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The total number of recording titles distributed by music d

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The total number of recording titles distributed by music d [#permalink] New post 06 Mar 2018, 15:34
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The total number of recording titles distributed by music distributors L and M is 9,300. The number of recording titles distributed by L is 7,100, and the number of recording titles distributed by M is 5,200. Which of the following statements must be true?

Indicate \(all\) such statements.

A More than half of the titles distributed by L are also distributed by M.
B More than half of the titles distributed by M are also distributed by L.
C No titles are distributed by both L and M.

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[Reveal] Spoiler: OA

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Re: The total number of recording titles distributed by music d [#permalink] New post 06 Mar 2018, 19:50
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This problem can be easily solved using an overlapping sets table. Unfortunately they are very hard to depict by typing and we're not allowed to post pictures. Fortunately this problem can be solved in a different way as well.

If 7,100 titles are distributed by L and 5,200 are distributed by M, but the grand total is 9,300, we should figure out the overlap. Adding 7,100 and 5,200 gets us a total of 12,300, which is exactly 3,000 more than the total we've been told. Therefore there must be an overlap of 3,000 titles.

A. If half the titles distributed by L totals 3,550, but the overlap is 3,000, then A is not true.

B. If half the titles distributed by M totals 2,600, and the overlap is 3,000, then B is true.

C. This is obviously not true since we've proven that 3,000 titles are sold by both.
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Re: The total number of recording titles distributed by music d [#permalink] New post 31 May 2018, 09:10
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Us this diagram to solve the answer
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Re: The total number of recording titles distributed by music d   [#permalink] 31 May 2018, 09:10
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