Question

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.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is C Both statements together are sufficient, but neither statement alone is sufficient.

1. Statement 1 clarifies that Company K and Company R together have $17$ individuals serving as directors. However, there is no information as to the distribution of the Company K directors, the Company R directors, and the joint directors; NOT sufficient.
   
2. From statement 2 we get the number of directors in each company but no information as to the number of joint directors; NOT sufficient.
   

• Taking (1) and (2) together, it is known from (2) that there are $20$ directorships in all. If at a joint meeting, there are only $17$ people present, then $20-17=3$ people must be joint directors. Thus, both statements together are sufficient, but neither statement alone is sufficient.