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 2B = 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).

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