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In a class of 78 students 41 are taking French, 22 are taking German.

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Bunuel
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In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   Updated on: 15 Mar 2019, 04:23
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In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6
B. 15
C. 24
D. 33
E. 54
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C

Originally posted by Bunuel on 03 Apr 2015, 05:12.
Last edited by Bunuel on 15 Mar 2019, 04:23, edited 1 time in total.
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Harley1980
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   Updated on: 03 Apr 2015, 06:00
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Bunuel wrote:
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6
B. 15
C. 24
D. 33
E. 54

Kudos for a correct solution.


Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total

so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 78
54 + NOT = 78
NOT = 78 - 54 = 24
So answer is C

Originally posted by Harley1980 on 03 Apr 2015, 05:16.
Last edited by Harley1980 on 03 Apr 2015, 06:00, edited 1 time in total.
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   03 Apr 2015, 05:20
Total: 78
French total: 41
French and German: 9
41-9 = 32

German total: 22
French and German: 9
22 - 9 = 13

78 - 9 - 13 - 32 = 24.

C.
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   03 Apr 2015, 09:24
Bunuel wrote:
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6
B. 15
C. 24
D. 33
E. 54

Kudos for a correct solution.



Total=French+German-Both+Neither
78=41+22-9+Neither
Neither=78-54
Neither=24

Answer: C
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   05 Apr 2015, 01:14
Total = F+G+neither-both
78=41+22-9+neither; therefore neither=24

Hence answer is C


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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   05 Apr 2015, 21:29
Using the set formula :
A'U'B - ~(A'U'B) = A + B - AB
need to find ~(A'U'B) = x, say.
78 - x = 41 + 22 - 9
=> x = 24.
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   06 Apr 2015, 06:44
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Bunuel wrote:
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6
B. 15
C. 24
D. 33
E. 54

Kudos for a correct solution.


OFFICIAL SOLUTION:

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither
78 = (41-9) + (22-9) + 9 + neither.

Not enrolled students = 24.

Answer: C.
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   18 Mar 2017, 08:43
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You could even do this way as well
P(F) = 41/78
P(G) = 22/78
P(FNG) = 9/78

1 - P(FUG) = 41/78 + 22/78 - 9/78
1- P(FUG) = 54/78
P(FUG) = 1 - 54/78
P(FUG) = 24/78

Therefore, answer is C
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   10 Apr 2018, 11:16
Expert Reply
Bunuel wrote:
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

A. 6
B. 15
C. 24
D. 33
E. 54


[Note: Here we are assuming that every student learns either Physics or Chemistry or both.]

Let’s let b = the number of students learning both Physics and Chemistry. Let’s also assume that there are 100 students. Since 70% of the students learn Physics and 65% of the students learn Chemistry, we could say that:

100 = 65 + 70 - b

100 = 135 - b

b = 35

Answer: C
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   31 May 2019, 00:32
I got to the answer in 21 seconds with quick mental math.

41 French + 22 German = 63
63 F&G - 9 in both = 54 in foreign language classes.
78-54 ends in a 4 and narrows my answer choices to 24 or 54. I know easily that 54+54 is too big so I’m left with only 24, C, as my option

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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   29 Oct 2021, 22:32
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Since 9 are taking both courses,

Only French = 41 - 9 =32

Only German = 22 - 9 =13

Total = Only French + Only German + Both + Neither

=> 78 = 32 + 13 + 9 + Neither

=> Neither = 78 - 54 = 24

Alternately,

Total=French + German -Both +Neither

=>78=41+22-9+Neither

=>Neither=78-54 = 24

(option c)

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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink] New post   06 Dec 2023, 09:23
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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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