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# In Country X, 1/2 of the population can speak English, 1/3 can speak

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Re: In Country X, 1/2 of the population can speak English, 1/3 can speak [#permalink]
Let the population of country X be 30

Those who can speak only English will be A
Those who can speak only French be C
Those who can speak both be B

Now,
1/2 of total can speak English.
That will be A+B = 30*1/2=15
(Since only English is not stated. So both and only English will be included)

1/3 of total can speak French.
That will be C+B = 30*1/3=10
(Since only French is not stated. So both and only French will be included)

1/5 of total can speak both:
B = 1/5*30 = 6

Therefore A will be 15-6=9
And C will be 10-6=4

Those who can't speak English or French will be 30-9+4+6 = 11
The fraction who can't speak either of the language will be 11/30

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In Country X, 1/2 of the population can speak English, 1/3 can speak [#permalink]
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Bunuel wrote:
In Country X, 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French. What fraction of the population of Country X can speak neither English nor French?

A. 2/15

B. 1/6

C. 3/10

D. 11/30

E. 13/30

PS20358

In Country X, 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French. What fraction of the population of Country X can speak neither English nor French?

Neither = Total - (English+ French - Both) = 1 - (1/2 + 1/3 - 1/5) = 1 - (15 + 10 - 6)/30 = 1 - 19/30 = 11/30

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Re: In Country X, 1/2 of the population can speak English, 1/3 can speak [#permalink]
Bunuel wrote:
In Country X, 1/2 of the population can speak English, 1/3 can speak French, and 1/5 can speak both English and French. What fraction of the population of Country X can speak neither English nor French?

A. 2/15

B. 1/6

C. 3/10

D. 11/30

E. 13/30

We can let the total number of people = 60 and create the equation:

60 = 30 + 20 - 12 + N

22 = N

Thus, 22/60 = 11/30 of the people speak neither language.

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Re: In Country X, 1/2 of the population can speak English, 1/3 can speak [#permalink]
­Classic overlapping sets we know and love:

Re: In Country X, 1/2 of the population can speak English, 1/3 can speak [#permalink]
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