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

Expert replies

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

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..

Source: Beat The GMAT — Problem Solving | Mon Sep 19, 2011 5:29 am

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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).

Cheers
Ami/-

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Mon Sep 19, 2011 6:24 am

x- all three cases
39 = 19+18+12-4-2x ; x=3

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

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)

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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.

Cheers
Ami/-

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Mon Sep 19, 2011 6:40 am

The formula is correct, but I am not sure what exactly you are looking for

leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Mon Sep 19, 2011 6:42 am

How can we derive to the answer 3 using the formula

prachi.sakhare: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Thu Sep 22, 2011 5:59 pm

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

gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

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

Cheers
Ami/-

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