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In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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03 Apr 2015, 05:12
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In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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Updated on: 03 Apr 2015, 06:00
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
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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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In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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03 Apr 2015, 05:20
Total: 78 French total: 41 French and German: 9 419 = 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]
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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+GermanBoth+Neither 78=41+229+Neither Neither=7854 Neither=24 Answer: C



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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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05 Apr 2015, 01:14
Total = F+G+neitherboth 78=41+229+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]
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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]
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06 Apr 2015, 06:44



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Re: In a class of 78 students 41 are taking French, 22 are taking German. [#permalink]
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18 Mar 2017, 08:43
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]
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10 Apr 2018, 11:16
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.
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