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the alien planet 'Fisto'

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by sanju09 » Mon Mar 26, 2012 12:59 am
50 percent of the inhabitants of the alien planet 'Fisto' own heaters and personal computing devices. What percentage of the inhabitants of the planet own personal computing devices, but not heaters?
(1) 60 percent of the inhabitants own personal computing devices.
(2) 70 percent of the inhabitants own heaters.
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Source: — Data Sufficiency |
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by ubhanja » Wed Mar 28, 2012 9:32 am
Statement A) enought to decide on % personal computing device.
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by [email protected] » Thu Mar 29, 2012 2:04 am
50 percent of the inhabitants of the alien planet 'Fisto' own heaters and personal computing devices. What percentage of the inhabitants of the planet own personal computing devices, but not heaters?
(1) 60 percent of the inhabitants own personal computing devices.
(2) 70 percent of the inhabitants own heaters.


According to me the correct answer is A.

Statement 1: Case(i): 100 = n(A) + n(B) - n(A intersection B)

you have 60 as whole of n(B) and when you subtract the common, you get 10 as inhabitants of the planet owning personal computing devices and not heaters.


Statement 2: Statement 2 gives 2 cases:

Case (i): if there are a total of 100 inhabitants and none of them are such that they do not own anything i.e the total is 100 on the LHS. In that case you will get the answer and hence statement 2 is sufficient.

Case (ii): if there are a total of 100 inhabitants and there are such inhabitants as to own none of the assets i.e neither Heater nor Computer Devices.

in that case the answer is impossible as you will get two variables.

(100-x) = n(A) + n(B) - n(A intersection B)

so you will have two variables here,

(100-x) = 20 + n(B)

As you cannot give an answer with surity, statement 2 is not sufficient...

By the way what is the OA...

Hope this helps!
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by Bill@VeritasPrep » Thu Mar 29, 2012 5:57 pm
The solutions already posted are correct, but one key takeaway from this problem is that we should always consider the potential for "neither" in a Venn diagram problem (unless it is explicity ruled out, of course). If we forget to do that, then it's possible to incorrectly interpret Statement 2 as sufficient.

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