Overlapping Sets - Double matrix method

[jay.mathew]

How do we use the double matrix method for the following Data Sufficiency question below?

How many people are directors of both charities A and B?

(1) Charity A has 16 directors and Charity B has 9 directors.

(2) 18 directors attended a joint meeting of the directors of Charity A and Charity B, and not one director was absent from the meeting.

1 - NOT SUFFICIENT
This statement does not provide any information as to the number of joint directors. Instead it only provides the number of directors in each charity.

2 - NOT SUFFICIENT
This statement shows that Charity A and Charity B together have 18 individuals who are directors. However, there is no information as to the arrangment of the Charity A directors, the Charity B directors, and the joint directors.

Taking 1 and 2 together we can see that there are 25 directors in total. If at a joint meeting there are only there are 18 directors present, then there must be 25-18 = 7 joint directors.

Therefore the answer is (C).

I'm just not quite sure on how to represent this answer using the double-matrix method.

By the way, incase you're wondering...I made up this question, but it was inspired from an OG question (OG 12 - DS 50). Hopefully this is acceptable.

[RonPurewal]

I'm just not quite sure on how to represent this answer using the double-matrix method.

COLUMNS: Charity A / NOT Charity A / Total

ROWS:
Charity B
NOT Charity B
Total

DESIRED QUANTITY is the TOP LEFT.

(a)
bottom left = 16
top right = 9
insufficient.

(b)
middle square = 0
bottom right = 18
insufficient.

(together)
if you have both statements, you can fill in the whole grid.
7 2 9
9 0 9
16 2 18
so, top left = 7.
sufficient.

[jay.mathew]

Thanks Ron.

For statement 2, I had trouble putting the 0 in the middle square (i.e. NOT A and NOT B). I overlooked the clause 'and not one director was absent from the meeting', and was therefore unable to continue populating the matrix.

[Ben Ku]

Glad that helped!