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Overlapping Sets Problem

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by vongdn » Tue Oct 05, 2010 9:16 pm
3000 families live in a certain town. How many families who live in the town own neither a car nor a television set?

(1) Of the families who live in the town, 2980 own a car.
(2) Of the families who live in the town, 2970 own both a car and a television set.


1. P(no car) = 3000-2980 = 20 --> Insufficient
2. P(car) + P(TV) - P(TV+Car) = Total = P(car) + P(TV) - 2970 = 3000 --> Insufficient

(1) and (2) together: 2980 + P(TV) - 2970 = 3000, P(TV) = 2990

P(no car) + P(no TV) - P(no car and no TV) = Total --> 20 + 10 - P(no car and no TV) = X

I get stuck there but I know the answer is that both statement together are not sufficient, so is that because I don't know what X is? Or did I approach the problem wrong.

Thanks
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Source: — Data Sufficiency |
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by neerajkumar1_1 » Tue Oct 05, 2010 10:20 pm
This problem can be solved simply using the following formula for sets..
Total = A + B - Both + Neither

from the question stem, u r given the total
u are asked to find Neither, so all u need is values A, B and both

In this questions assume A = having a car
and B = having a television

Statement 1)
gives u A but nothing else... insufficient

Statement 2)
gives u Both but nothing else... insufficient

Together,
U still need the value for B, in order to find neither...
hence insufficient...

IMO: E
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by blaster » Wed Oct 06, 2010 2:37 am
in order solve this kind of question ,you need following category information

Tv
Car
nether
either
and the result

statement 1 and 2 gives us only 3 of them, that's why it's not possible to solve this question, therefore IMO E
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by Yanat » Wed Oct 06, 2010 7:45 am
IMO, the answer is E.
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