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how many employees are trained to work in all 3 restaurants?

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how many employees are trained to work in all 3 restaurants?

by leonswati » Mon Sep 19, 2011 5:29 am
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
a 2
b 3
c 4
d 5
e 6

The IMO is B.... Can some one help me solve it using the formula for three intersecting sets..
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by gmatclubmember » Mon Sep 19, 2011 6:09 am
leonswati wrote:At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
a 2
b 3
c 4
d 5
e 6

The IMO is B.... Can some one help me solve it using the formula for three intersecting sets..
Is the OA a (2).

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by sl750 » Mon Sep 19, 2011 6:24 am
x- all three cases
39 = 19+18+12-4-2x ; x=3
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by leonswati » Mon Sep 19, 2011 6:29 am
Is the formula not:

P(A u B u C) : P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)
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by gmatclubmember » Mon Sep 19, 2011 6:35 am
Yes leon the formula is what you have written.
And I think P (A n B) = P (A n C) = P(B n C) = 4.
which gives us x=2.

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by sl750 » Mon Sep 19, 2011 6:40 am
The formula is correct, but I am not sure what exactly you are looking for
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by leonswati » Mon Sep 19, 2011 6:42 am
How can we derive to the answer 3 using the formula
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by prachi.sakhare » Fri Sep 23, 2011 11:16 am
Ami,
Could you please explain this formula a bit more...? I though the answer should be 2 here.

Prachi
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by gmatclubmember » Fri Sep 23, 2011 11:28 am
Please see the explanation of Geva@MasterGMAT
here
https://www.beatthegmat.com/how-many-emp ... 91285.html

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