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by baladon99 » Sun Jun 26, 2011 11:16 am
Out of 100 families in the neighborhood 50 have radios, 75 have TVs and 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If some families have radio only , how many have only TV ?

A) 30
B) 35
C) 40
D) 45
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by baladon99 » Sun Jun 26, 2011 11:43 am
As per my calculation the answer is 30. Can anybody confirm it ? Thanks in advance :)
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by Gissinggy » Sun Jun 26, 2011 3:25 pm
First, we need to find out how many families have both TV and Radio.

50+75+25-15(both TV and VCR)-X(both TV and Radio)-20(2 times all)=100
so the number of families that have both TV AND Radio is 15.

The number of families with TV only is: 75-25(tv & cvr)-15(both tv and radio)=35.

How did you get your answer?
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by baladon99 » Sun Jun 26, 2011 9:33 pm
I noticed that I went wrong in calculation. I am getting 35 now.Thank you Gissinggy .
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by GMATGuruNY » Mon Jun 27, 2011 6:59 am
baladon99 wrote:Out of 100 families in the neighborhood 50 have radios, 75 have TVs and 25 have VCRs. Only 10 families have all three and each VCR owner also has a TV. If some families have radio only , how many have only TV ?

A) 30
B) 35
C) 40
D) 45
I received a PM asking me to comment.

Draw a Venn Diagram.
Insert the known values, working from the center out.

10 own all three and each VCR owner has a TV:
Image

Plug in the answers, which represent the number who own only a TV.
Fill in the remaining values.
When the correct answer is plugged in, Total = 100.

Answer choice B: 35 own only a TV.
Image
Adding all the values in the Venn Diagram:
25+15+35+10+15 = 100.
Success!

The correct answer is B.
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