Hi,
I'm overthinking this question. Can someone help?
"Of the people who had a sandwich or soup, z people had both a sandwich and soup"
Because it's
NOT "of w people, z people had both a sandwich and soup"
I set overlap = a, so a/x+y-a = z
Of course, I can't find the answer based on this. Can someone explain why this is wrong?
Thanks.
gmatophobiaGmatKnightTutorBunuelDerekLin
Of
w people in a room,
x people had a sandwich for lunch and
y people had soup for lunch. Of the people who had a sandwich or soup,
z people had both a sandwich and soup. In terms of
w,
x,
y, and
z, what fraction of the people in the room had neither a sandwich nor soup?
A. \(\frac{w - x - y + 2z}{w-z}\)
B. \(\frac{x + y + z}{w-z}\)
C. \(\frac{w - x - y - z}{w}\)
D. \(\frac{w - x - y + z}{/w}\)
E. \(\frac{w - x - y + 2z}{w}\)
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z is not a ratio; it is the actual count of people who had both a sandwich and soup, out of those who had either or both. So there is no need to write z as a fraction or solve for it.
People who had sandwich or soup (or both) = x + y - z. We subtract z once to avoid double-counting.
People who had neither = w - (x + y - z) = w - x - y + z.
So the fraction is (w - x - y + z)/w.