The seventh grade French and Spanish classes each have 15

Question

The 7th grade French and Spanish classes each have 15 students in them, and there are five students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?

5
10
15
20
25

A. 5
B. 10 
C. 15 
D. 20 
E. 25

ezhilkumarank · Accepted Answer

Total = 15 students.

15 = n(F) + n (S) - n (AnB) + Neither

Neither F nor S is zero.

15 = (F - 5) + (S - 5) - 5
15 = (F + S) - 10 + 5

15 = (F + S) - 5

Hence (F+S) = 20. Answer choice D.

Bunuel · Answer

Draw a matrix: Classes.JPG As "everyone in the 7th grade is in at least one of the two language classes " then there is no student (0) who are not in either of classes. # of students who are taking just one of the two classes equals to: {# of students who are only in French class} + {# of students who are only in Spanish class} = {15-5}+{15-5}=20. Answer: D.

ezhilkumarank · Answer

I have thought of another way.

Let X represent 5 students

Hence

French students -- X -- X -- X

Spanish students -- X -- X -- X

Total number of Students

French *** Spanish
 X -- X --    X *** X    -- X -- X

X    represents the number of students who study in both the class and  X  represents students who study in only one of the two class.

Hence the number of students who study only one of the two class is 20

rakshaki · Answer

Hi Bunuel,

Can you please tell where I am going wrong?

French No French Total

Spanish 5 x 5+x
No Spanish y 0 y
Total 5+y x 30

Value asked in x+y. We get 5+x+y = 30 from the above. Thus x+y = 30-5 = 25.

Bunuel · Answer

Total is 25, not 30. Check here: the-seventh-grade-french-and-spanish-classes-each-have-99366.html#p766137

rawjetraw · Answer

Hi bunuel,

I get the same answer with all the methods explained above. i.e the table method and the one explained by you. but i have a doubt.

since i know the total is 25. Cant I use the formula given in GMATclub quant pdf. which is 
total = a + b - (exactly one) - 2*both + neither.

so, as per available info in this ques.. we have .. 
total=25 .... a =15 b=15 .. lets say "exactly one"= x (to be determined) ... both = 5 ... neither = 0.

so we get ...

25 = 15 + 15 - x - 2*5 + 0
25 = 15 + 15 - x - 10
25 = 30 - x - 10
25 = 20 - x 
x = -5 ??????

Please tell me what am I doing wrong? Is it incorrect to use this formula here... 
Total = A + B + C - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither.

Thanks!

AkshdeepS · Answer

Can anyone tell me why we did't take total students 30 in number. As we have 15 students in each class. (15+15). getting confused

EgmatQuantExpert · Answer

Hi akshdeep28 Let me answer your query with the help of Venn diagram https://e-gmat.com/blogs/wp-content/uploads/2015/06/GCsets1.jpg The question tells us that 15 students attend the French class and 15 students attend the Spanish class. There would have been a total of 30 students had there been no student who attends both French & Spanish classes. However we are given in the question that there are 5 such students who attend both the classes. From the Venn diagram, we can say that b = 5 We are also told that 15 students attend French class, so we can write a + b = 15 which would give us a = 10 i.e. the number of students who attend only the French class. Similarly b + c = 15 which would give us c = 10 i.e the number of students who attend only the Spanish class. Hence the number of students who attend just one class = a + c = 20. Also, the total students would be a + b + c = 10 + 5 + 10 = 25 Hope it's clear

Regards Harsh

clarkie · Answer

double set matrix to the rescue

bumpbot · Answer

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The seventh grade French and Spanish classes each have 15

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