Ditrama is a federation made up of three autonomous regions. Korva. Mi

Question

Ditrama is a federation made up of three autonomous regions. Korva. Mitro, and Guadar, 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 statements above are true, which one of the following must also have been shown by the population survey on which last year's revenue-sharing in Dirama was based?

(A) Of the three regions Korva had the smallest number of residents

(B) The population of Korva grew by a smaller percentage than it did in previous years

(C) The populations of Mitro and Guadar each increased by a percentage that exceeded the percentage by which the population of Korva increased.

(D) Of the three regions. Korva's numerical increase in population was the smallest

(E) Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.

chetan2u · Accepted Answer

Hi,
In response to a PM and also to few posts above..

Lets do first thing first-- rephrase the PARA

three regions K ,M and G have certain people of D residing in them. K, M and G recieve funds proportionate to that population. Although K's population has increased, but its share of funds has dropped..

Inference-- 
Clearly its share is now going to ONE of the other two or may be BOTH depending on their increase, but we are sure that atleast ONE has eaten into the share..

Choices:- 
(A) Of the three regions Korva had the smallest number of residents
 We are talking of change in share, so this is not valid here..

(B) The population of Korva grew by a smaller percentage than it did in previous years
 the distribution of funds is relative to all three, so does not depend on alone K and may be other have increased by even smaller %

(C) The populations of Mitro and Guadar each increased by a percentage that exceeded the percentage by which the population of Korva increased.
 We cannot say for sure both would have increased. Its possible that only ONE is eating into the share of other TWO..

(D) Of the three regions. Korva's numerical increase in population was the smallest
 A small numerical increase may be a large % increase .. 2 person increase in population of 4 is 50%.

(E) Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.
 YES, we can say this for SURE as atleast someone would have taken that share..

Bunuel · Answer

OFFICIAL EXPLANATION

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, and 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:

Before After (Last Year)  
 Total Population of Ditrama 30 (100%) 100 (100%) 
 Population of Korva 10 (33%) 15 (15%) 
 Population of Mitro 10 (33%) 10 (10%) 
 Population of Guadar 10 (33%) 75 (75%)

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 country 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.

kevincan · Answer

E. Clearly its population rose less than the overall average and at least one of the other regions show a greater percentage increase in population

buckkitty · Answer

I debated between C and E for a long time. Eventually picked E because, it only has to be true that one country exceeded the growth rate Korva's population to decrease Korva's share of total population. It is not NECESSARILY true that both of the other two countries exceeded the population percentage increase of Korva.

GMATBLACKBELT · Answer

we can easily rule out AB as discussed earlier.

Essentially what MUST BE TRUE?
C: Can be true, but again does not have to be true. Perhaps only Mitro grew by a large amount. This large amount could dwarf any increase made by Korva. Thus, less money would be available for Korva. One other region must increase greater than Korva for the paradox to be solved, but two regions is not a requirement.


D: numerical pop. increased the smallest for Korva. 

M and G have 100 people K has 1. Numerical increase for M and G is 5. for K its 1. Can see why % went down. So Can be true.

Here is where it can get tricky, and D becomes more of a math problem than a CR. Lets say M and G have 50 and 45 people again (respectively). K has 5 this time. 

Total amount of people is 100. K is 5% of the total. Now lets say we increase M and G by 6 and K by 5. We now have 56+51+10 --> 117

10/117 is def bigger than 5%. b/c 10/200 is 5%. Thus, D does not have to be true. Numerical increase can double the amount in K, thus increasing its % of the total population by a few % points. (its now aprox 8%). 
D does not finish the paradox. 

E: Must be true. If no other population increased in size greater than K, then the argument would be false. 

Lets go back to the numerical example again: 

G, M, K. 50, 45, 5. If K increases by 5, but M increase by 4 and G increase by 4. then K should have more funds.

10/113 is def. greather than 5/100. 

Same with one being static: 50, 45, 5. K increases by 5, M increases by 4. 10/104> 5/100. 

One more example: K: 90. M: 5, G: 5. K increases by 5. M increase by 1. 95+5+6---> 106. 6/106. M's overall % increases slightly. K's overall % decreases slightly. This extreme example shows that one other MUST have a % increase greater than that of K regardless of the number of people in each region.

You can try any number of possibilites. If the other region does not have a population % increase greater than that of K, then the argument will crumble. 

This is why E is correct.


This was a very hard CR, took me about 3 1/2-4min to solve. I honestly suggest going through it in detail as I did. I feel I have a much better understanding of how %'s and #'s work in CRs.

betofx · Answer

Hi everyone. I know this is an old post and that the OE is E, but i still have some doubts. Please explain.

What about if our analysis goes this way (Check the attachment please)

Attachment:

Ditrama.png [ 6.59 KiB | Viewed 24177 times ]

It would prove that if just one of the other regions grows by a greater percentage than Korva did, Korva would not always have a decreased share of population. Please your help.

Thanks in advanced

Attachments

Ditrama.xlsx [9.13 KiB]
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To download please login or register as a user

havoc7860 · Answer

Hope this helps, i found it on another forum and found it useful

Argument states that although K's population increased their revenue went down, which means K's population increase was less than the COMBINED increase of M and G

Let's start with 2010 (last/base year)
2010 - Total population 100
K - 40 (40% of total)
M - 40 (40% of total)
G - 20 (20% of total)

Inference 1 : In order for K's population to increase but also for its percentage to decrease total population of Ditrama had to have increased
Inference 2 : For the sake of proving E, there are 3 possible scenarios. K has a smaller increase than none, at least 1, or both other countries

2011 Total population 110 - smaller increase than one other country
K - 43 (7.5% increase; 39.09% of total)
M - 46 (15% increase; 41.82% of total)
G - 21 (5%% increase; 19.09% of total)
2011 Total population 110 - smaller increase than both countries
K - 41 (2.5% increase; 37.27% of total)
M - 46 (15% increase; 41.82% of total)
G - 23 (15% increase; 20.91% of total)

You can see that in both scenarios K's population increased while decreasing their share of the revenue pool (% of total population)

Now let's say that K had a bigger increase than both countries:
2011 Total population 110 
K - 46 (15% increase; 41.82% of total)
M - 43 (7.5% increase; 39.09% of total)
G - 21 (5% increase; 19.09% of total)

In this scenario, K increased their population but also increased their share of the revenue pool (% of total population) which cannot be true according to the argument stated

I know this is a very simplified example but it seems like whatever number you plug in with accordance to the restrictions in the argument, it's impossible for K's population increase (%-wise) to be bigger than BOTH the other countries.

Hope this wasn't too confusing and if anyone finds anything wrong with my reasoning please inform!

aryabhatta · Answer

The key here is which of the following  must  be true.. 
C is an answer which cannot must be true option, even one of the federation population % can give you the required answer. and hence E provides best answer.

JarvisR · Answer

I tried to solve it without using any calculation. Please share your strategy to solve similar problem without any calculation..
 
Ditrama is a federation made up of three autonomous regions. Korva. Mitro, and Guadar.
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.

Paradox:
Argument says that though K's population increased, the money allotted to the region decreased.
As per premise:
money allotment to a region is proportional to the population of region. This means that the population growth in one or more region was greater than that of K.

If the statements above are true, which one of the following  must  also have been shown by the population survey on which last year's revenue-sharing in Dirama was based?

(A) Of the three regions Korva had the smallest number of residents
 >> Not necessary. K can have second highest growth also.
 (B) The population of Korva grew by a smaller percentage than it did in previous years
 >> Not necessary; previous year doesn't matter . Also, it doesn't compare the growth with other regions. so avoid it.
 (C) The populations of Mitro and Guadar each increased by a percentage that exceeded the percentage by which the population of Korva increased.
 >> Like A, not a correct answer.
 (D) Of the three regions. Korva's numerical increase in population was the smallest.
 >> Like A, not a correct answer.
  
(E) Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.

LeonidK · Answer

This is exactly what answer E says:
(E) Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.
Korva's population increased. But in a smaller percentage than at least one of the other regions

anairamitch1804 · Answer

This is an inference question. The right answer to an inference question is something that must be true based on one or more statements in the passage. Here, we can make a deduction, and predict the correct answer.

We know that Korva's revenue share decreased even though their population increased. This must mean that, collectively, the other two countries experienced a greater proportional increase in population. Now, a key thing to understand is that in order for the other two countries to have experienced a collective increase, it doesn't have to be the case that both of these countries did. But at least one of them would have had to. Thus, choice E is correct.

CEdward · Answer

C is a trap. It may or may not be true. D must be true, else there's no way it's population increased, yet it received less revenue.

Ditrama is a federation made up of three autonomous regions. Korva. Mitro, and Guadar, 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 statements above are true, which one of the following must also have been shown by the population survey on which last year's revenue-sharing in Dirama was based?

(A) Of the three regions Korva had the  smallest number  of residents
-doesn't have to be true

(B) The population of Korva grew by a  smaller percentage than it did in previous years 
-doesn't have to be true

(C) The populations of Mitro and Guadar each increased by a percentage that exceeded the percentage by which the population of Korva increased. 
-TRAP

(D) Of the three regions. Korva's numerical increase in population was the  smallest 
-maybe, maybe not

(E) Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.
CORRECT

nandini14 · Answer

But how does E make sure that Korva's population had increased but its share decreased, that means the total population would have definitely increased but Korva's increase was a lesser percentage value than others

chetan2u · Answer

Option E does not require to prove 'Korva's population had increased but its share decreased ' as this is already given in argument. Rather it is opposite, 'Korva's population had increased but its share decreased' should lead us to option E.

The question stem starts with assuming whatever is given in argument to be true and we have to find what else will be true in lieu of the given study..

egmat · Answer

Hi nandini14,

Good news first: the second half of your sentence is exactly right. Korva's population went up, yet its  share  fell, so the total population must have risen  faster  than Korva did, which means Korva's percentage growth was smaller than at least one neighbor's. You've nailed the logic.

The only thing to untangle is the  direction  of your question. You're asking how E "makes sure" the scenario (population up, share down) happens. But in a  must be true  / inference question, the scenario is  given to us as a fact  - the stimulus tells us it already happened. We don't ask E to prove or cause it. We ask the reverse:  given that this happened, what is forced to be true?

Think of Korva's share as a fraction:

- Korva's share = Korva's population / total population
- Korva's population (the top) went  up , but the fraction went  down 
- The only way a fraction shrinks while its top grows is if the  bottom grew by a larger percentage 
- The bottom is Korva + Mitro + Guadar, so Mitro and Guadar  together  outgrew Korva - which forces  at least one  of them to have grown by a greater percentage than Korva

Therefore , that "at least one" is precisely choice  E . E doesn't need to recreate the scenario; it's simply something that  had to be true  for the given scenario to occur.

A quick parallel to feel the direction

Suppose I tell you, "My slice of the pizza got smaller this week, even though I ate more slices than last week." You can safely infer:  someone else must have taken an even bigger extra helping.  You're not proving I ate more - that's given. You're just stating what's forced by it. Same move here.

Answer: E

Ditrama is a federation made up of three autonomous regions. Korva. Mi

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Ditrama is a federation made up of three autonomous regions. Korva. Mi

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