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The seventh grade French and Spanish classes each have 15

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The seventh grade French and Spanish classes each have 15  [#permalink]

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New post Updated on: 15 Sep 2010, 06:57
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A
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D
E

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Question Stats:

67% (00:49) correct 33% (00:39) wrong based on 353 sessions

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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?

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

Originally posted by Financier on 18 Aug 2010, 09:41.
Last edited by Financier on 15 Sep 2010, 06:57, edited 1 time in total.
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Re: Overlapsing sets (600+)  [#permalink]

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New post 18 Aug 2010, 09:52
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1
Financier wrote:
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



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.
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Re: Overlapsing sets (600+)  [#permalink]

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New post 18 Aug 2010, 14:46
1
1
Financier wrote:
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


Draw a matrix:
Attachment:
Classes.JPG
Classes.JPG [ 10.49 KiB | Viewed 7267 times ]

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.
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Re: Overlapsing sets (600+)  [#permalink]

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New post 18 Aug 2010, 18:56
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 [X + X + X + X]
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Re: The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 25 Aug 2013, 11:38
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.
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Re: The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 25 Aug 2013, 11:43
rakshaki wrote:
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.


Total is 25, not 30. Check here: the-seventh-grade-french-and-spanish-classes-each-have-99366.html#p766137
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Re: The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 14 Jan 2014, 10:23
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!
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The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 31 May 2015, 10:49
ezhilkumarank wrote:
Financier wrote:
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



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.


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
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The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 01 Jun 2015, 00:15
1
akshdeep28 wrote:
ezhilkumarank wrote:
Financier wrote:
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



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.


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


Hi akshdeep28

Let me answer your query with the help of Venn diagram

Image

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
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The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 06 Nov 2015, 15:36
Financier wrote:
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?

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


double set matrix to the rescue
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Re: The seventh grade French and Spanish classes each have 15  [#permalink]

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New post 08 Sep 2018, 05:48
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Re: The seventh grade French and Spanish classes each have 15 &nbs [#permalink] 08 Sep 2018, 05:48
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