the test, do you have faster way solve this question without assuming numerical values and percentages?

Thank you!

[Dave Killoran]

Hi J,

This is truly one of my favorite numbers and percentages problems of all time, and it's so powerful that I included it in the LSAT Logical Reasoning Bible (in Chapter 17, on page 561, problem #2). If you have the LRB, take a look at the full explanation there. If you are in our full-length or Live Online course, let me know and I'll direct you to the explanation. If you don't have any of those materials, let me know and we'll talk about this one.

Thanks!

[jiyounglee]

Hello Dave,

I am currently taking Live online course, would you be able to direct me where to find the explanation?
Thank you!

[Dave Killoran]

Hi J,

Since that explanation should be here and isn't, I'm going to post it in:

Complete Question Explanation

The situation in Ditrama is as follows:

• Under the federal revenue‑sharing plan, each region receives a share of federal revenues
  equal to the share of the total population of Ditrama residing in that region, as shown by a
  yearly population survey.
  
  Last year, the percentage of federal revenues Korva received for its share decreased
  somewhat even though the population survey on which the revenue‑sharing was based
  showed that Korva’s population had increased.

If the total population of Korva increased but at the same time they experienced a decrease in
revenue allocation, the only possible solution is that the total population of Ditrama increased by
more than the Korva increase. Thus, you must seek an answer that indicates that the total population
increased more than Korva’s population increased. But be careful: this question is one of high
difficulty because the test makers do not make it easy to spot the correct answer.

Answer choice (A): Either Mitro or Guadar could have a smaller number of residents than Korva.

Answer choice (B): This answer is impossible to prove because we do not have information about
the population growth of Korva in the years prior to the last one.

Answer choice (C): This is the most popular wrong answer choice. The key error is the claim that
“Mitro and Guadar each increased by a percentage that exceeded” Korva’s increase. Although
it must be true that at least one exceeded Korva’s increase, it does not have to be true that both
exceeded Korva, as shown by the following example:

• powerscore_lrb_2016_p564.png

In the example above, only one of the other regions had a population increase that exceeded Korva;
the other did not. Hence this answer choice is incorrect. Note also that this example disproves answer
choice (A) as well.

Answer choice (D): As shown by the previous example, this answer is incorrect.

Answer choice (E): This is the correct answer. From the stimulus we know that Korva had a
population increase, but a revenue drop. So, the total population of Ditrama must have increased
by more than Korva’s increase, and for this to happen, at least one other region must have had an
increase in population that exceeded Korva’s.

Note that the scenario in answer choice (C) would force answer choice (E) to be correct, and based
on the Uniqueness Rule of Answer Choices, answer (C) is incorrect for that reason alone.

[jiyounglee]

Hello Dave,

Thank you so much for thorough explanation!
The chart really helped me to understand why each answer choice is wrong.

[Dave Killoran]

Great, I'm glad that helped! It's a really cool question, and it is perfect for showing you how the test makers think and how they can attract you with answer such as (C). It's the kind of question that helps you to be better at correctly answering other problems that deal with numbers and percentages.

[hrhyoo]

Hi Powerscore,

Even after reading the full explanation, I don't fully understand why E is correct. I did get the question right because all the other answer choices were worse, but I couldn't stop wondering what if Korva's population was so small that the % increase was huge and the one of the other regions had a huge population to begin with that a little increase in % would suffice to decrease Korva's revene sharing %. It feels as though E is making one of the misconceptions explained in the Bible, assuming that smaller % growth than one of the ohther regions somehow guarantees smaller number increase.

The question stem talks about population in term of number increase only but E talks about % increase in population - I don't think you could jump between those two terms and make comparion with other reigions.

Please clarify this question for me. Thank you for your timely response in advance.


Hanna

[Dave Killoran]

I couldn't stop wondering what if Korva's population was so small that the % increase was huge and the one of the other regions had a huge population to begin with that a little increase in % would suffice to decrease Korva's revene sharing %.

Hi Hannah,

Thanks for the message! this is one where instead of me trying to explain it again, I'd suggest instead that you try to find a scenario that fits what you discuss above. See if you can make a numerical scenario that causes an issue with (E) in the same fashion I made a numerical chart to explain this one. I think playing with it that way will do far more to unlock this than any additional comment will!

Thanks!

[sqmusgrave]

Hi, could you help me clarify the relationship between percentage increases and total increases in something.
For example, I remember some other question that had a trap answer which played on the fact that a country could have increased their GDP by 40% while still having less of a total GDP than a country who increased by 10% (since it's easier to increase by 40% if your number is 10 vs. 10 million).
It's because of this that E threw me off, since I thought Korva could have the highest % increase, but still the lowest absolute value of population, and each region's absolute value would determine their share of revenue.

I see the reasoning you provided and it's very helpful, and while I understand that my reasoning is wrong I can't clearly articulate why we can compare the value of change in each regions %, but we can't do that in other questions. Thanks!