Jason H.

asked • 11/28/16

Can you solve a math problem?

Of the 67 students studying a foreign language at Green Hills High School, 24 are studying Spanish, 24 are studying French, and 28 are studying German. There are 6 students studying Spanish and French, 4 studying French and German, 7 studying German and Spanish, and 3 studying all three languages. How many students are not studying any of these three languages?

1 Expert Answer


Kenneth S. answered • 11/28/16

4.8 (62)

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Jason H.

Ok, I tried that but then I ended up with a number bigger than the total of 67. How am I supposed to find how many students of 67 do not study any languages? 


Kenneth S.

The circle representing Spanish consists of four parts:
3 in the intersection of all 3 circles
3 in the part where French & Spanish are recorded, NOT COUNTING the 3 that takes all 3 languages
4 in the part where Spanish and German are recorded NOT COUNTING the 3 that takes all 3 languages.
So far, that is 14 persons, therefore the remaining part, Spanish only, must be 14.
Similarly, French only should be 17, German only should be 20, French and German (but not all 3) is 1, and altogether that is 62 persons. Therefore 5 took none of these languages.
To summarize, you have to be sure not to "double count" anyone.


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