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by [email protected] » Wed Jun 30, 2010 9:12 pm
) At an international conference, 100 delegates spoke English, 40 spoke French, and 20 spoke both English and French. How many delegates could speak at least one of these two languages?
A) 110 B) 100 C) 140 D) 120
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by selango » Wed Jun 30, 2010 9:21 pm
P(E)=100

P(F)=40

P(EnF)=20

People who speak only English =P(E)-P(EnF)=100-20=80

People who speak only French=P(E)-P(EnF)=40-20=20

total who speak atleast one language=100
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by raunakrajan » Wed Jun 30, 2010 9:54 pm
[email protected] wrote:) At an international conference, 100 delegates spoke English, 40 spoke French, and 20 spoke both English and French. How many delegates could speak at least one of these two languages?
A) 110 B) 100 C) 140 D) 120

its simpler using Venn Diagram Rathi,

Image

we know English = 100 (this would include both eng and french too!)
French = 40 (includes eng and french!)
so basically the intersection of the two = 20 therefore only english will be 100-20 = 80
likewise french = 40 - 20= 20
now, they have asked how many could at least speak one language?
which implies, either french or english
=80+20=100
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by deepaks04 » Wed Jun 30, 2010 10:36 pm
The question is looking for atleast one language meaning one or more language

so
only english = 100-20 =80
only french = 40-20=20
both english n french = 20(given)

atleast one language = only english + only french + both neglish and french = 120
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by selango » Wed Jun 30, 2010 10:47 pm
yes its 120.
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by Stuart@KaplanGMAT » Thu Jul 01, 2010 12:40 am
[email protected] wrote:) At an international conference, 100 delegates spoke English, 40 spoke French, and 20 spoke both English and French. How many delegates could speak at least one of these two languages?
A) 110 B) 100 C) 140 D) 120
Here's another way of solving:

100 delegates speak English. Of the 40 delegates who speak French, 20 also speak English. So, there are 20 French speakers who don't speak English.

So, we have 100 people who speak English (alone or with French) and 20 people who speak just French.

100 + 20 = 120.

As an aside, of course this isn't a real GMAT question, since there are only 4 choices. What's the source? I've noticed that bubblyrathi has posted quite a few non-GMAT questions; without the source, people should be very wary of these posts, since studying non-GMAT questions can actually hurt your GMAT performance.

Also, not sure why this thread it titled "probability", since this certainly isn't a probability question.
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