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13 Feb 2024, 21:55
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D
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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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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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13 Feb 2024, 22:32
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DerekLin
The number of people who had either a sandwich or soup for lunch = \(x + y - z\)
Note: We are subtracting 'z' from x + y because the number has been double-counted.
The number of people who neither had soup nor had a sandwich for lunch = \(w - (x + y - z) = w - x - y + z\)
Required fraction = \(\frac{w - x - y + z}{w}\)
Option D
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17 Feb 2024, 10:21
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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?
(Total people - people who had a sandwich - people who had soup + people who had both a sandwich and soup) / (Total people)
The reason you ADD the people who had BOTH a sandwich and soup is because you don't want to double-count them.
w - x - y + z / (w)
(Total people - people who had a sandwich - people who had soup + people who had both a sandwich and soup) / (Total people)
The reason you ADD the people who had BOTH a sandwich and soup is because you don't want to double-count them.
w - x - y + z / (w)
