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# In Jefferson School, 300 students study French or Spanish or

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Intern
Joined: 17 May 2012
Posts: 37
In Jefferson School, 300 students study French or Spanish or  [#permalink]

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08 Oct 2014, 10:35
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.
Math Expert
Joined: 02 Sep 2009
Posts: 52905
Re: In Jefferson School, 300 students study French or Spanish or  [#permalink]

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11 Oct 2014, 12:35
1
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:
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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Joined: 23 Nov 2014
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Location: China
Concentration: Entrepreneurship, General Management
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Re: In Jefferson School, 300 students study French or Spanish or  [#permalink]

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27 Dec 2014, 18:33
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.

Thanks Bunuel. Now its clear.This is an interesting problem because I assumed there would be some students who study neither. But I have learnt a new way to look at these problems and read carefully to understand the exact meaning.

Insanity: doing the same thing over and over again and expecting different results. - Holds True for Learning for GMAT
Intern
Joined: 17 May 2012
Posts: 37
Re: In Jefferson School, 300 students study French or Spanish or  [#permalink]

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16 Mar 2015, 22:58
Hi All,

I found the Venn Diagram approach is the best way to solve this Q. For more details check out the below link:
http://www.gmatquantum.com/og13/138-dat ... ition.html

Thanks,
AJ
Manager
Joined: 09 Aug 2016
Posts: 65
In Jefferson School, 300 students study French or Spanish or  [#permalink]

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23 Sep 2016, 14:49
In general for two overlapping sets we have (For convenience I use S & F for Spanish and Frence):

Total = f + s + Both + Neither where s,f are the areas Ony Spanish or Only French i.e. if f = F - Both, s = S - Both

Total = (F-Both) + (S-Both) + Both + Neither.

For this question Neither = 0, s = 100 (or S-Both = 100) and Total = 300

(i) f = 60 (or F-Both = 60) . So the first equation becomes Total = 60 + 100 + Both = 300 hence Both = 300 - 160 = 140 Sufficient

(ii) S = 240. So S = s + Both Therefore by just replacing the values we have 240 = 100 + Both give Both = 140 Sufficient

Although under GMAT conditions all these equations are overkill and perhaps the best thing is just simple Venn.
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Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Re: In Jefferson School, 300 students study French or Spanish or  [#permalink]

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23 Feb 2017, 04:50
Prompt analysis
No. of student learning french = f
No. of students learning spanish = s

Therefore 300 =f +s +f and s and s =100.

Superset
The value of fs will lie in the range of 0 to 200.

Translation
In order to find f and s, we need:
1# the value of f.
2# the exact value of f and s
3# any equation to find f and f and s.

Statement analysis

St 1: f =60. Therefore from the above equation, we can find f and s =140 .ANSWER.
St 2: s +f and s =240. f and s =140. ANSWER.

Option D
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Re: In Jefferson School, 300 students study French or Spanish or  [#permalink]

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12 Sep 2018, 13:20
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.

$$? = {\text{French}} \cap {\text{Spanish}} = x\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)$$

$$\left( 1 \right)\,\,\,300 = 60 + x + 100\,\,\,\,\, \Rightarrow \,\,\,\,x\,\,\,{\text{unique}}$$

$$\left( 2 \right)\,\,\,240 = x + 100\,\,\,\,\, \Rightarrow \,\,\,\,x\,\,\,{\text{unique}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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12Set18_4r.gif [ 19.03 KiB | Viewed 179 times ]

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Re: In Jefferson School, 300 students study French or Spanish or   [#permalink] 12 Sep 2018, 13:20

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