Data Sufficiency

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.













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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.

Statement 1 tells us that Country X was, at best, the fifth-highest contributing country. On its own, this isn't terribly helpful. Maybe it was fifth. Maybe it was seventh. Clearly, not sufficient.

Statement 2 gives us what percent Country X offered. On its own, this is pretty clearly not enough. To illustrate, let's generate simple scenarios for the top 6 countries, keeping in mind that the top 6 percentages will sum to 67.8% (Note that 67.8 % for 6 countries is just a bit over 11% per country on average.)

Case 1 Top 6: 12.8%, 11%, 11%, 11%, 11%, 11% --> clearly 4.8% is not in the top 6; so the answer is NO
Case 2 Top 6: 23%, 10%, 10%, 10%, 10%, 4.8% --> 4.8% is in the top 6, so answer is YES
Not sufficient.

Together: We know that the top 4 must sum to 56% and that X contributed 4.8%. Again, we'll generate simple scenarios. (I can simply tweak the numbers so that the first 4 sum to 56. I also know that the final two terms must sum to 67.8 - 56, or 11.8%.)

Case 1: 26%, 10%, 10%, 10%, 7%, 4.8% --> 4.8% in top 6, so YES
Case 2: 26%, 10%, 10%, 10%, 6%, 5.8% ---> 4.8% not in top 6, so NO

Together they're not sufficient. Answer is E

abhasjha wrote: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.

Statement 1: 56 percent of the total expenditures was paid by the 4 highest-contributing countries, each of which paid more than Country X.
Test the percentage given in Statement 2.
Let X = 4.8%.

Case 1: X is among the 6 highest-contributing countries
Here, the percentage for the 5th-highest country = (percentage for the 6 highest) - (percentage for the 4 highest) - (percentage for X) = 67.8 - 56 - 4.8 = 7%.

Case 2: X is NOT among the 6 highest-contributing countries
Here, the total percentage for the 4th-highest and 5th-highest countries = (percentage for the 6 highest) - (percentage for the 4 highest) = 67.8 - 56 = 11.8%.
In this case, it's possible that the 5th-highest = 6% and that the 6th-highest = 5.8%.

Cases 1 and 2 satisfy both statements.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.