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In Jefferson School, 300 students study French or Spanish or [#permalink]

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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.

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

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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 [ 32.48 KiB | Viewed 11984 times ]

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?

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

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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

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.
_________________

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}.

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?
_________________

KUDOS me if you feel my contribution has helped you.

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)

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

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

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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??

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

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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!

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

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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).

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

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28 Jul 2013, 00:42

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.
_________________

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

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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.

gmatclubot

Re: In Jefferson School, 300 students study French or Spanish or
[#permalink]
19 Nov 2013, 18:21

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