It looks like most of the posters in this thread recognized that this question is a variation on an Overlapping Sets question. It can be solved in a variety of ways (mostly algebraic), but there is an opportunity to TEST VALUES. You just have to be careful with your notes:
We're given 4 variables to work with:
Z = Total number of students
X = Total who study French
Y = Total who study German
W = Total who study French AND German
We're asked for the number that study NEITHER French NOR German.
Let's TEST VALUES. I'm going to keep things simple, but the note-taking here is crucial to getting the correct answer.
1 studies just French
1 studies just German
1 studies BOTH French and German
X = 2 (since 1 speaks just french and another speaks both)
Y = 2 (since 1 speaks just German and another speaks both
W = 1
Now we can set the "neither" group to any positive value we want; I'm going to choose a larger number to set it apart from the others.
Neither = 5
That makes the TOTAL number of students: 1 + 1 + 1 + 5 = 8
Z = 8
So, using the values....
X = 2
Y = 2
W = 1
Z = 8
We're looking for an answer that equals 5.
Answer A: 8+1-2-2 = 5 This IS a match
Answer B: 8-1-2-2 = 3 This is NOT a match
Answer C: 8-1-2+2 = 7 This is NOT a match
Answer D: 1+2+2-5 = 0 This is NOT a match
Answer E: 1-2-2-5 = -8 This is NOT a match
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