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# Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R,

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R, [#permalink]

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06 Jan 2012, 03:56
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ssarkar wrote:
Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R, 25 bought S, 8 bought both Q and S, 7 bought both R and S, 9 bought both Q and R, the number of the people bought all the three is the same as the number of the people who bought none, and 39 people bought at least one newspaper. How many people bought exactly one newspaper?

There are 45 people.
"the number of the people bought all the three is the same as the number of the people who bought none, and 39 people bought at least one newspaper."
Of 45, 39 people bought at least one paper so 6 people bought none. Therefore, 6 people bought all 3 newspapers.
Attachment:

Ques3.jpg [ 16.43 KiB | Viewed 1276 times ]

We see from the diagram that
17 - 3 - 6 - 2 = 6 people bought only Q
15 - 3 - 6 - 1 = 5 people bought only R
25 - 2 - 6 - 1 = 16 people bought only S

Number of people who bought exactly one paper = 6+5+16 = 27
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Kudos [?]: 17834 [1], given: 235

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Kudos [?]: 304 [0], given: 16

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Re: Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R, [#permalink]

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06 Jan 2012, 04:44
27 using venn diagrams
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Kudos [?]: 304 [0], given: 16

Re: Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R,   [#permalink] 06 Jan 2012, 04:44
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# Of the 45 people who plan to buy newspapers, 17 bought Q, 15 bought R,

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