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# m04q19- Six students study Russian, Ukrainian & Hebrew

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Senior Manager
Joined: 29 Mar 2008
Posts: 348

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05 Sep 2008, 07:58
Nerdboy wrote:
I got A as well. Why is it incorrect?

I mentioned earlier that, I made a silly mistake and lost my ability to think further at 1 am and posted the message
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"Leave no stone unturned."
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VP
Joined: 17 Jun 2008
Posts: 1381

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05 Sep 2008, 21:36
leonidas 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?
a) 0
b) 1
c) 2
d) 3
e) 4

Even i got A
Good question !!
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cheers
Its Now Or Never

Manager
Joined: 03 Jun 2008
Posts: 137
Schools: ISB, Tuck, Michigan (Ross), Darden, MBS

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06 Sep 2008, 05:20
A for me too!!!
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Manager
Joined: 30 Jul 2007
Posts: 129

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10 Sep 2008, 18:44
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?

* 0
* 1
* 2
* 3
* 4
Director
Joined: 14 Aug 2007
Posts: 727

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10 Sep 2008, 20:02
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?

* 0
* 1
* 2
* 3
* 4

http://gmatclub.com/forum/7-t69804
Manager
Joined: 17 Dec 2008
Posts: 173

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24 Jan 2009, 22:41
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?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

Can somebody explain with Venn diagram if possible?
Intern
Joined: 19 Jan 2009
Posts: 17

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27 Jan 2009, 11:14
n(RuUuH)= n(R)+n(U)+n(H)-n(RnU)-n(UnH)-n(HnR)+n(RnUnH)

6 = 4 + 3 + 2 - [3] + n(RnUnH)
6 = 6 + n(RnUnH)
0 = n(RnUnH)
Manager
Joined: 17 Dec 2008
Posts: 173

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28 Jan 2009, 06:21
Thanks, a lot!
I got it now.
VP
Joined: 17 Feb 2010
Posts: 1491
6 students in a group study different languages [#permalink]

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30 Aug 2010, 11:11
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.
Manager
Joined: 25 Jun 2010
Posts: 91
Re: 6 students in a group study different languages [#permalink]

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30 Aug 2010, 11:28
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 ?
Manager
Joined: 17 Apr 2010
Posts: 99

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11 Oct 2010, 07:08
The anwer is 0 . its A
Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
Joined: 30 Sep 2010
Posts: 27

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11 Oct 2010, 11:16
For a related question and explanation check out:

overlapping-sets-99114.html
Manager
Joined: 09 Sep 2009
Posts: 57

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11 Oct 2010, 12:48
Well i did it this way...

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..

R J
Manager
Joined: 07 Aug 2010
Posts: 79

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11 Oct 2010, 22:29
A

fresh outta my set questions yesterday :D
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Manager
Joined: 29 Sep 2008
Posts: 143

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14 Oct 2010, 19:53
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
Intern
Joined: 19 Dec 2009
Posts: 33

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03 Jan 2011, 17:19
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?

a 0
b 1
c 2
d 3
e 4
Intern
Status: Sophomore
Affiliations: President of Student Associoation
Joined: 09 Dec 2010
Posts: 37
Schools: HBS 2+2, IESE YTP

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05 Jan 2011, 01:36
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.
Intern
Joined: 24 Jun 2010
Posts: 17

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05 Jan 2011, 02:29
6= 9 - 3(two languages)+x(all three)+0(who dont study any of the languages)
6=9-3+X+0
X=0---Ans.A
Manager
Joined: 20 Dec 2010
Posts: 247
Schools: UNC Duke Kellogg
Re: 6 students in a group study different languages [#permalink]

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25 Jun 2011, 10:42
A!

Used the formula

T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)

Nice question!
Director
Joined: 01 Feb 2011
Posts: 755
Re: 6 students in a group study different languages [#permalink]

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25 Jun 2011, 15:04
$$A U B U C=A+B+C-A intersection B-B intersection C- C intersection A + A intersection B intersection C$$

=>6 = 4+3+2-3+all three
=> all three = 0

Re: 6 students in a group study different languages   [#permalink] 25 Jun 2011, 15:04

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# m04q19- Six students study Russian, Ukrainian & Hebrew

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