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Anthony and Michael sit on the six member board of directors for company X.

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by BTGModeratorVI » Sat Jun 27, 2020 6:37 am

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A

B

C

D

E

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Difficulty—

Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%

Answer: C
Source: Manhattan prep
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Re: Anthony and Michael sit on the six member board of directors for company X.

by Brent@GMATPrepNow » Thu Jul 02, 2020 4:52 am
BTGModeratorVI wrote: ↑
Sat Jun 27, 2020 6:37 am
 Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%

Answer: C
Source: Manhattan prep
We can think of this as a probability question: What is the probability that Anthony and Michael are on the same subcommittee?

Now, assume that we're creating subcommittees.
We want to place 6 people in the following spaces:
_ _ _ | _ _ _

First, we place Michael in one subcommittee; it makes no difference which one:
M _ _ | _ _ _

When we go to place Anthony, we see that there are 5 spaces remaining.
2 spaces are on the same subcommittee as Michael.
So the probability that they are on the same subcommittee is 2/5 = 40%

Answer: C
Brent Hanneson - Creator of GMATPrepNow.com
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