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On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He

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Bunuel
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On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   21 Apr 2016, 00:36
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On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40
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C
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OptimusPrepJanielle
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   21 Apr 2016, 02:27
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Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40


Assume the total members = x
Farsi = .4x
Hebrew = .75x
Farsi + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only Farsi = .25x, Only Hebrew = .6x, both = .15x

Since these are all people, all of these should be whole numbers.

Checking the options:

A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only Farsi = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 20 Only Farsi = .25*20 = 5, Only Hebrew = .6*20 = 12, both = .15*20 = 3. We have the people as whole numbers. CORRECT
D. 24
E. 40

Since we have to find the lowest number, no need to calculate for the rest of the options.

Correct Option: C
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   21 Apr 2016, 02:45
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F = 0.4x; H = 0.75x

F + H + 2(Both) = 1.15x
F + H + Both = x
Therefore, Both = 0.15x = (3/20)x

For (3/20)x to be an integer the least value of x that can cancel out the denominator is 20. No need to check for each answer choice.

Answer: C
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On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   24 Apr 2016, 20:37
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Hi,

Let's keep it simple without getting into any of Algebra.

It's asking the SMALLEST TOTAL. Let's work backwards in order A-E as it is asking the MINIMUM.

We can straight away reject A, B, D as they DO NOT produce number value for given fractions (Passengers got to be in numbers but not decimals). First such no is 20 and next is 40. Down to C and E.

At this point, we should not be worried about how the overlap works and all. That's a simple distraction as it add no value for what we want to conclude.

Answer C.

Key is to avoid cumbersome equations when they're not required. Hope this helps!

Posted from my mobile device
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   05 Aug 2019, 03:21
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Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40



Total number of passengers on plane must be the LCM of denominators of fractions given.


LCM ( 5,4) = 20.

we are looking for smallest number of passengers on plane .

Thus , 20 is the correct answer.
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   11 Aug 2019, 19:26
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Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40


Since the number of passengers on the place must be divisible by 5 and 4, the smallest number of passengers on the plane is 20.

Answer: C
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   21 Apr 2016, 02:59
Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40



let total no. passengers be X and passengers who speak both is Y
then 2/5X + 3/4X-Y=X
=>3/20X=y
the minimum possible value for which Y is integer is X=20.
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   15 Oct 2019, 12:33
Bunuel wrote:
On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40


You need the least multiple of 5 and 4 which is 20
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Re: On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak He [#permalink] New post   08 Jun 2022, 08:38
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