Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Sep 2014, 10:46

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

m04q19- Six students study Russian, Ukrainian & Hebrew

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
m04q19- Six students study Russian, Ukrainian & Hebrew [#permalink] New post 13 Apr 2008, 14:52
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
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
4 KUDOS received
Director
Director
avatar
Joined: 10 Sep 2007
Posts: 950
Followers: 7

Kudos [?]: 187 [4] , given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 13 Apr 2008, 16:04
4
This post received
KUDOS
Use Set Theory.

Total = A + B + C - (AB+BC+CA) + ABC
Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6
So ABC = Total - A - B - C + (AB+BC+CA) = 6 - 4 - 3 - 2 + 3 = 0

Answer A.
2 KUDOS received
CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 507 [2] , given: 19

GMAT Tests User
Re: m04 q19 [#permalink] New post 26 Jan 2009, 12:52
2
This post received
KUDOS
ConkergMat 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?

Can somebody explain with Venn diagram if possible?


r + u + h - (ru+uh+hr) - 2(rhu) + none = 6
4 + 3 + 2 - (3) - 6 + 0 = 2 (rhu)
2 (rhu) = 0


no. of students studying all languages (rhu) = 0

The picture is attached.
Attachments

VENN DIAGRAM.JPG
VENN DIAGRAM.JPG [ 31.09 KiB | Viewed 3007 times ]


_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

1 KUDOS received
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1467
Followers: 6

Kudos [?]: 102 [1] , given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 06:01
1
This post received
KUDOS
watch out for "exactly two" question...

http://www.gmatclub.com/forum/7-p374736 ... n+#p374736
1 KUDOS received
Manager
Manager
avatar
Joined: 21 Jul 2010
Posts: 56
Followers: 1

Kudos [?]: 7 [1] , given: 3

GMAT ToolKit User
Re: overlapping sets [#permalink] New post 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.

Dunno if it is clear ;-)

Ans A. 0
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 13 Apr 2008, 18:54
abhijit_sen wrote:
Use Set Theory.

Total = A + B + C - (AB+BC+CA) + ABC
Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6
So ABC = Total - A - B - C + (AB+BC+CA) = 6 - 4 - 3 - 2 + 3 = 0

Answer A.


I tried this and messed up somewhere.
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 17

Kudos [?]: 286 [0], given: 1

Premium Member CAT Tests
Re: students in a group : fastest way to solve [#permalink] New post 13 Apr 2008, 22:51
kyatin wrote:
abhijit_sen wrote:
Use Set Theory.

Total = A + B + C - (AB+BC+CA) + ABC
Given A = 4, B = 3, C = 2, AB+BC+CA = 3, Total = 6
So ABC = Total - A - B - C + (AB+BC+CA) = 6 - 4 - 3 - 2 + 3 = 0

Answer A.


I tried this and messed up somewhere.


@Abhijit
The colored is not "plus" :lol:

@kyatin,
Total = A+B+C -2*(ABC) - (AB+BC+CA)
Let try :)
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 05:35
Sondenso + is correct.

It should be written more like this


Total = A + B + C - { (AB+BC+CA) - 3(ABC) }

I believe Abhijit did miss 3 in the equation but has it in the final calculation.
Director
Director
avatar
Joined: 10 Sep 2007
Posts: 950
Followers: 7

Kudos [?]: 187 [0], given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 07:40
kyatin wrote:
Sondenso + is correct.

It should be written more like this


Total = A + B + C - { (AB+BC+CA) - 3(ABC) }

I believe Abhijit did miss 3 in the equation but has it in the final calculation.


I have used the correct formula. 3 is not coming from multiplication but from the value mentioned in the question (as given "It is also known that exactly 3 students learn exactly 2 languages").

Also see my explanation earlier, in which I have mentioned what all of these values mentioned in formula should be and we are getting value of ABC and not Total.
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 10:57
Abhijit,

You are correct.

Total = A + B + C - [ (AB+BC+CA) - (ABC) ]

is the right formula.

Thanks
Kyatin
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3404
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 160 [0], given: 2

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 19:36
the way I approached this..

4+3+2-3-2(abc)=6

6-2(abc)=6

2(abc)=0..therefore no one takes all 3 courses..
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2007
Posts: 451
Location: Earth
Followers: 2

Kudos [?]: 38 [0], given: 0

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 14 Apr 2008, 22:53
bkk145 wrote:
watch out for "exactly two" question...

http://www.gmatclub.com/forum/7-p374736 ... n+#p374736


That was neat thread bkk145. Kudos.
SVP
SVP
avatar
Joined: 04 May 2006
Posts: 1941
Schools: CBS, Kellogg
Followers: 17

Kudos [?]: 286 [0], given: 1

Premium Member CAT Tests
Re: students in a group : fastest way to solve [#permalink] New post 15 Apr 2008, 18:03
abhijit_sen wrote:
kyatin wrote:
Sondenso + is correct.

It should be written more like this


Total = A + B + C - { (AB+BC+CA) - 3(ABC) }

I believe Abhijit did miss 3 in the equation but has it in the final calculation.


I have used the correct formula. 3 is not coming from multiplication but from the value mentioned in the question (as given "It is also known that exactly 3 students learn exactly 2 languages").

Also see my explanation earlier, in which I have mentioned what all of these values mentioned in formula should be and we are getting value of ABC and not Total.


At the moment, I think, I am being confused. The comment I made is from GmatCAt. And now I am advived by the link provided by bkk145. I think I need a thorough material about this concept.

Friend, do you have a good material about the Set theory and may you share with me?
Many thank and appreciation!
_________________

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 06 Jan 2008
Posts: 560
Followers: 2

Kudos [?]: 98 [0], given: 2

GMAT Tests User
Re: students in a group : fastest way to solve [#permalink] New post 17 Apr 2008, 16:41
bkk145 wrote:
watch out for "exactly two" question...

http://www.gmatclub.com/forum/7-p374736 ... n+#p374736


Thanks for the link.
Senior Manager
Senior Manager
User avatar
Joined: 29 Mar 2008
Posts: 350
Followers: 4

Kudos [?]: 48 [0], given: 0

GMAT Tests User
Sets- Language [#permalink] New post 04 Sep 2008, 23:42
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
_________________

To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton

Director
Director
avatar
Joined: 14 Aug 2007
Posts: 735
Followers: 7

Kudos [?]: 102 [0], given: 0

GMAT Tests User
Re: Sets- Language [#permalink] New post 04 Sep 2008, 23:57
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


A.

I solved using a venn diagram, consider x, y and z to be students studying 2 languages and let a be num. of students who study all 3.

then

2 - x -y -a + 4 -x -z -a + 3 -y -z -a + x + y + z + a = 6

9 - (x +y+z ) -2a = 6

We know that x + y + z = 3

giving us a =0
Senior Manager
Senior Manager
User avatar
Joined: 29 Mar 2008
Posts: 350
Followers: 4

Kudos [?]: 48 [0], given: 0

GMAT Tests User
Re: Sets- Language [#permalink] New post 05 Sep 2008, 00:05
Thanks, alpha_plus_gamma.

I forgot to include ( x + y + z + a) and was getting incorrect answer....Duh :oops: .....Should stop making these kind of mistakes.
_________________

To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton

Senior Manager
Senior Manager
avatar
Joined: 16 Jul 2008
Posts: 290
Schools: INSEAD Dec'10
Followers: 2

Kudos [?]: 14 [0], given: 4

GMAT Tests User
Re: Sets- Language [#permalink] New post 05 Sep 2008, 00:11
I got A as well. Why is it incorrect?
_________________

http://applicant.wordpress.com/

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1579
Followers: 12

Kudos [?]: 184 [0], given: 0

GMAT Tests User
Re: Sets- Language [#permalink] New post 05 Sep 2008, 01:08
I got 0 as well....but using formula....AUBUC = A + B + C - AB - BC - CA + ABC.
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1550
Followers: 8

Kudos [?]: 208 [0], given: 1

GMAT Tests User
Re: Sets- Language [#permalink] New post 05 Sep 2008, 02:40
I got A as well:

Total = U + R + H - 3(because 3 people study exactly 2 languages, 3 has been counted twice so you need to subtract it once) - 2x (because the number of people studying all the 3 languages have been counted 3 times, you want to subtract by twice the amount so that you can count it only once instead of 3 times).

so:

6= H+R+U - 3 - 2x

6 = 2+4+3 - 3 -2x

6= 9 - 3 - 2x

6 = 6 - 2x

0 = -2x

x = 0

Answer A
Re: Sets- Language   [#permalink] 05 Sep 2008, 02:40
    Similar topics Author Replies Last post
Similar
Topics:
Each of six students, four girls and two boys, spent an arjtryarjtry 3 03 Sep 2008, 00:43
six students are equally divided into 3 groups. then the arjtryarjtry 8 11 Aug 2008, 00:31
Each of six students, four girls and two boys, spent an arjtryarjtry 2 25 Jul 2008, 02:38
Experts publish their posts in the topic Russian applicants Markovich 15 29 Dec 2007, 11:28
MBA Students cheat the most: Study Praetorian 2 22 Sep 2006, 17:02
Display posts from previous: Sort by

m04q19- Six students study Russian, Ukrainian & Hebrew

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2   3    Next  [ 52 posts ] 

Moderators: Bunuel, WoundedTiger



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.