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Ditrama: Prep Test 17, Section 3 #24

Posted: Thu Aug 16, 2012 6:15 pm
by Captain Rodeo
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 are 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.

Any help would be awesome! 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 :D

Edit: I just finished the LRB section on Percentages and Numbers- it was great and helped a ton. This one problem is just bugging the crud out of me.

Re: Ditrama: Prep Test 17, Section 2 #24

Posted: Thu Aug 16, 2012 10:47 pm
by Captain Rodeo
SOoOOoo... I guess nobody likes this Q either, eh?

Re: Ditrama: Prep Test 17, Section 2 #24

Posted: Fri Aug 17, 2012 12:02 am
by lederhosen

Re: Ditrama: Prep Test 17, Section 3 #24

Posted: Fri Aug 17, 2012 2:39 pm
by Captain Rodeo
Thank you very much lederhosen! Great explanation!

I guess I was paying too close attention to how the numbers related to the percentages. The fact is, the revenue is allocated by share (percentage)... if Korva gets less of a share- it's because at least one of the other countries has or took more of the share (percentage) away from Korva- regardless of what happened to Korva's population. I think that's right...

Anyway, thank you again. I definitely need to work on these # and % problems... or just review some good ol' basic math.

Re: Ditrama: Prep Test 17, Section 2 #24

Posted: Fri Aug 17, 2012 2:47 pm
by C_Koschier
lederhosen wrote:Its actually PT17 S3 #24

This is like a market share problem.

Korva's population went up but its market share went down. How does that happen? it means that Korva increased by a smaller % than that of Ditrama as a whole. If Korva is dragging the average down, that means another (or several other) regions have gained a larger % and are pulling the average up.

Korva could actually have gained more population (in absolute #) than the others, and still lose market share. For example:

Year 1:
Ditrama = 100 total
Korva: 80 -> 80%
Mitro: 10 -> 10%
Guadar: 10 -> 10%

Year 2:
Ditrama = 200 total
Korva: 140 -> 70% (Gain of 75% over Year 1)
Mitro: 50 -> 25% (Gain of 400% over Year 1)
Guadar: 10 -> 5% (Gain of 0% over Year 1)

Korva gained 60 residents (more than the others combined), yet it dropped from 80% to 70% market share. Thats b/c Ditrama as a whole gained by 100%, Korva only gained by 75%. Korva's bringing the average down, someone must be bringing it up.

I also chose those numbers to represent that Korva did not have to beat Mitro and Guadar (Which C & D are trying to trap you with). Only 1 other needs to outpace Korva's gains.


Year 1:
Korva: 10
Mitro: 1000
Guadar: 1000

Year 2:

Korva: 20 (Gain of 100%)
Mitro: 1500 (Gain of 50%)
Guadar: 1500 (Gain of 50%)

Korva gained 20 residents, less than the other two combined, yet still maintained a higher percentage rate growth... thereby fulfilling the conditions within the stimulus, and indicating that Answer (E) does not fulfill the condition that it "must also have been shown". Note as well that the answer choice (E) dictates that the percentage being increased was Korva's alone, not the percentage increase of the autonomous region that is representative of the whole (which would indeed validate (E)).

Am I missing something here? This question seems wrong to me.

Edit: I think the problem is simply how "percentage" is unspecified. Obviously, for Question E to be correct, Korva's percentage increase would have had to have been representative of Ditrama as a whole. However, there is nothing within the stimulus or answer choice that would indicate that the percentage referenced was anything other than Korva's alone.

Re: Ditrama: Prep Test 17, Section 2 #24

Posted: Fri Aug 17, 2012 3:06 pm
by lederhosen

Re: Ditrama: Prep Test 17, Section 3 #24

Posted: Fri Aug 17, 2012 3:12 pm
by C_Koschier
Aha, so it is my math that failed me. Of course, in order for the share to decrease no matter the extremely high numerical value of the other two regions, one of the other regions will need to have at least grown by a larger percent than Korva did.

Thanks for the help man.

Re: Ditrama: Prep Test 17, Section 3 #24

Posted: Fri Aug 17, 2012 3:13 pm
by lederhosen

Re: Ditrama: Prep Test 17, Section 3 #24

Posted: Fri Aug 17, 2012 7:11 pm
by sdwarrior403
I am not so sure about this one.

Year 1:

Korva: 2 people (0.13%)
Mitro: 500 people (33.28%)
Guadar: 1,000 people (66.58%)

Total Population: 1,502

Year 2:

Korva: 4 people (.08%)
Mitro: 500 people (11%)
Guadar: 4,496 people (89.92%)

Total Population: 5,000

In this example Korva has jumped 50% population, while neither country grew at a bigger percentage than did Korva. Guadar jumped about 23% and Mitro went down in %. Or am I misreading answer choice E in what it is describing by "grew by smaller percentage?"

I see that Korva grew by 50% and the others did not grow at a bigger % rate than they did, which disproves answer choice E.