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Ditrama is a federation made up of three autonomous regions. [#permalink]
28 Feb 2007, 14:37

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A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

47% (02:28) correct
53% (01:46) wrong based on 242 sessions

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.

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.

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.

E. I was happy when I saw C but only after I read E, i realized that C was assuming that population of both other areas increased. Always a good practice to read all choices :)

If the Korva's population increase is less than that of the other two then it also proves the stated case.

terp26 wrote:

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.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
21 Dec 2013, 06:14

I do not agree with the OA.

If the population of K is 100, the one of M is 10 and the one of G is 5 , then according to question E, we could have such as increase in population : +50% for K, 51% for M and 0% for G (K's population grew by a smaller percentage then at least one of the two others). Before the increase, the proportion of inhabitant living in K was 86.9%, after the increase it is 89.5%.... And this in contrary with the statement made in the statement!

Therefore in this case answer E does not apply and is wrong.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
26 Dec 2013, 11:55

I think the answer should be C. For D , I can have an example like Say init : K = 1, M = 2, G=2. On increase say K' = 3 ( Increase of 2) and M' = 5 ( increase of 3) and G' = 5. Previous % of K = 1/5. After increase %k = 3/(3+5+5)= 3/13. Now 3/13 > 1/5 thus the statement that it decreased is negated.

For c: We can assume that the % increase for K is 10% and G,M increased by 20% . Then the new ratio is 1.1K / (1.1k + 1.2G + 1.2M) . K/(K+M+G) is always greater than 1.1K/(1.1k + 1.2G+1.2M). These 2 ratios are same when G,M are 1.1 and K/K+M+G is lesser if G,M are less than 1.1.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
26 Dec 2013, 16:31

anjancgc wrote:

I think the answer should be C. For D , I can have an example like Say init : K = 1, M = 2, G=2. On increase say K' = 3 ( Increase of 2) and M' = 5 ( increase of 3) and G' = 5. Previous % of K = 1/5. After increase %k = 3/(3+5+5)= 3/13. Now 3/13 > 1/5 thus the statement that it decreased is negated.

For c: We can assume that the % increase for K is 10% and G,M increased by 20% . Then the new ratio is 1.1K / (1.1k + 1.2G + 1.2M) . K/(K+M+G) is always greater than 1.1K/(1.1k + 1.2G+1.2M). These 2 ratios are same when G,M are 1.1 and K/K+M+G is lesser if G,M are less than 1.1.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
15 Apr 2014, 11:48

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 2055 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.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
20 Aug 2014, 10:10

betofx wrote:

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

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

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!

Ditrama is a federation made up of three autonomous regions. [#permalink]
21 Aug 2014, 07:34

1

This post received KUDOS

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.

Re: Ditrama is a federation made up of three autonomous regions. [#permalink]
14 Sep 2015, 02:05

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.

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