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Max/Min in Venn Diagram

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by jswesth » Mon Jul 11, 2016 9:59 am
Can someone explain algebraically how you arrive at C here? I understand conceptually how it works, but not sure how to arrange the variables in a classic Venn Diagram.
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by GMATGuruNY » Mon Jul 11, 2016 10:38 am
In a certain city, 80% of the households have cable television and 60% of the households have videocassette recorders. If there are 150000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from
  • A) 30000 to 90000 inclusive
    B) 30000 to 120000 inclusive
    C) 60000 to 90000 inclusive
    D) 60000 to 120000 inclusive
    E) 90000 to 120000 inclusive
Since 60% have VCRs, no more than 60% can have BOTH.
60% of 150,000 = 90,000.
Thus, no more than 90,000 households can have both.
Eliminate B, D and E.

Check whether the minimum value in A -- 30,000 -- is possible.
30,000 = 20% of 150,000.
If 20% own both, the following Venn Diagram is yielded:
Image
Not possible, since the sum of the percentages in the circles is greater than 100%:
60+20+40 = 120%.
Since it is not possible that only 30,000 households have both, eliminate A.

The correct answer is C.
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by jswesth » Mon Jul 11, 2016 10:47 am
Thanks, Mitch. Makes sense now.
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