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# M10 Q17

Author Message
Intern
Joined: 17 Aug 2009
Posts: 36

Kudos [?]: 17 [0], given: 8

Location: India
Concentration: General Management, Finance
Schools: Babson (A), Smith (D)
GMAT 1: 580 Q49 V21
GMAT 2: 650 Q49 V29
GPA: 3.85
WE: Information Technology (Computer Software)

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28 May 2010, 00:33
Can someone please explain in detail how both the statements are not sufficient to answer the question?

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

1) There are no students studying all of the three subjects.
2) None of those who study math study chemistry.

Kudos [?]: 17 [0], given: 8

Manager
Joined: 15 Apr 2010
Posts: 190

Kudos [?]: 18 [0], given: 29

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28 May 2010, 02:19
sandeepnerli wrote:
Can someone please explain in detail how both the statements are not sufficient to answer the question?

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

1) There are no students studying all of the three subjects.
2) None of those who study math study chemistry.

just draw the overlapping venn diagram and things become clearer. even after the above 2 pieces of information, we still dont know how many study physics and chemistry or physics and maths and hence we cannot figure out how many are not taking any one of the above 3 subjects.

There is a formula for these but i cant remember it now. basically u have to get sum up the number of students who are studying physics only +chem only + math only + all 3 + any 2 (3 combinations) and then subtract by 20....for final answer!

Kudos [?]: 18 [0], given: 29

Intern
Joined: 17 Aug 2009
Posts: 36

Kudos [?]: 17 [0], given: 8

Location: India
Concentration: General Management, Finance
Schools: Babson (A), Smith (D)
GMAT 1: 580 Q49 V21
GMAT 2: 650 Q49 V29
GPA: 3.85
WE: Information Technology (Computer Software)

### Show Tags

28 May 2010, 22:49
Hi,

I did the following -

Given -
Students - 20
Math - 5
Physics - 10
Chemistry - 6

Total - P + M + C + PC + PM + MC + PCM (Where P = Physics only, M = Maths Only, C = Chemistry only, PC = Physics and Chemistry only,
MC = Maths and Chemistry only, PM = Physics and Maths only, PCM = Physics, Chemistry and Maths)

P+C+M+PC+PM+MC+PCM = 20

Statement 1 - PCM = 0
-> P+C+M-PC-PM-MC = 20 -------------------------- (1)

P+PC+PM = 10
C+PC+MC = 6
M+PM+MC = 5
P+C+M+2(PC+PM+MC) = 21 ------------------------ (2)

Consider P+C+M = X
PC+PM+MC = Y

(1) & (2)

X+Y = 20
X+2Y = 21

Y = 1

X = 19

From this Total = X + Y, hence students who do not study any of the above-mentioned subjects = 0

sufficient

Statement 2 -

Not sufficient

Please point where I'm going wrong. I know the methodology I have followed sounds stupid, but this is what I got when solved. I need to improve my Venn diagram problems, and these are the ones that are taking out on my score

Thanks for you help

Kudos [?]: 17 [0], given: 8

Manager
Joined: 15 Apr 2010
Posts: 190

Kudos [?]: 18 [0], given: 29

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29 May 2010, 04:06
whats the OA?

the issue here is that you cannot assume sum = 20. there are some out of 20 not enrolled in any of the 3 subjects....

Kudos [?]: 18 [0], given: 29

Intern
Joined: 17 Aug 2009
Posts: 36

Kudos [?]: 17 [0], given: 8

Location: India
Concentration: General Management, Finance
Schools: Babson (A), Smith (D)
GMAT 1: 580 Q49 V21
GMAT 2: 650 Q49 V29
GPA: 3.85
WE: Information Technology (Computer Software)

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31 May 2010, 00:10
Thanks pranrasvij,

This may help to solve the DS. The OA is E.

Kudos [?]: 17 [0], given: 8

Manager
Joined: 18 Aug 2010
Posts: 88

Kudos [?]: 20 [0], given: 22

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01 Feb 2011, 13:24
the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total .
am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ?
thanks

Kudos [?]: 20 [0], given: 22

Manager
Joined: 20 Dec 2010
Posts: 168

Kudos [?]: 62 [1], given: 5

Location: Stockholm, Sweden

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01 Feb 2011, 14:01
1
KUDOS
tinki wrote:
the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total .
am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ?
thanks

20 is the total number of students.

We have three variables here (with both statements in consideration), a, b and x.
5-a+6-b+10 + x = 20
21+x-a-b = 20
1 + x = a+b
x = a+b-1

x could be zero and a=1, b=0, or a=2 and x=1

_________________

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Kudos [?]: 62 [1], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128603 [0], given: 12180

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01 Feb 2011, 14:34
tinki wrote:
the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total .
am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ?
thanks

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

First of all note that total # of students is 20. Next:

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

20 = 5 + 10 + 6 - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups};

So: {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1.

Question: is {people in none of the groups} > 0? --> is {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1 > 0

(1) There are no students studying all of the three subjects --> {people in exactly 3 groups} = 0 --> question becomes is {people in none of the groups} = {people in exactly 2 groups} - 1 > 0. Now, if {people in exactly 2 groups} = 1 then the answer will be NO (for example if there is only one student who study exactly two subjects: math and physics and all other students study only one subject) but if {people in exactly 2 groups} = 2 then the answer will be YES (for example if there are two students who study exactly two subjects: math and physics and all other students study only one subject). Not sufficient.

(2) None of those who study math study chemistry. Clearly insufficient.

(1)+(2) Examples from (1) are still valid, thus we have both YES and NO answers. Not sufficient.

Check this for more on 3 overlapping sets: formulae-for-3-overlapping-sets-69014.html#p729340
_________________

Kudos [?]: 128603 [0], given: 12180

Manager
Joined: 18 Aug 2010
Posts: 88

Kudos [?]: 20 [0], given: 22

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02 Feb 2011, 01:47
Bunuel wrote:
tinki wrote:
the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total .
am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ?
thanks

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

First of all note that total # of students is 20. Next:

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

20 = 5 + 10 + 6 - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups};

So: {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1.

Question: is {people in none of the groups} > 0? --> is {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1 > 0

(1) There are no students studying all of the three subjects --> {people in exactly 3 groups} = 0 --> question becomes is {people in none of the groups} = {people in exactly 2 groups} - 1 > 0. Now, if {people in exactly 2 groups} = 1 then the answer will be NO (for example if there is only one student who study exactly two subjects: math and physics and all other students study only one subject) but if {people in exactly 2 groups} = 2 then the answer will be YES (for example if there are two students who study exactly two subjects: math and physics and all other students study only one subject). Not sufficient.

(2) None of those who study math study chemistry. Clearly insufficient.

(1)+(2) Examples from (1) are still valid, thus we have both YES and NO answers. Not sufficient.

Check this for more on 3 overlapping sets: formulae-for-3-overlapping-sets-69014.html#p729340

Great explanation ! thanks

Kudos [?]: 20 [0], given: 22

Intern
Joined: 07 Oct 2011
Posts: 29

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

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02 Jun 2012, 21:17
None of those who study math study chemistry >> Can someone explain what it is exactly, probably rephrase it? or put it on venn diagram?

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

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128603 [0], given: 12180

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03 Jun 2012, 04:03
karthiksms wrote:
None of those who study math study chemistry >> Can someone explain what it is exactly, probably rephrase it? or put it on venn diagram?

That means that there are no students who study both math and chemistry. On diagram it would be so that the circles of math and chemistry do not intersect.
_________________

Kudos [?]: 128603 [0], given: 12180

Senior Manager
Joined: 15 Sep 2009
Posts: 263

Kudos [?]: 76 [0], given: 6

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16 Jun 2012, 10:47
Straight E. We need info on the two other intersections, videlicet: (students who study both chem and physics, and those study maths and physics) in order to determine how many do not study any of the three subjects.

Cheers.
_________________

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

Kudos [?]: 76 [0], given: 6

Re: M10 Q17   [#permalink] 16 Jun 2012, 10:47
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# M10 Q17

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