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555-605 Level|   Overlapping Sets|                     
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In Jefferson School, 300 students study French or Spanish or Updated on: 15 Feb 2012, 12:36
Originally posted by ISBtarget on 11 Dec 2009, 13:34.
Last edited by Bunuel on 15 Feb 2012, 12:36, edited 1 time in total.
Edited the question and added the OA
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

71% (01:45) correct 29% (01:59) wrong based on 3713 sessions

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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.
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D
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In Jefferson School, 300 students study French or Spanish or 02 Jan 2014, 11:50
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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 57382 times ]

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In Jefferson School, 300 students study French or Spanish or 15 Feb 2012, 12:50
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tom09b
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??
Show more

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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In Jefferson School, 300 students study French or Spanish or 11 Dec 2009, 19:05
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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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In Jefferson School, 300 students study French or Spanish or 15 Feb 2012, 12:26
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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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In Jefferson School, 300 students study French or Spanish or 15 Feb 2012, 12:53
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tom09b
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.
Show more

I should have paid more attention to If 100 of these students. Thanks again!
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In Jefferson School, 300 students study French or Spanish or 22 Sep 2012, 05:14
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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
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matrix.png
matrix.png [ 8.79 KiB | Viewed 57769 times ]

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In Jefferson School, 300 students study French or Spanish or 22 Jan 2014, 12:21
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If you are making the matrix, you have to realize that No Spanish and No French = 0. That's the tricky part about the matrix.
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In Jefferson School, 300 students study French or Spanish or 22 Jan 2014, 18:11
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ISBtarget
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.
Show more

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 54081 times ]

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In Jefferson School, 300 students study French or Spanish or 08 Oct 2014, 11:35
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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}
Show more

But how do you infer this
Quote:
{Spanish}-{Both}=100
Show more
and this
Quote:
{French}-{Both}=60
Show more
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.
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In Jefferson School, 300 students study French or Spanish or 11 Oct 2014, 13:35
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aj0809
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.
Show more

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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In Jefferson School, 300 students study French or Spanish or 27 Dec 2014, 19:33
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Bunuel
tom09b
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.
Show more


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. :-D :-D :-D :-D :-D :-D :-D

Insanity: doing the same thing over and over again and expecting different results. - Holds True for Learning for GMAT
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In Jefferson School, 300 students study French or Spanish or 16 Mar 2015, 23:58
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Hi All,

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

Thanks,
AJ
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In Jefferson School, 300 students study French or Spanish or 23 Feb 2017, 05:50
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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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In Jefferson School, 300 students study French or Spanish or 12 Sep 2018, 14:20
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ISBtarget
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.
Show more

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

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

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

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

Regards,
Fabio.
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In Jefferson School, 300 students study French or Spanish or 26 Apr 2020, 08:05
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ISBtarget
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.
Show more

Hi ISBtarget

Another good question involving Sets Theory this time.

So let's try to figure this out...

Question stem:
Total students = 300
Students study: French only [F], Spanish only [S] or both[F&S]
Students not studying French = 100 = [S]

Thus, 300 = [F] + [S] + [F&S]
==> 300 = [F] + 100 + [F&S]. {Equation 1}

To find: [F&S]

Statement 1: Of the 300 students, 60 do not study Spanish.
So, [F] = 60
Substituting this in equation 1:
300 = 60 + 100 + [F&S]
Thus, [F&S] = 140

Now, we know answer could be A or D

Statement 2: A total of 240 of the students study Spanish.
So, [S] + [F&S] = 240
==> 100 + [F&S] = 240
Thus, [F&S] = 140

As both statements are independently able to give us the solution, Answer is (D).

Is my explanation fine? Would anyone here like me to explain anything else?
Pls share your thoughts. Thank you :)
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In Jefferson School, 300 students study French or Spanish or 25 Jan 2021, 21:04
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Good question.

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?

F (only) + S (only) + Both = 300
100 DO NOT study F <--- Implies that S = 100
F + Both = 200
Both = 200 - F <--- If we can figure out F, then we have an answer.

(1) Of the 300 students, 60 do not study Spanish.

Implies that F = 60

Sufficient.

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

Implies that Both + Spanish only = 240.
Both + 100 = 240
Both = 140

Sufficient.

Answer is D.
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In Jefferson School, 300 students study French or Spanish or 06 Apr 2021, 08:20
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ISBtarget
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.
Show more

Answer: Option D

Video solution by GMATinsight

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In Jefferson School, 300 students study French or Spanish or 29 Jun 2022, 10:35
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ISBtarget
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.
Show more


While applying statement 2.
It’s given in statement 2 that Spanish has 240 students. That means 240 students would include students that are enrolled only in Spanish(let that be S) as well as students enrolled both in Spanish and French(let that be x) .
=> 240 = S + x
AND we are given in the Question stem that Spanish alone (S) has 200 students.
=> 240-200 = x = 40
Thus, if we subtract Spanish only (S) from Both Spanish and French (x) students , we get 40 and not 140.
Please let me know where am I wrong? :)
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In Jefferson School, 300 students study French or Spanish or 24 Jul 2023, 22:40
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ISBtarget
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.


While applying statement 2.
It’s given in statement 2 that Spanish has 240 students. That means 240 students would include students that are enrolled only in Spanish(let that be S) as well as students enrolled both in Spanish and French(let that be x) .
=> 240 = S + x
AND we are given in the Question stem that Spanish alone (S) has 200 students.
=> 240-200 = x = 40
Thus, if we subtract Spanish only (S) from Both Spanish and French (x) students , we get 40 and not 140.
Please let me know where am I wrong? :)
Show more

Consider the table below:


Study SpanishDon't Study SpanishTotal
Study French??200 (300 - 100)
Don't Study French?0100
Total240 (from statement 2)60 (300 - 240)300

Note that in statement 1 also, we are given the value of 60 so we can find all other values.



Study SpanishDon't Study SpanishTotal
Study French?200 - ?200
Don't Study French100 - ?0100
Total24060300


So,
From statement 1, we can infer that 60 students study French only. Therefore, 140 students study both languages. So, the number of students who study both French and Spanish is 140. So, statement 1 is sufficient.

Checking statement 2, we have 240 students study Spanish, from this 100 students don't study French so they are the ones who study only Spanish. Therefore, 140 students study both. Statement 2 is also sufficient.



Study SpanishDon't Study SpanishTotal
Study French14060200
Don't Study French1000100
Total24060300

So option D is correct.
The trick here is to take the value of 0 in the (Don't study French and Don't study Spanish) cell.
I also fell for that trap before.
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