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# m04q19- Six students study Russian, Ukrainian & Hebrew

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Intern
Joined: 16 Jun 2011
Posts: 30

Kudos [?]: 1 [0], given: 6

Re: 6 students in a group study different languages [#permalink]

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25 Jun 2011, 14:23
Substitution is fast but inelegant. Sub 0 for all three - 0 students used. Then subtract the 3 paired students from 4 Russian and 3 Ukrainian leaving 1 Russian and 2 Hebrew student. 3 pairs + 1 Russian + 1 Hebrew = 6 students. 0 yields 6=6 students

Kudos [?]: 1 [0], given: 6

Senior Manager
Joined: 17 May 2010
Posts: 285

Kudos [?]: 56 [0], given: 7

GMAT 1: 710 Q47 V40
Re: 6 students in a group study different languages [#permalink]

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13 Jul 2011, 18:43
Use formula

Total = A + B + C + neither - 2*all3 - atleast2

Neither = 0.

Plug it in and we get answer as 0.
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Kudos [?]: 56 [0], given: 7

Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 261

Kudos [?]: 1261 [0], given: 48

Re: 6 students in a group study different languages [#permalink]

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27 Aug 2011, 11:48
Total = A+B+C -(exactly 2) -2(exactly 3) + Neither

you'll get A
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Kudos [?]: 1261 [0], given: 48

Intern
Joined: 13 Jul 2010
Posts: 2

Kudos [?]: 12 [0], given: 4

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12 Sep 2011, 18:03
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

Kudos [?]: 12 [0], given: 4

Senior Manager
Joined: 24 Mar 2011
Posts: 428

Kudos [?]: 223 [0], given: 20

Location: Texas

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12 Sep 2011, 18:49
gokoli wrote:
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

i dont think we need a venn diagram here..

from given -
1) each student studies atleast 1 language, so 6 students studies 6 languages atleast...
2) 3 students studies exactly 2 languages.. = 6
so alltogether from the info, 6 students studies 6+3 = 9 languages (we are adding 3 because 1 language isalready considered before)..

now its also given that total 4+3+2 =9 languages are studied..
so none student studies all 3 languages. answer A.

Kudos [?]: 223 [0], given: 20

Senior Manager
Joined: 08 Nov 2010
Posts: 388

Kudos [?]: 133 [0], given: 161

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12 Sep 2011, 19:56
I try always to use the formula:

Total = A+B+C-Both-2*all

so:

6=4+3+2-3-2x -----> x=0
_________________

Kudos [?]: 133 [0], given: 161

Intern
Joined: 24 Jul 2009
Posts: 29

Kudos [?]: 6 [0], given: 1

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12 Sep 2011, 20:10
agdimple333 wrote:
gokoli wrote:
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

I believe this is correct, but please help me find the flaw in my reasoning here...if it exists

1. From the info we know all 6 students have at least 1 language and 3 have exactly two. Therefore we have (3+6) =9 languages at minimum. Because we know 3 have exactly 2, the number studying all three must be 3 or less, so rule out d.

2. Because the numbers next to the languages added together represent the total of all possible combinations, when we add them we get the same number as with the requirements above. So, we know that the requirements must be 1 language for 3 and 2 languages for 3. Therefore, we have 0 students studying all 3.

Kudos [?]: 6 [0], given: 1

Manager
Status: Prepping for the last time....
Joined: 28 May 2010
Posts: 180

Kudos [?]: 34 [0], given: 21

Location: Australia
Concentration: Technology, Strategy
GMAT 1: 630 Q47 V29
GPA: 3.2

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12 Sep 2011, 20:21
(4+3+2) -3 -2x = 6
=> x=0
_________________

Two great challenges: 1. Guts to Fail and 2. Fear to Succeed

Kudos [?]: 34 [0], given: 21

Intern
Joined: 13 Oct 2011
Posts: 4

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

Re: m04q19- Six students study Russian, Ukrainian & Hebrew [#permalink]

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14 Oct 2011, 05:22
I Have a special formula for this case.....
S-X=TWO+2*THREE
Here s is the sum of sets which equals to 4+3+2=9
x is the no.of people who study at least one language which is 6 bcoz six people r there nd each reads at least one language so 6*1=6
nd exactly 3 students study 2 language..
so S=9,X=6,No.of student exactly studying two language=3
so 9-6=3+2*3 which equals to 0...

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

Manager
Joined: 16 Sep 2010
Posts: 219

Kudos [?]: 136 [0], given: 2

Location: United States
Concentration: Finance, Real Estate
GMAT 1: 740 Q48 V42
Re: m04q19- Six students study Russian, Ukrainian & Hebrew [#permalink]

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16 Nov 2011, 22:16
A. Just work with the three who study two and you see its impossible for one to study three.

Kudos [?]: 136 [0], given: 2

Director
Joined: 27 Jun 2011
Posts: 879

Kudos [?]: 247 [0], given: 57

Re: students in a group : fastest way to solve [#permalink]

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24 Nov 2011, 13:57
kyatin wrote:
Abhijit,

You are correct.

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

is the right formula.

Thanks
Kyatin

This is the right way to solve.........
_________________

Kudos [?]: 247 [0], given: 57

Senior Manager
Joined: 15 Sep 2009
Posts: 263

Kudos [?]: 78 [0], given: 6

Re: m04q19- Six students study Russian, Ukrainian & Hebrew [#permalink]

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15 Oct 2012, 05:26
I almost never advocate memorizing formulas but the 3-set Venn calls for an exception.

The formula is fast, clean, and highly recommended.

A+B+C - (partcipants in exactly two activities) - 2(participants in all three activities)= Total number of participants.

Applying this formula to the given problem:

4+3+2-3-2x=6
Where x=participants in all three activities

-2x=6-6=0
x=0

Cheers,
Der alte Fritz.

Posted from my mobile device
_________________

+1 Kudos me - I'm half Irish, half Prussian.

Kudos [?]: 78 [0], given: 6

Re: m04q19- Six students study Russian, Ukrainian & Hebrew   [#permalink] 15 Oct 2012, 05:26

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# m04q19- Six students study Russian, Ukrainian & Hebrew

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