The number of people who purchased book

*A* is twice the number of people who purchased book

*B*. The number of people who purchased both books

*A* and

*B* is 500, which is twice the number of people who purchased only book

*B*. What is the number of people who purchased only book

*A*?

A. 250

B. 500

C. 750

D. 1000

E. 1500

The original Venn diagram is the following:

(D) First, let's define some values:

*B* = number of people who purchased book

*B*2

*B* = number of people who purchased book

*A*500 = number of people who purchased both

*A* and

*B*500/2 = 250 = number of people who purchased only

*B*.

We are looking for the number of people who purchased ONLY book

*A*. The number of people who purchased ONLY

*A* is the total number of people that purchased

*A* minus the number of people that purchased both

*A* and

*B*.

Since 250 people purchased ONLY

*B*, and 500 people purchased both books, 750 people in all must have purchased

*B*.

Thus, 1500 people in all purchased book

*A*.

Since 500 of these people purchased both books, the number who have purchased ONLY

*A* is:

1500 – 500 = 1000.

The correct answer is choice (D).

The solved Venn diagram is the following: