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by pkw209 » Mon Feb 01, 2010 4:28 pm
Taken from GMAT PREP. Detailed explanation please!

In a certain year the total expenditure the united nations were $1.6 billion. of this amount, 67.8% 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?

A) 56 percent of the total expenditures was paid by the 4 highest contributing countries, each of which paid more than country X

B) Country X paid 4.8 percent of the total expenditures.

E
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by papgust » Mon Feb 01, 2010 6:52 pm
Total Expenditure = $1.6 billion

Top 6 countries contribution = 1.6 * 10^7 * 68 = $1.08 billion
Remaining Countries contribution = 1.6 * 10^7 * 32 = $0.51 billion

Country X among Top 6 OR Remaining?

(A) Top 4 contributions = 1.6 * 10^7 * 56 = $0.90 billion

So, 5th and 6th Countries contributed = 1.08 - 0.90 = $0.18 billion
We only know that top 4 countries contributed more than Country X. But we don't know how much each contributed. It is possible for country X to be among Top 6 or in the remaining section. Not enough info. Insufficient.

(B) Country X = $0.075 billion
Again, not info to deduce Country X's position. Insufficient.

Combined,
Still it is possible to have 2 cases.
1) Top4 = $0.90 billion, 5th country = $0.1725 billion, Country X = $0.075 billion (6th place).
2) Top4 = $0.90 billion, 5th and 6th country > $0.075 billion. Country X = $0.075 billion (Any place other than top6).
Insufficient.
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pls explain

by swapna » Mon Feb 01, 2010 10:29 pm
Hi...can u pls explain...how 5th country = $0.1725 billion,cos it exceeds the total of 1.08 bn??. Can u also explain the 2nd possibility in the combined option??

thanks
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by papgust » Mon Feb 01, 2010 11:05 pm
Sorry it's a calculation mistake. But still the answer is not affected. Here's why,

Top 4 countries contributed $0.90 billion

5th and 6th Countries contributed = 1.08 - 0.90 = $0.18 billion [From Statement I]

Country X contributed $0.075 billion [From Statement II]

In Case (i), if we consider country X among Top 6, then it is possible to have,

Top4 = $0.90 billion, Country X as $0.075 billion
So, 5th country = 0.18 - 0.075 = $0.105 billion --> 6th place.

In Case (ii), It is possible for 5th and 6th countries to contribute all of the remaining $0.18 billion and eventually knock off Country X from Top 6 list.
So,
Top4 = $0.90 billion, 5th and 6th country (Combined $0.18 billion) > $0.075 billion.
Country X = $0.075 billion (NOT AMONG Top 6)

So, Insufficient.

Let me know if you have any further questions.
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by pkw209 » Tue Feb 02, 2010 1:23 pm
Top4 = $0.90 billion, 5th and 6th country (Combined $0.18 billion) > $0.075 billion.
Country X = $0.075 billion (NOT AMONG Top 6)

That part above is confusing. What needs to be explained is that you can have 5th and 6th each paying .09 billion, which would knock country X (.075 billion form statement 2) out of the top 6.

What I'm looking for is a quicker way of solving this problem. I think most people can compute this given enough time. I guess it comes down to breaking it down logically, although that doesn't always work.
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by Stuart@KaplanGMAT » Tue Feb 02, 2010 10:58 pm
pkw209 wrote:Taken from GMAT PREP. Detailed explanation please!

In a certain year the total expenditure the united nations were $1.6 billion. of this amount, 67.8% 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?

A) 56 percent of the total expenditures was paid by the 4 highest contributing countries, each of which paid more than country X

B) Country X paid 4.8 percent of the total expenditures.
There's really no reason to convert from %s to actual $, since all the information in the statements is in percents.

(1) top 4 paid 56% out of the 67.8% of the top 6.

Well, X could be in the bottom 2 of the top 6 or in the remaining 153 countries... insufficient.

(2) The top 6 paid 67.8%, which could be roughly 11% each, so X could be in the bottom 153; the top 5 may have paid all of the 67.8% other than 4.8%, so X could have been 6th... Insufficient.

Combined: if the top 4 pay 56% and X pays 4.8%, X could be 6th; alternatively, the remaining members of the top 6 could pay 11.8%/2 each and X could be 7th... still insufficient, choose E.
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by papgust » Tue Feb 02, 2010 11:03 pm
First up, there are a couple of calculations for calculating contributions. If you are quick enough to do that, then this prob can be solved within 2 minutes, which is a fair enough time for GMAT math!

Alternatively, i guess you could just work out with the given percentages without doing any calculation.

1) Top 6 countries - 68% (rounded off for the sake of simplicity)
2) Remaining countries - 32%

Country X among (1) OR (2)?

A. Top 4 countries - 56%

We are not sure how much Country X paid. Insufficient.

B. Country X - 4.8%

Clearly insufficient.

Combined,
Top 4 countries - 56%
Remaining contribution from the total 68% - 12%

(1) Of this 12% b/w 5th and 6th country, Country X MAY have paid 4.8% and another country MAY have paid 7.2%. So, Country X IS among Top 6.

(OR)

(2) Of this 12% b/w 5th and 6th country, Two different countries MAY have paid all of 12% - each contributing more than Country X. So, Country X CANNOT be among Top 6.

Insufficient.
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by sanju09 » Wed Feb 03, 2010 3:56 am
pkw209 wrote:Taken from GMAT PREP. Detailed explanation please!

In a certain year the total expenditure the united nations were $1.6 billion. of this amount, 67.8% 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?

A) 56 percent of the total expenditures was paid by the 4 highest contributing countries, each of which paid more than country X

B) Country X paid 4.8 percent of the total expenditures.

E
While discussing a problem here on this forum, we should ignore the phraseology as long as it doesn't challenge our common senses, really.

Now, statement (1) very clearly brings up that the country X is definitely NOT among the top 4 contributors. Hence, it may or may not be among the top 6 or among all the 159 contributors. Hence, (1) is insufficient.

See, statement (2) includes X among the contributing countries, with its contributed amount. Now, with 4.8 percent of the total expenditures as contribution, country X still may or may not be among the 6 highest contributing countries. Hence, (2) is insufficient.

Blending (1) and (2) keeps us wondering that with 4.8 percent as contribution, can the country X be one of the bottom two contenders of the top 6 contributors or not; as the remaining 11.8 percent of the fair share of the top 6 still may or may not include country X. Still, insufficient.

[spoiler]E[/spoiler]
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