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GMAT Overlapping Sets
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Author:  Gennadiy [ Sat Nov 13, 2010 11:56 am ]
Post subject:  GMAT Overlapping Sets

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:
Image

(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).

The solved Venn diagram is the following:
Image

Attachments:
venn_diagram-2.gif [9.63 KiB]
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venn_diagram-1.gif [9.6 KiB]
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Author:  questioner [ Sun Jul 28, 2013 1:06 pm ]
Post subject:  Re: GMAT Overlapping Sets

Please explain this question a bit thoroughly. I'm not able to understand how B = 750.

Author:  Gennadiy [ Sun Jul 28, 2013 1:10 pm ]
Post subject:  Re: GMAT Overlapping Sets

questioner wrote:
Please explain this question a bit thoroughly. I'm not able to understand how B = 750.
The question statement tells us
Quote:
The number of people who purchased both books A and B is 500 …
500 = readers of B and A
Quote:
… is 500, which is twice the number of people who purchased only book B.
250 = readers of B only

Readers of B = [readers of B and A] + [readers of B only]

750 = 500 + 250

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