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In Jefferson School, 300 students study French or Spanish or

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In Jefferson School, 300 students study French or Spanish or [#permalink] New post 11 Dec 2009, 12:34
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In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

(1) Of the 300 students, 60 do not study Spanish.
(2) A total of 240 of the students study Spanish.
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Feb 2012, 11:36, edited 1 time in total.
Edited the question and added the OA
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In Jefferson School, 300 students study French or Spanish or [#permalink] New post 15 Feb 2012, 11:50
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tom09b wrote:
I do not understand how we assume that Jefferson School has only 300 students. If this is not the total number then we cannot say anything from the statements, so answer is E. Am I right??


We are not assuming that. We are told that "in Jefferson School, 300 students study French or Spanish or both", there might be more students who study neither French nor Spanish. But this piece of information tells us that among these 300 students there is none who study neither French nor Spanish. So, 300={French}+{Spanish}-{Both}.

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

Given: 300 = {French} + {Spanish} - {Both} and {Spanish} - {Both} = 100 --> 300 = {French} + 100 --> {French} = 200.
Question: {Both}=?

(1) Of the 300 students, 60 do not study Spanish --> {French} - {Both} = 60 --> 200 - {Both} = 60 --> {Both} = 140. Sufficient.

(2) A total of 240 of the students study Spanish --> {Spanish} = 240 --> 240 - {Both} = 100 ---> {Both} = 140. Sufficient.

Answer: D.
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 22 Sep 2012, 04:14
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Please check the attachment for matrix approach ...which is actually easier than than the set approach

First one is for option A and second one is for option B

NS n NF = 0 as stated all of them either take Spanish of French
Attachments

matrix.png
matrix.png [ 8.79 KiB | Viewed 6158 times ]


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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 22 Jan 2014, 17:11
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ISBtarget wrote:
In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

(1) Of the 300 students, 60 do not study Spanish.
(2) A total of 240 of the students study Spanish.


The answer is D.
Its easy to solve with venn diagram approach
Attachments

File comment: Now
F= total number of students studying french =F
S= total number of students studying Spanish =S
F' = Students studying only french
S'=Students studying only spanish
F & S = students studying both french and spanish
Now we need to find out F & S
We have F + S =300 (whether french or spanish or both)
S' =100 (Students who study spanish but not french)
1.Of the 300 students, 60 do not study Spanish
this 60 = F'( students who study only french but not spanish)
so now looking at diagram F'+S'+ F&S = F+S =300
substituting 100+60+ F&S =300
F&S =140
2. A total of 240 of the students study Spanish
i.e. S'+ F&S =240 (total who study spanish)
we know S' =100
so F&S =140.
Give me KUDOS if this helps

Untitled.png
Untitled.png [ 10.01 KiB | Viewed 2813 times ]

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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 02 Jan 2014, 10:50
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This problem can be solved using a table:

Step 1: Using the prompt, we can fill in total students, students who do not study French, students who study French, and students who don't study either French or Spanish.
Step 2: Both statements give us the same information: number of students who do and do not study spanish.
Step 3: Fill in the blanks.

View the file for a graphical depiction of this process.

I hope this helps.
Attachments

Screen Shot 2014-01-02 at 7.51.40 PM.png
Screen Shot 2014-01-02 at 7.51.40 PM.png [ 32.48 KiB | Viewed 2991 times ]

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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 11 Oct 2014, 12:35
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aj0809 wrote:
Hi Bunuel,

It might seem as a stupid question and I will request you to bare with me. I seem to understand how you get this part
Quote:
Given: 300={French}+{Spanish}-{Both}


But how do you infer this
Quote:
{Spanish}-{Both}=100
and this
Quote:
{French}-{Both}=60
is beyond me. Shouldn't {French}-{Both} = 240? I don't know what I am missing; I really like the equation approach but I am missing a vital link to form the quoted equations. Thanks a million if you can help on this.


We are told that 100 of these students do not study French, so 100 students study Spanish only, which is {Spanish} - {Both}.
The same with {French} - {Both} = 60. 60 do not study Spanish, means that 60 students study French only, which is {French} - {Both}.

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65
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Re: OG 12th edition - DS [#permalink] New post 11 Dec 2009, 18:05
Is the answer D, either statement is sufficient?

Given
Total students who who study S or F or both=300
Those who study S=200

(1) Of the 300 students, 60 do not study Spanish.
Those who study F = 300-60=240

240+200=440 students in F and S classes

Since only 300 students are in the school, the overlap is 440-300=140, who study both

====>sufficient

(2) A total of 240 of the students study Spanish.

240+200=440 students in F and S classes

Since only 300 students are in the school, the overlap is 440-300=140, who study both


====>sufficient
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Re: OG 12th edition - DS [#permalink] New post 21 Jun 2010, 14:37
ISBtarget wrote:
In Jefferson School, 300 students study French or
Spanish or both
. If 100 of these students do not study
French, how many of these students study both French
and Spanish?
(1) Of the 300 students, 60 do not study Spanish.
(2) A total of 240 of the students study Spanish.

I think on the basis of the underlined parts, we take number of neither French nor Spanish = 0?
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Re: OG 12th edition - DS [#permalink] New post 18 Jul 2010, 11:47
What is the OA here?

Can someone please qualify this statement "I think on the basis of the underlined parts, we take number of neither French nor Spanish = 0?"

When to decide on this? Will a GMAT question be very explicit?
I have never seen a scenario before where we took 'neither X nor Y = 0' (this particular stem is now making me think about all those previous GMAT questions that i had practiced in the past. Not sure, how exactly where they phrased)

Can someone please comment? Thanks.

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Re: OG 12th edition - DS [#permalink] New post 11 Oct 2010, 02:05
since we come to know from the main statement that 100 study only Spanish. What about the F+ S student num?
from 1) Of the 300 students, 60 do not study Spanish.
So 60 study french ==> 240 study spanish so 240 -100 ( only spanish from main statement) = 40 both F+ S

1. is suffi...

(2) A total of 240 of the students study Spanish.

240 - 100 ( only spanish ) = 140 is F+S students

(2) also Suffi....
So, D wins
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 15 Feb 2012, 11:26
I do not understand how we assume that Jefferson School has only 300 students. If this is not the total number then we cannot say anything from the statements, so answer is E. Am I right??
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 15 Feb 2012, 11:53
Bunuel wrote:
tom09b wrote:
I do not understand how we assume that Jefferson School has only 300 students. If this is not the total number then we cannot say anything from the statements, so answer is E. Am I right??


We are not assuming that. We are told that "in Jefferson School, 300 students study French or Spanish or both", there might be more students who study neither French nor Spanish. But this piece of information tells us that among these 300 students there is none who study neither French nor Spanish. So, 300={French}+{Spanish}-{Both}.

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

Given: 300={French}+{Spanish}-{Both} and {Spanish}-{Both}=100 --> 300={French}+100 --> {French}=200.
Question: {Both}=?

(1) Of the 300 students, 60 do not study Spanish --> {French}-{Both}=60 --> 200-{Both}=60 --> {Both}=140. Sufficient.

(2) A total of 240 of the students study Spanish --> {Spanish}=240 --> 240-{Both}=100 ---> {Both}=140. Sufficient.

Answer: D.


I should have paid more attention to If 100 of these students. Thanks again!
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 28 Aug 2012, 12:27
I tried to create a table for this, but I'm having trouble. So far it has French, no French, Spanish and no Spanish. For some reason I can get 2) to work but not 1).
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 28 Aug 2012, 13:46
We know that 100 speak Spanish only and there are 300 total.

So, given 1), 60 speak French only. 300 - 60 - 100 = 140 who speak both?
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 28 Jul 2013, 00:14
Can we not get an answer of

200 -Both
40 -Spanish but not French
0- French but not Spanish
60- Niether

Does this conflict with the rules stated?
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 28 Jul 2013, 00:42
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maxlevenstein wrote:
Can we not get an answer of

200 -Both
40 -Spanish but not French
0- French but not Spanish
60- Niether

Does this conflict with the rules stated?


Yes,it does. The question specifically states that out of the given 300 students, everyone studies either French, or Spanish or both. Thus, there is no one out of the given 300 who doesn't study neither.
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 19 Nov 2013, 18:13
BukrsGmat wrote:
Please check the attachment for matrix approach ...which is actually easier than than the set approach

First one is for option A and second one is for option B

NS n NF = 0 as stated all of them either take Spanish of French


How would we solve it with matrix/table approach? The attached image does not show any solutions/numbers in the inner boxes.

Last edited by RustyR on 21 Nov 2013, 19:53, edited 2 times in total.
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 19 Nov 2013, 18:21
Bunuel wrote:
tom09b wrote:
I do not understand how we assume that Jefferson School has only 300 students. If this is not the total number then we cannot say anything from the statements, so answer is E. Am I right??


We are not assuming that. We are told that "in Jefferson School, 300 students study French or Spanish or both", there might be more students who study neither French nor Spanish. But this piece of information tells us that among these 300 students there is none who study neither French nor Spanish. So, 300={French}+{Spanish}-{Both}.

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

Given: 300={French}+{Spanish}-{Both} and {Spanish}-{Both}=100 --> 300={French}+100 --> {French}=200.
Question: {Both}=?

(1) Of the 300 students, 60 do not study Spanish --> {French}-{Both}=60 --> 200-{Both}=60 --> {Both}=140. Sufficient.

(2) A total of 240 of the students study Spanish --> {Spanish}=240 --> 240-{Both}=100 ---> {Both}=140. Sufficient.

Answer: D.


Bunuel, of the several methods for overlapping sets, equations, table, venn diagram, can you give us an idea of which method is appropriate for which situation?

Thanks.
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 20 Nov 2013, 01:41
Expert's post
bschoolaspirant9 wrote:
Bunuel wrote:
tom09b wrote:
I do not understand how we assume that Jefferson School has only 300 students. If this is not the total number then we cannot say anything from the statements, so answer is E. Am I right??


We are not assuming that. We are told that "in Jefferson School, 300 students study French or Spanish or both", there might be more students who study neither French nor Spanish. But this piece of information tells us that among these 300 students there is none who study neither French nor Spanish. So, 300={French}+{Spanish}-{Both}.

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

Given: 300={French}+{Spanish}-{Both} and {Spanish}-{Both}=100 --> 300={French}+100 --> {French}=200.
Question: {Both}=?

(1) Of the 300 students, 60 do not study Spanish --> {French}-{Both}=60 --> 200-{Both}=60 --> {Both}=140. Sufficient.

(2) A total of 240 of the students study Spanish --> {Spanish}=240 --> 240-{Both}=100 ---> {Both}=140. Sufficient.

Answer: D.


Bunuel, of the several methods for overlapping sets, equations, table, venn diagram, can you give us an idea of which method is appropriate for which situation?

Thanks.


It depends on a question, as well as on one's personal preferences to pick which approach to apply to some particular problem.
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Re: In Jefferson School, 300 students study French or Spanish or [#permalink] New post 21 Nov 2013, 19:54
bschoolaspirant9 wrote:
BukrsGmat wrote:
Please check the attachment for matrix approach ...which is actually easier than than the set approach

First one is for option A and second one is for option B

NS n NF = 0 as stated all of them either take Spanish of French


How would we solve it with matrix/table approach? The attached image does not show any solutions/numbers in the inner boxes.


Anybody? It would be beneficial if we could know how this problem could be solved using a table.
Re: In Jefferson School, 300 students study French or Spanish or   [#permalink] 21 Nov 2013, 19:54
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