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If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E

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Bunuel
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If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   10 Jul 2015, 02:37
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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
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D
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   Updated on: 10 Jul 2015, 10:55
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Bunuel wrote:
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

Kudos for a correct solution.


Method 1:

Let T=total passengers

From US = T/3
China = T/5
Japan = T/6
Europeans = T/4

Now, total of the countries above = 57/60

Remaining = T-57T/60 = 3T/60

Given, remaining = 9 ---> 3T/60 =9 ----> T=180, thus D is the correct answer.

Method 2:

LCM of 3,4,5,6 = 60, and as passengers need to be integers, there is only 1 number divisible by 60 in the given options. Thus D is the correct answer,.

Originally posted by ENGRTOMBA2018 on 10 Jul 2015, 04:12.
Last edited by ENGRTOMBA2018 on 10 Jul 2015, 10:55, edited 1 time in total.
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   10 Jul 2015, 10:21
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D

Total = x

x/3 + x/4 + x/5 + x/6 + 9 = x

19x/20 + 9 = x

180 = x
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   10 Jul 2015, 10:50
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Add each fraction using the GCF of 60.

1/3 + 1/4 + 1/5 + 1/6 = 57/60

That leaves 3 other people, but there are 9 other people. Multiple 60 by 3 to get 180.

Answer: D
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   10 Jul 2015, 15:40
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Convert the fractions into decimals. Notice the answer choices are fairly spread out, so should be okay to estimate.

.33 + .25 + .20 + .17 = .95.

So all of the passengers other than the 9 account for 95% of the total.

9 is 5% of what number? 9 * 20 = 180.

D.
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   11 Jul 2015, 09:15
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Bunuel wrote:
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

Kudos for a correct solution.


Total no of passengers= x
US Citizens=x/3, Europeans=x/4, Chinese=x/5, Japanese=x/6 Remaining=9
Therefore,l x-x/3-x/4-x/5-x/6=9
x=180
Answer D
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   13 Jul 2015, 02:41
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Bunuel wrote:
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

Kudos for a correct solution.


800score Official Solution:

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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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   24 May 2017, 10:37
1/3 + 1/4 + 1/5 + 1/6
20/60 + 15/60 + 12/60 + 10/60
57/60

3/60x = 9
3x = 9(60)

x = 180

Answer is D
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   26 May 2017, 11:49
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Bunuel wrote:
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


If we let n = the total number of passengers on the plane, we can create the following equation:

(1/3)n + (1/4)n + (1/5)n + (1/6)n + 9 = n

Multiplying the entire equation by 60, we have:

20n + 15n + 12n + 10n + 540 = 60n

540 = 3n

180 = n

Answer: D
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink] New post   27 Nov 2023, 05:31
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Re: If 1/3 of passengers on board flight #453 are U.S. citizens, 1/4 are E [#permalink]
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