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

Question

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.

ozhan · Accepted Answer

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

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

Bunuel · Answer

Theory on advanced overlapping sets problems: advanced-overlapping-sets-problems-144260.html Hope it helps.

bsahil · Answer

Thanks....just missed the "at-least"...

mvictor · Answer

damn..this question is easier than it appears to be..the solution given above is awesome.

pikolo2510 · Answer

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?

Amirfunc · Answer

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

GMATYoda · Answer

Veritas Prep Solution:

weiwang922 · Answer

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.

Bunuel , can you explain please.

amanvermagmat · Answer

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.

weiwang922 · Answer

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

Thank you.

Basshead · Answer

We don't need to draw any diagrams for this particular problem; we only need to think logically.

The questions asks for the number of people who are able to interact with each other in English and German.

Statement 1 tells us 4 people speak exactly two languages (English and German). HOWEVER, this figure does not include the individuals that can speak all three languages. An individual that can speak all three languages can certainly interact in English and German. INSUFFICIENT.

Statement 2 tells us that 5 individuals speak more than one language. Clearly insufficient.

Combined, we know 5 individuals speak more than one language. We also know that 4 people speak exactly two languages (English and German). Add the person that can speak all three languages, and we have 5 people who can interact with each other in English and German.

dadaquest · Answer

Very poor question from Veritas

Afn24 · Answer

Here's an easier way to understand the solution

bumpbot · Answer

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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

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