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 Post subject: GMAT FractionsPosted: Thu Nov 25, 2010 4:44 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are Europeans, 1/5 are from China, 1/6 are from Japan and the remaining 9 people are citizens of other countries then how many passengers are on board flight #453?

A. 90
B. 108
C. 135
D. 180
E. 270

(D) Let’s count what part of all the passengers on board flight make citizens of other countries. We can do that by deducting fractions of passengers from known countries:
1 – 1/3 – 1/4 – 1/5 – 1/6 = 1 – (1/3 + 1/4 + 1/5 + 1/6)
The common denominator is 2 × 2 × 3 × 5 = 60.
1/3 + 1/4 + 1/5 + 1/6 = (20 + 15 + 12 + 10)/60 = 57/60 = 19/20
So citizens of other countries make 1/20 of all the passengers on board. Therefore there are 9 × 20 = 180 passengers on board.
The correct answer is choice (D).
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How did you come up with the number 9 from the fraction 19/20?

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 Post subject: GMAT FractionsPosted: Thu Nov 25, 2010 4:47 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
The question statement tells us that ".. the remaining 9 people are citizens of other countries ..". We've calculated that it makes 1/20 of the total number of passengers. Therefore, if we denote the total number of passengers by x, then we get:
x × (1/20) = 9
x = 9 × 20 = 180

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