In a certain year the United Nations’ total expenditures wer

[rschunti]

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.

What is the best approach to solve this question quickly?

[RonPurewal]

first, realize that the $1.6bn figure is irrelevant, since everything else in the problem is stated purely in terms of percentages. therefore, you should concentrate only on percentages.

(2) alone
- to try to make country x NOT in the top six, distribute the percentages as evenly as possible: it's possible that each of the six highest-contributing countries paid 67.8/6 = 11.3 percent of the total. if that were the case, then country x, at 4.8%, would be lower than sixth place.
- to try to get country x INTO the top six, make the distribution as lopsided as possible: say one country paid 60% of everything. then country x could be second at 4.8%, and the 3rd, 4th, 5th, 6th place countries could combine to pay 67.8 - 64.8%.
INSUFFICIENT

(1) alone
taken alone, this condition only tells you that country x is in fifth place or lower.
INSUFFICIENT

(together)
the fifth- and sixth-place countries together paid out 67.8 - 56 = 11.8 percent of the total. at this point the strategy is roughly the same as for statement (2) alone:
- to try to make country x NOT in the top six, distribute the percentages as evenly as possible: the fifth- and sixth-place countries could both have contributed 11.8/2 = 5.9 percent. this would mean country x = not in the top six.
- to try to get country x INTO the top six, let the fifth-place country pay 11.8 - 4.8 = 7 percent; therefore country x is in sixth place.
INSUFFICIENT

answer = e

[ashish.jere]

Thanks Ron.

[Ben Ku]

Glad it helped!

[pratik.munjal]

Ron, is there a specific reason, that you've evaluated st. 2 first and then st. 1?

Is it just for this question, or is that your, um...style? :)

[RonPurewal]

Ron, is there a specific reason, that you've evaluated st. 2 first and then st. 1?

Is it just for this question, or is that your, um...style? :)

i am lazy; statement 2 has fewer words.

[pratik.munjal]

i am lazy; statement 2 has fewer words.

:) I doubt that!

[RonPurewal]

i am lazy; statement 2 has fewer words.

:) I doubt that!

serious.

[pratik.munjal]

Now I doubt it all the more--you've posted 2 days before Christmas! So you aren't lazy at all. Anyway, Merry X Mas to the Manhattan Trainers team!

[RonPurewal]

Now I doubt it all the more--you've posted 2 days before Christmas! So you aren't lazy at all. Anyway, Merry X Mas to the Manhattan Trainers team!

well, i have a lot more time to post during the holidays.

i actually enjoy posting here, so i don't count it as "work" in considering the laziness equation. perhaps that's the secret -- i'm fortunate enough to like my work, so i can do a lot of it because it doesn't feel like "work".

in any case, we should probably end this particular side discussion at this point, so as not to clutter up the thread. happy holidays, whatever holidays you observe.