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Percent - Hard Question

by prat_agl » Fri Nov 09, 2012 8:31 pm
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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
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by GMAT Kolaveri » Fri Nov 09, 2012 11:36 pm
each region receives a share of federal revenues equal to the share of the total population of Ditrama.

% of revenue that Korva received Decreased though Population of Korva increased.

Revenue is a % of TOTAL population. Hence although population of Korava increased the (i)other two (mitro or Gauadar) could have increased by a greater number. Korava could ve contributed just 1 and Mitro could have increased by 1000 and Gauadar by 100000). Hence taking a large portion of the revenue while leaving less for Korva and hence Korva's revenue could have decreased though population increased ( it did increase by 1).

(ii) Korava could have increased by 5. Mitro could have increased by 1 while Guadar could have increased by a large number 1,00,000 taking a major portion of the share. There could be many more such combinations which could show that though Korava population increased its revenue could have decreases since revenue is a % of TOTAL population.

Hence the only option that MUST be true according to the argument is E ( Korva's population grew by a smaller percentage than did the population of at least one of the other two autonomous regions.)

a) Korva had the smallest number of residents.
Could be false. This is not supported by the argument.
b) The population of Korva grew by a smaller percentage than it did in previous year.
We dont have facts to support this conclusion.
c) The population of Mitro and Guadar each increased by a percentage that exceeded the percentage by which the population of Korva increased.
Can be false. Mitro could ve decreased and Guadar could ve increased by a very large percentage. Case ii.
d) Of the three regions, Korva's numerical increase in population was the smallest.
could be false as explained in Case ii
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by GMATGuruNY » Sat Nov 10, 2012 2:34 am
prat_agl 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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
Three years ago:
K=100, M=100, G=100.

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

Last year:
K=300, M=200, G=29500.
Percentage of revenue received by Korva = 300/30,000 = 1%.

In the case above -- which satisfies all of the constraints given in the passage -- answer choices A, B, C and D are not true.

The correct answer is E.
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by prat_agl » Sat Nov 10, 2012 9:26 am
GMATGuruNY wrote:
prat_agl 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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
Three years ago:
K=100, M=100, G=100.

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

Last year:
K=300, M=200, G=29500.
Percentage of revenue received by Korva = 300/30,000 = 1%.

In the case above -- which satisfies all of the constraints given in the passage -- answer choices A, B, C and D are not true.

The correct answer is E.
Thanks for the details.
In such question is it required to take another scenario with one of M or G with decrease in population?
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by Sapana » Sat Dec 29, 2012 8:16 pm
Your explanation for E being the correct answer is Brilliant. Isn't C equally plausible?
From your example:

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

From Option C:
K=300, M=200, G=150
percentage of revenue by Korva= 150/650= 23% which is less than 33%

I am confused!
Please enlighten me!

GMATGuruNY wrote:
prat_agl 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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
Three years ago:
K=100, M=100, G=100.

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

Last year:
K=300, M=200, G=29500.
Percentage of revenue received by Korva = 300/30,000 = 1%.

In the case above -- which satisfies all of the constraints given in the passage -- answer choices A, B, C and D are not true.

The correct answer is E.
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by GMATGuruNY » Sat Dec 29, 2012 10:45 pm
Sapana wrote:Your explanation for E being the correct answer is Brilliant. Isn't C equally plausible?
From your example:

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

From Option C:
K=300, M=200, G=150
percentage of revenue by Korva= 150/650= 23% which is less than 33%

I am confused!
Please enlighten me!

GMATGuruNY wrote:
prat_agl 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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
Three years ago:
K=100, M=100, G=100.

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

Last year:
K=300, M=200, G=29500.
Percentage of revenue received by Korva = 300/30,000 = 1%.

In the case above -- which satisfies all of the constraints given in the passage -- answer choices A, B, C and D are not true.

The correct answer is E.
It is not sufficient to cite one case in which C is true.
The question stem asks for the answer choice that MUST be true -- not just in one case, but in EVERY case.
Since I have cited a case in which C is not true. C can be eliminated.
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by KenanGarrett » Wed Jan 02, 2013 11:59 pm
But Sapana's example is one that makes E not true. In her example, K's population increased by a percentage greater than that of the two other regions. So, since she found one example where E is not true, does that mean we can rule that out as well?

-Kenan
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by KenanGarrett » Thu Jan 03, 2013 12:03 am
Never mind. After revisiting her post, I now notice that she miscalculated the new proportion of K.
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by gmat6087 » Thu Jan 03, 2013 3:51 am
GMATGuruNY wrote:
Sapana wrote:Your explanation for E being the correct answer is Brilliant. Isn't C equally plausible?
From your example:

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

From Option C:
K=300, M=200, G=150
percentage of revenue by Korva= 150/650= 23% which is less than 33%

I am confused!
Please enlighten me!

GMATGuruNY wrote:
prat_agl 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 yearly population survey. Last year , the percentage of federal revenue that 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 statement 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 year.
c) The population 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 suggest
Three years ago:
K=100, M=100, G=100.

Two years ago:
K=100, M=100, G=100.
Percentage of revenue received by Korva = 100/300 = 33.33%.

Last year:
K=300, M=200, G=29500.
Percentage of revenue received by Korva = 300/30,000 = 1%.

In the case above -- which satisfies all of the constraints given in the passage -- answer choices A, B, C and D are not true.

The correct answer is E.
It is not sufficient to cite one case in which C is true.
The question stem asks for the answer choice that MUST be true -- not just in one case, but in EVERY case.
Since I have cited a case in which C is not true. C can be eliminated.
Mitch,

I just need one clarification:
Say K=100, M=25, G=25.

Share of revenue was
K=66.7%, M=16.7%, G=16.7% (Roughly calculating)

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

Let K now be 105 ; 105-100=5 increased.
Let M now be 50 ; 50-25=25 increased.
Let G now be 50 ; 50-25=25 increased.

Now percentage of share among the 3 regions is:
K=51.2% ;M=24.4%, G=24.4%
This also satisfies relating to the percentage drop in K's share.

Then in such cases which one to choose it is the one for which the given condition is always true?

Regards
Satya
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