Bunuel wrote:

How many people are directors of both Company K and Company R ?

(1) There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent.

(2) Company K has 12 directors and Company R has 8 directors.

We must determine how many individuals are directors for both Company K and Company R. To solve this "overlapping sets" problem, we can employ the following equation:

Total Directors = Directors in Company K + Directors in Company R – Directors in both Companies K and R

Statement One Alone:

There were 17 directors present at a joint meeting of the directors of Company K and Company R, and no directors were absent.

From statement one we know that there are 17 total directors. This is not enough information to determine how many individuals are directors of both Company K and Company R. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Company K has 12 directors and Company R has 8 directors.

Although we know that Company K has 12 directors and Company R has 8 directors, we still do not have enough information to determine how many individuals are directors of both Company K and Company R. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two, we know that there are 17 total directors and that Company K has 12 directors and Company R has 8 directors. We can use this information in the our equation to determine the number of individuals who are directors of both Company K and Company R.

Total Directors = Directors in Company K + Directors in Company R – Directors of both Companies K and R

17 = 12 + 8 – Both

17 = 20 – Both

Both = 3

There are 3 individuals who are directors of both Company R and Company K.

Answer: C

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Jeffery Miller

Head of GMAT Instruction

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