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Percent expenditure problem

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Intern
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Percent expenditure problem [#permalink]

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New post 13 Jun 2009, 10:21
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Hi guys was wondering if anyone could offer a good method to solve this problem:

In a certain year the United NAtions' total expenditures was 1.6 billion. Of this amount, 67.8 percent was paid by the 6 highest-contributing countries, and the balance was paid by the remaining 153 countries. Was country X among the 6 highest-contributing countries?

(1) 56 percent of the toal expenditures was paid by the 4 highest contributing countries, each of which paid more than country X.

(2) Country X paid 4.8 percent of the toal expenditures.

Answer: E.
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Re: Percent expenditure problem [#permalink]

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New post 20 Jun 2009, 15:03
In a certain year the United NAtions' total expenditures was 1.6 billion. Of this amount, 67.8 percent was paid by the 6 highest-contributing countries, and the balance was paid by the remaining 153 countries. Was country X among the 6 highest-contributing countries?

(1) 56 percent of the toal expenditures was paid by the 4 highest contributing countries, each of which paid more than country X. - In this question ignore the 1.6 billion. For simplicity just take the total expenditures as 100$.

=> 67.8 (Paid by 6 highest countries) + 32.2 (Paid by remaining 153 countries) = 100
=> 56 (Paid by 4 highest countries ) + 16.8(Paid by next 2 highest countries) + 32.2 = 100

Let us assume for simplicity all 4 highest countries paid equally. That means Each of the first 4 countries paid $14 (56/4).
Let us also safely assume that remaining 153 countries all paid equally = 32.2/153 = some small number < 1
And we are given that country X paid less each of the first 4 countries, which means it paid less than $14.
So country X can be either one out of the next 2 highest paid countries (which make a sum of 16.8), or it can one among those 153 countries. So INSUFF.


(2) Country X paid 4.8 percent of the toal expenditures. - This is clearly INSUFF.

Country X can be among the first 6 countries or it can be among the 153 countries as well.

Even combining (1) and (2) we can have 2 scenarios -

Let country X be one among the first 6 countries - Since it paid 4.8, and first 4 countries already paid 56, the 6th country must pay (67.8 - (4.8+56)) = 7$

Let country X be one among those 153 countries - if it already paid 4.8, remaining 152 will pay (32.2-4.8).

Hence insufficient. E is the answer
Re: Percent expenditure problem   [#permalink] 20 Jun 2009, 15:03
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