In a class of 25 students, every student takes either Spanish, Latin,

Question

In a class of 25 students, every student takes either Spanish, Latin, or French, or two of the three, but no students take all three languages. 9 take Spanish, 7 take Latin and 5 take exactly two languages. What is the number of students who take French ?

A. 10
B. 11
C. 12
D. 13
E. 14

A. 10
B. 11
C. 12
D. 13
E. 14

mohammadfaraaz123 · Accepted Answer

Total = 25
Spanish = 9, Latin = 7, Two languages = 5, All 3 languages = 0

Total - Neither = Spanish + Latin + French - (Two languages) - 2(All three languages) 
25 - 0 = 9+7 + French - (5) - 2(0)
25= 11 + French
French = 25-11 = 14
 
Answer option E

BrentGMATPrepNow · Answer

I'm not a big fan of memorizing formulas, so here's a way to solve the question using diagrams. 
We're going to start from the center and work our way out.

Each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages.  
First we can place 0 in the intersection of all three circles. 
 https://i.imgur.com/KDqab4o.png

5 study exactly two language  
Since we aren't told that the distribution of those five students who study exactly two languages, we can distribute them anyway we want. 
Here's one option:
 https://i.imgur.com/L5CYZkA.png

9 study Spanish, 7 study Latin  
We'll add 5 and 4 in order to meet the conditions above 
 https://i.imgur.com/PBaiFdc.png

There are 25 students in the class  
So far, we've accounted for 14 of the 25 students. 
So the remaining 11 students must study only French
 https://i.imgur.com/guZ2T48.png

So the TOTAL number of students studying French = 2 + 0 + 1 + 11 =  14

Answer: E

Diablo21 · Answer

We know that total no of students are 25
And students taking exactly 2 subjects are 5. 
So,
Lets say A= students taking exactly 1 subject and
B= students taking exactly 2 subjects =5

Now,Total no of students= 25= A+B

So, A+5= 25 or, A= 20

Also, 
No of students taken Latin (L) + No of students taken Spanish (S) + No of students taken French (F) = A + 2*B

Or, 9+7+F= 20+2*5

Hence, F=30-16=14
So.Total no of students taken french = 14
Hence, E

Posted from my mobile device

georgecambridge · Answer

Hi there,
Is it possible to solve this question with a double matrix method?

ManifestDreamMBA · Answer

S 
 Not S 
 T 
 
  L 
 5 
  2  
 7 
 
  Not L 
  4  
  14  
  18  
 
  T 
 9 
  16  
 25

We can think of French as neither Spanish and nor Latin. As highlighted here in yellow
The only other assumption i made was that both category is all Spanish and Latin. It doesn't matter as we have the sum and the distribution can be anything.
Hope this helps.

PS: I think this was the unique case given the way the values were provided. i usually stick to venn diagram for 3 category situations. But may be this way can work, I am yet to try this on other similar problems.

In a class of 25 students, every student takes either Spanish, Latin,

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In a class of 25 students, every student takes either Spanish, Latin,

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