Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages?

Re: m04 - languages [#permalink]
10 Sep 2008, 19:02

sarzan wrote:

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages?

6 students in a group study different languages as specified:

* Russian: 4 * Ukrainian: 3 * Hebrew: 2

Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

6 students in a group study different languages as specified: Russian: 4 Ukrainian: 3 Hebrew: 2 Each student studies at least 1 language. It is also known that exactly 3 students learn exactly 2 languages. How many students are studying all languages?

Can somebody explain with Venn diagram if possible?

6 students in a group study different languages [#permalink]
30 Aug 2010, 10:11

6 students in a group study different languages as specified:

Russian: 4 Ukrainian: 3 Hebrew: 2

Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

0 1 2 3 4

How can we derive the answer with the below formula?

Total = n(A) + n(B) + n(C) – 2(Exactly 2) – 2 (A n B n C) + Neither.

Re: 6 students in a group study different languages [#permalink]
30 Aug 2010, 10:28

I normally use Venn diagram, however isn't the formula is Total = n(A) + n(B) + n(C) – (Exactly 2) – 2 (A n B n C) + Neither ? That gives the answer "0".

6 students and 9 places up for grabs ( as R=4,U=3,H=2)... Now exactly 3 students study exactl;y 2 subjects..tht means 3x2=6 places out of the total 9.... 3 places remain...and 3 students remain. Since every student studies atleast one language, and only 3 places remain..therefore no single student studies all 3 languages..

like in mgmat book they have solved some questions by table method while others through Venn diagram method.When i look at an overlapping set question,i get confused as which one of the two methods to apply.Any inputs

6 students in a group study different languages as specified:

Russian: 4 Ukrainian: 3 Hebrew: 2 Each student studies at least 1 language. If it is also known that exactly 3 students study exactly 2 languages, how many students are studying all three languages?

Re: overlapping sets [#permalink]
04 Jan 2011, 00:19

1

This post received KUDOS

A for me!

The question says that 3 students study exactly 2 languages each. THerefore from the total of languages being studied by the 6 individual, 9

9-6=3

There are 3 people left for 3 languages left. Moreover, every person has to study at least one language so it is no feasible to have one person studying 3 languages and the other 2 studying none.

Re: overlapping sets [#permalink]
05 Jan 2011, 00:36

yep it is 0. Students who are taking 2 languages: 1 stud(Rus, Ukr) 1 stud(Rus, Heb) 1 stud(Ukr, Rus)=>in this case 2 rus+1 urk+1 heb=4, if one takes 3 languages, then one student will be left with 0. , so no one can take three languages. In other cases, still no one can take three languages.