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DerekLin
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General formula for 2-overlapping SETS:

A+B-BOTH+Neither=TOT

TOT:w
A:x
B:y
BOTH:z

x+y-z+neither=w --> neither=w-x-y+z as a fraction on the total is w-x-y+z/w­

Answer D­
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Very easy to visualize using Venn diagram, check,




DerekLin
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.

B.

C.

D.

E. ­
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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.

gmatophobia
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Bunuel

DerekLin
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.

B.

C.

D.

E. ­
Attachment:
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jin.h
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.

gmatophobia
GmatKnightTutor
Bunuel

DerekLin
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. \(\frac{w - x - y + 2z}{w}\)

Attachment:
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Attachment:
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Attachment:
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Attachment:
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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.

Answer: D.
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