SOLUTION: Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of st

Question 3921: Of the z students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
(A) z + w � x � y
(B) z � w � x � y
(C) z � w � x + y
(D) w + x + y � z
(E) w � x � y � z

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
think of an enclosed box with 2 circles inside, overlapping each other - the classic Venn diagram.

Let F - circle1 for those who study French
Let G - circle2 for those who study German

If you think of the 2 circles as apart, first, then some people must be in both circles (since they study both French and German). As you merge the 2 circles, these people will be in the overlapping area (FnG) but will have been counted twice.

Now the total number of people in the circles = all in F circle + all in G circle minus one lot of those in both

In maths notation, FuG, meaning (F union G) is everyone in the 2 sets (circles).
Whilst FnG (F intersection G) is those people just in BOTH sets ( circles)...i remember this by the n symbol looking like the n in iNtersection. Petty, but it works for me :-).

So, (FuG) = F + G - (FnG)

In your question, you have different lettering, so lets put them in instead:

FuG = x + y - w

Now, since FuG are those STUDYING the languages, then those who don't study them must be all the rest, surely?

As the total number of students is z, then those NOT studying F and/or G will be:

z-(x+y-w) which becomes z-x-y+w, which is answer A.

jon.

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