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Max/Min in Venn Diagram
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Since 60% have VCRs, no more than 60% can have BOTH.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
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:
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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