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In a group of 25 people, only three languages are spoken –

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In a group of 25 people, only three languages are spoken –  [#permalink]

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New post 21 Aug 2013, 23:27
4
13
00:00
A
B
C
D
E

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  75% (hard)

Question Stats:

52% (01:08) correct 48% (00:56) wrong based on 396 sessions

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In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German?

(1) 4 people speak two languages but do not speak Spanish
(2) One fifth of the group speaks more than one language.


Please help with this question. I am getting A as answer
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Re: In a group of 25 people, only  [#permalink]

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New post 22 Aug 2013, 03:23
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2
There are 25 people and AT LEAST one of them speaks all three languages.

We are trying to find the people who can interact with each other in English and German. That means these people can either speak English and German or English, German and Spanish.

So we need to find the number of people that fall under these two categories.

Let's look at the remaining information

1) 4 people speak two languages but not Spanish ==> this is enough for the first category( i.e. the people that speak English and German only), but we do not know how many people speak all three languages (the question stem says AT LEAST one person)

INSUFFICIENT

2) One fifth of the group speaks more than one language. ==> let's break this down.

one fifth of the group is 25/5 = 5 people. 5 people speaks more than one language. We do not know how many of these people speak only English and German or all three languages.

INSUFFICIENT.

Now let's look at both informations together.

We know that 4 people speak English and German, and only 5 people speak more than one language(i.e. 2 languages or 3 languages). The information in question stem indicated that there is at least one person who speaks all three languages, but with these information we can definitely say that there is exactly one person who speaks all three languages. Thus determining that 5 people can interact with each other in English and German.

Answer:C

Hope this helps.

Cheers
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Re: In a group of 25 people, only three languages are spoken –  [#permalink]

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New post 22 Aug 2013, 04:48
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bsahil wrote:
In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German?

(1) 4 people speak two languages but do not speak Spanish
(2) One fifth of the group speaks more than one language.


Please help with this question. I am getting A as answer


Theory on advanced overlapping sets problems: advanced-overlapping-sets-problems-144260.html

Hope it helps.
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Re: In a group of 25 people, only  [#permalink]

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New post 22 Aug 2013, 10:33
ozhan wrote:
There are 25 people and AT LEAST one of them speaks all three languages.

We are trying to find the people who can interact with each other in English and German. That means these people can either speak English and German or English, German and Spanish.

So we need to find the number of people that fall under these two categories.

Let's look at the remaining information

1) 4 people speak two languages but not Spanish ==> this is enough for the first category( i.e. the people that speak English and German only), but we do not know how many people speak all three languages (the question stem says AT LEAST one person)

INSUFFICIENT

2) One fifth of the group speaks more than one language. ==> let's break this down.

one fifth of the group is 25/5 = 5 people. 5 people speaks more than one language. We do not know how many of these people speak only English and German or all three languages.

INSUFFICIENT.

Now let's look at both informations together.

We know that 4 people speak English and German, and only 5 people speak more than one language(i.e. 2 languages or 3 languages). The information in question stem indicated that there is at least one person who speaks all three languages, but with these information we can definitely say that there is exactly one person who speaks all three languages. Thus determining that 5 people can interact with each other in English and German.

Answer:C

Hope this helps.

Cheers



Thanks....just missed the "at-least"...
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Re: In a group of 25 people, only three languages are spoken –  [#permalink]

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New post 16 Feb 2016, 20:23
damn..this question is easier than it appears to be..the solution given above is awesome.
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Re: In a group of 25 people, only three languages are spoken –  [#permalink]

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New post 24 Sep 2017, 13:02
Hey Bunuel, VeritasPrepKarishma

According to this question, we won't have any person who speaks "English and Spanish" and "Spanish and German". Both are zero - am i right?
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Re: In a group of 25 people, only three languages are spoken –  [#permalink]

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New post 04 Aug 2018, 19:05
Hi All,

Can someone help by applying the overlapping sets formula in the question above?

I just know of the two of them from advance overlapping problems

1) Total= A+B+C - (Sum of 2 group overlaps) +All three+ Neither
2) Total= A+B+C -(Sum of exactly 2 group overlaps)_2(All three) + Neither

Thanks
Re: In a group of 25 people, only three languages are spoken – &nbs [#permalink] 04 Aug 2018, 19:05
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