Critical Reasoning

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.

IMO C

Given, 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. For the sake of clarity, lets put some numbers to understand this argument.

Lets assume initially following number of people were in each of the regions:
Korva = 100 --> represents 30% ((100/300)*100)
Mitro = 100 --> represents 30% ((100/300)*100)
Guadar = 100 --> represents 30% ((100/300)*100)

Last year:
Korva = 110 --> represents 27.5% ((125/400)*100)
Mitro = 140 --> represents 35% ((125/400)*100)
Guadar = 150 --> represents 37.5% ((125/400)*100)

Vemuri wrote:IMO C

Given, 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. For the sake of clarity, lets put some numbers to understand this argument.

Lets assume initially following number of people were in each of the regions:
Korva = 100 --> represents 30% ((100/300)*100)
Mitro = 100 --> represents 30% ((100/300)*100)
Guadar = 100 --> represents 30% ((100/300)*100)

Last year:
Korva = 110 --> represents 27.5% ((125/400)*100)
Mitro = 140 --> represents 35% ((125/400)*100)
Guadar = 150 --> represents 37.5% ((125/400)*100)

k - 100 - represents 1/6
m - 200 - represents 2/6
g - 300 - represents 3/6

after
k - 200 - 100% rise - represents 1/7
m - 800 - 300% rise - represents 4/7
g - 400 -- 33% rise - rep 2/7

g's rise is lesser than k's?? c is out

2010gmat wrote:

Vemuri wrote:IMO C

Given, 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. For the sake of clarity, lets put some numbers to understand this argument.

Lets assume initially following number of people were in each of the regions:
Korva = 100 --> represents 30% ((100/300)*100)
Mitro = 100 --> represents 30% ((100/300)*100)
Guadar = 100 --> represents 30% ((100/300)*100)

Last year:
Korva = 110 --> represents 27.5% ((125/400)*100)
Mitro = 140 --> represents 35% ((125/400)*100)
Guadar = 150 --> represents 37.5% ((125/400)*100)

k - 100 - represents 1/6
m - 200 - represents 2/6
g - 300 - represents 3/6

after
k - 200 - 100% rise - represents 1/7
m - 800 - 300% rise - represents 4/7
g - 400 -- 33% rise - rep 2/7

g's rise is lesser than k's?? c is out

Good point byy 2010gmat...
In that case answer could be E. What's the OA?

OA is E

OA is E

nice one!! whats the source?
i think C is out coz it says that The populations of Mitro and Guadar each
increased by a percentage that exceeded the
percentage by which the population of
Korva increased and this means that it MIGHT be possible that one of the region's population is decreased so we cannot be sure about whether k received less money percentage.
please lemme know if i am wrong..

Lets summarize the passage.... revenue share increase---->population in number of the region.

Conclusion:- revenue in korva decrease---->increase in population in number.


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

This does not relate decreasing revenue to increased population


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

This does not compare the share in revenue to other regions. We need an explanation why the revenue was less than other regions.


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

Percentage increase cannot determine the actual variation in population. Eg:- if Korva has 3000 people, Mitro has 1000 and Guadar has 2000, a 20% increase in Korva population makes it 3,600 and 50% increase in Mitro and Guadar makes it 1500 and 3000 resp. This does not vaildate the claim of decrease in revenue.


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

Imagine 2 years ago, K had 3000, M had 1000 and G had 2000. If an increase of 50 for K, 200 for M and 500 for G, then the additional share earned by each region shows that K had earned the least. This if true, definitely validates the conclusion stated above.

Hence D it is!!

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

"Atleast one of the other two autonomous
regions" phrase is not required here. Out of scope!!

Good question. I will go with C