eyunni 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 Ditrama 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.
Please explain your answers.
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.