Overlapping Sets - Double matrix

[DileepW137]

Hello there,


I am struggling to do this question using your overlapping sets matrix. How do you do this using the technique as described in the Word Problems book?

At the beginning of each month, a certain book club offers its members the opportunity to purchase one or more books at a discount. At the beginning of January, the number of book club members who elected to purchase both The Brothers Karamazov and Pride and Prejudice was equal to the number of members who elected to purchase neither of those books. How many members were in the book club at the beginning of January?

1) 128 book club members purchased The Brothers Karamazov and 212 book club members purchased Pride and Prejudice.
2) Exactly half of the book club members who purchased The Brothers Karamazov also purchased Pride and Prejudice.



I have the following so far..


B not B Total
P x 212
not P x
Total 128 ?


Using Venn Diagram method, I am getting A as the answer. (since the x's cancel out below)
(128 − x) + x + (212 − x) + x = 128 + 212 = 340



Thank you so much for your support.

[Sage Pearce-Higgins]

I replied to this post in the non-CAT Math folder.