Q24 - Ditrama

[austindyoung]

So, any thoughts would be awesome.

Here's what's going on: there is the country called Ditrama, and there are three autonomous regions in it: Korva, Mitro, and Guadar.

There is something called the federal revenue-sharing plan, that allows each region to get a share of federal revenues that is equal to the share of the population residing in that given region- based upon annual surveys.

For one country, Korva, the percentage of revenue that it received decreased, even though it's population increased.

So, that means that the total population of Ditrama, must have increased by a number more than the number of people that Korva's population gained (If I'm wording it correctly...)- so that even though Korva's raw number increased, the general population increased enough that it's share of the pie actually goes down.

Ok- I just am having a hard time of understanding why (E) is correct. I think I understand the mechanics and the false assumptions that this question wants to catch you doing, involving numbers and percentages, however, I don't get, as (E) states, (paraphrased) that: the population of Korva grew by a smaller percentage than the population of one of the other two countries.

Could it have grown by a larger percentage (relative to itself) and the other countries grew smaller percentages and their populations are just so huge that Korva's share of revenue would decrease?

Or does that scenario I just described change what the stimulus is saying? I know it has to do with the amount (percent) of the 100% of shares being allocated.

Obviously- I know my reasoning is flawed somewhere, because (E) is right.

I know all that matters is that Korva now has less of a share of the pie-- that's why it's allocated revenue dropped... I guess I just get confused as to how the solid numbers come into play.

Any help from would be awesome! Also, to the Geeks, if you can point to some resources or have any percentage numbers tips you keep in mind for problems like this, that would be sweet

[timmydoeslsat]

So we know that Ditrama has 3 parts:

K, M and G, and only these 3 parts.

The revenue % is = to the population %

So in this case, we know that K's revenue % went down, which means that K's population % of ditrama went down even though they actually had an increase in people. This means that at least one of those 2 other countries will take up more % of the pie now, since it all equals 100% among the three.

For K to have regressed its population % of Ditrama, it must be the case that another country gained population % of Ditrama.

[barbossusus]

assume K, M and D have equal populations: 10 mil. ppl. (33.33% each)

K (pop. goes up)^ by 4% = 10.4 mil = 33.54%
M (pop. goes up)^ by 5% = 10.5 mil = 33.87%
D (pop. goes up)^ by 1% = 10.1 mil = 32.58%

I still do not understand why E is correct. As you can see "the population of Korva grew by a smaller percentage than the population of one of the other two countries" is satisfied, but the revenue is actually increased.

Could anyone explain what is wrong?
Thank you.

[dean.won]

Here's my reasoning for E:

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!

[mfowler]

assume K, M and D have equal populations: 10 mil. ppl. (33.33% each)

K (pop. goes up)^ by 4% = 10.4 mil = 33.54%
M (pop. goes up)^ by 5% = 10.5 mil = 33.87%
D (pop. goes up)^ by 1% = 10.1 mil = 32.58%

I still do not understand why E is correct. As you can see "the population of Korva grew by a smaller percentage than the population of one of the other two countries" is satisfied, but the revenue is actually increased.

Could anyone explain what is wrong?
Thank you.

I also thought of a similar scenario. Here's mine:

Original population sizes. Population size in second year.

TOTAL: 100 (100%) -------------------> 103.5 (100%)
K: 15 (15%) ----> increase by 10% ----> 16.5 (~15.94%)
M: 10 (10%) ----> increase by 20% ----> 12 (~11.59%)
G: 75 (75%) ----> increase by 0% ----> 75 (~72.46%)

In this case, even though it satisfies answer choice (E) - K's population grew by a smaller percentage than the population of at least one of the others -, its percentage share of the total still increased.

We're trying to prove, I think, that the increase in the total population of Ditrama was %-wise larger than the increase of Korva. Answer choice E can create scenarios in which that isn't the case, as shown above.

I'm having a hard time wrapping my head around this one. Any help would be much appreciated.

[maryadkins]

In this case, even though it satisfies answer choice (E) - K's population grew by a smaller percentage than the population of at least one of the others -, its percentage share of the total still increased.

We're trying to prove, I think, that the increase in the total population of Ditrama was %-wise larger than the increase of Korva. Answer choice E can create scenarios in which that isn't the case, as shown above.

We don't need to prove that since the population of K increases a smaller amount than the population of another region then it would absolutely be true that its revenue share would not increase. We already know its revenue share increased. We need to find a statement that makes that the case, which is (E).

In other words, just because (E) can also enable other scenarios doesn't mean that this particular one we're working with makes (E) necessary for IT.

In this scenario, say the 3 regions each had a population of 10 to start and each got 1/3 of revenue:

K - 10
M - 10
G - 10

Then K's population goes up to 11. But it's SHARE has to go down. Well, if the other 2 stayed the same, it would take more than 1/3 of the revenue:

K - 11
M - 10
G - 10

So how would we make that not true? We could give another region a bigger share. Say, add one more:

K - 11
M - 11
G - 10

But now, K's share is still more than it was when it was 1/3"”K and M both get more than G.

But what if we gave M even MORE:

K - 11
M - 13
G - 10

Now, K has less than 1/3 (11 out of 34 is less than a third).

(E) must be true: one of the other populations grew more than K.

As for the other answer choices:

(A) needn't be true"”see int he above example that G could have fewer (or M).

(B) Previous years don't matter.

(C) needn't be true"”both don't have to beat K, just one of them (see example above)

(D) again, in the example above, G had a smaller increase than K.

[AnnaC659]

Hi,

I see all those numeric examples above are helpful in understanding why (E) is the correct answer.
But can someone go through the answer choices as how you would go about it during the exam?

I definitely did not have the time to give numbers and try things out under the time constraint and was left with (D) and (E) from which I chose the wrong answer. I would like to know how one can confidently eliminate (A) - (D) quickly for this kind of question involving percentages and numbers.

Thank you in advance!