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

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In a class of 78 students 41 are taking French, 22 are takin [#permalink] New post 01 Feb 2018, 21:32
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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
[Reveal] Spoiler: OA
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Re: In a class of 78 students 41 are taking French, 22 are takin [#permalink] New post 01 Feb 2018, 23:18
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This is a double overlapping set. Venn diagrams are OK for these but can be confusing. There's an equation as well, but the best way to solve these is to use an Overlapping Sets Matrix. Just make a matrix with French and Not French, German and Not German, and fill in the boxes that they give you. See first attachment.

Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.

So, the answer is 24.
Attachments

French and German.jpg
French and German.jpg [ 31.8 KiB | Viewed 1663 times ]

French and German complete.jpg
French and German complete.jpg [ 34.74 KiB | Viewed 1668 times ]


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Last edited by SherpaPrep on 04 Feb 2018, 22:07, edited 1 time in total.
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Re: In a class of 78 students 41 are taking French, 22 are takin [#permalink] New post 02 Feb 2018, 02:38
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SherpaPrep wrote:
This is a double overlapping set. Venn diagrams are OK for these but can be confusing. There's an equation as well, but the best way to solve these is to use an Overlapping Sets Matrix. Just make a matrix with French and Not French, German and Not German, and fill in the boxes that they give you. See first attachment.

Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.

So, the answer is 22.


The question asks for those that are not enrolled in either courses so from the double-matrix diagram the number that should give the ans is those that are not enrolled in German and Those that are not enrolled in French = 24.
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Re: In a class of 78 students 41 are taking French, 22 are takin [#permalink] New post 04 Feb 2018, 22:08
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Oops. Typo. Thanks for spotting that Amorphous.
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Re: In a class of 78 students 41 are taking French, 22 are takin [#permalink] New post 05 Feb 2018, 00:21
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SherpaPrep wrote:
Oops. Typo. Thanks for spotting that Amorphous.

No problem
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Re: In a class of 78 students 41 are taking French, 22 are takin   [#permalink] 05 Feb 2018, 00:21
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In a class of 78 students 41 are taking French, 22 are takin

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