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

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

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21 Aug 2013, 23:27
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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.
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Re: In a group of 25 people, only three languages are spoken – English, Sp  [#permalink]

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22 Aug 2013, 03:23
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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.

Hope this helps.

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

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22 Aug 2013, 04:48
1
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.

Hope it helps.
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Re: In a group of 25 people, only three languages are spoken – English, Sp  [#permalink]

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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.

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 – English, Sp  [#permalink]

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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 – English, Sp  [#permalink]

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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 – English, Sp  [#permalink]

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

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02 Oct 2018, 11:58
pikolo2510 wrote:
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?

Veritas Prep Solution:

Quote:
Statement (1): The four people who speak two languages other than Spanish must be speaking English and German. However they may not be the only people who can interact with each other in English and German since people who speak all three languages can also interact in English and German. Hence statement (1) alone is not sufficient.

Quote:
Statement (2): One fifth of the group, a total of 5 people, speaks more than one language. Since we do not know how many of them speak English and German, statement (2) alone isn’t sufficient.

Quote:
Using both statements together, we know that 4 people speak English and German only and one speaks all the three languages (since at least one person speaks all the three languages). All others speak only one language or no language. So the number of people who can interact with each other in English and German is 5. Both statements together are sufficient to answer the question.

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

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07 Oct 2018, 14:11
ozhan wrote:

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

Im confused here at your response. if 4 people speak two languages but not Spanish, I think this statement implies E+G speakers only. How can you argue that this statements include E+G+S if the 4 people described here speak 2 languages but not spanish? it says plainly that they dont speak spanish. so imho, i think it is A. Unless I'm wrong.

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

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07 Oct 2018, 21:26
1
weiwang922 wrote:
ozhan wrote:

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

Im confused here at your response. if 4 people speak two languages but not Spanish, I think this statement implies E+G speakers only. How can you argue that this statements include E+G+S if the 4 people described here speak 2 languages but not spanish? it says plainly that they dont speak spanish. so imho, i think it is A. Unless I'm wrong.

Hello

I got your point - I think you have interpreted it correctly that first statement implies 'there are 4 such people who can speak E+G only'. But the question asks 'How many can interact with each other in English and German?' So according to the question, we need to know the number of people who are E+G only, as well as people who are E+G+S all three. From first statement we have E+G only = 4 (as you have interpreted correctly), but we still dont have how many are E+G+S all three.

Hence first statement alone is not sufficient.
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Re: In a group of 25 people, only three languages are spoken – English, Sp  [#permalink]

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08 Oct 2018, 14:05
amanvermagmat wrote:
weiwang922 wrote:
ozhan wrote:

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

Im confused here at your response. if 4 people speak two languages but not Spanish, I think this statement implies E+G speakers only. How can you argue that this statements include E+G+S if the 4 people described here speak 2 languages but not spanish? it says plainly that they dont speak spanish. so imho, i think it is A. Unless I'm wrong.

Hello

I got your point - I think you have interpreted it correctly that first statement implies 'there are 4 such people who can speak E+G only'. But the question asks 'How many can interact with each other in English and German?' So according to the question, we need to know the number of people who are E+G only, as well as people who are E+G+S all three. From first statement we have E+G only = 4 (as you have interpreted correctly), but we still dont have how many are E+G+S all three.

Hence first statement alone is not sufficient.

ah, I see. this makes so much more sense now.

Thank you.
Re: In a group of 25 people, only three languages are spoken – English, Sp   [#permalink] 08 Oct 2018, 14:05
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