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In a certain year the United Nations’ total expenditures wer [#permalink]

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07 Dec 2011, 17:50

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In a certain year the United Nations’ total expenditures were $1.6billion. 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 total 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 total expenditures.

Re: In a certain year the United Nations’ total expenditures wer [#permalink]

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07 Dec 2011, 22:42

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Statement 1 tells us that the top 4 accounted for 56% of the expenditures. Since it makes no statement of X we have no idea where X may fall. Therefore insufficient. Statement 2 tells us that X paid 4.8% and gives us no info on the top 6. Since the prompt tells us the top 6 accounted for 67.8% lets just assume they were all evenly distributed that would make X at 4.8% not included. If however the top 2 accounted for something like 57.8% then X could be included since the remaining 4 would account for 10% of which we now X is at 4.8%. So insuff.

Together we know that the top 4 are 56%. This leaves 11.8% for the remaining two. If the two are evenly distributed then X wouldn't be included. However, if the remaining 2 are not evenly distributed than X would be included. So insuff.

In a certain year the United Nations’ total expenditures were $1.6billion. 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 total expenditures was paid by the 4 highest-contributing countries, each of which paid more than Country X --> just tells us that country X is 5th contributor or lower. Not sufficient.

(2) Country X paid 4.8 percent of the total expenditures --> if all 6 highest contributors paid equal amount then each paid \(\frac{67.8}{6}=11.3%>4.8%\), and the answer would be NO but if first contributor paid 51%, country X - 4.8% and the other 4 paid \(\frac{67.8-51-4.8}{4}=3%\), then the answer would be YES. Not sufficient.

(1)+(2) From (1) 5th and 6th contributed \(67.8-56=11.8%\) (average of 4 highest contributing countries is \(\frac{56}{4}=14%\)). Now, if 5th and 6th contributed equal amount then \(5_{th}=6_{th}=\frac{11.8}{2}=5.9>4.8%\), and the answer would be NO but if 5th contributed \(11.8-4.8=7%\) and \(6_{th}=X=4.8%\) then the answer would be YES. Not sufficient.

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