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PS: In an internet research company 1200

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by netcaesar » Mon Sep 07, 2009 5:51 am
In an internet research company 1200 clients were surveyed. The survey asked about 3 characteristics of the system: the price, the speed, and the stability. 56% answered it was a cheap service, 48% answered that it was a fast service, 30% answered that it was both a fast service and a cheap service and 42% answered that it was a stable service. What is the maximum amount of people that could answered that it was a stable service but not a cheap service nor a fast service?
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by tom4lax » Mon Sep 07, 2009 11:46 am
100 = (56+48+42) - (30+x) (x is defined as those who mentioned stability as well as some other trait)

100 = 146 - 30 - x
x = 16%

So 16% mentioned not Stability and some other combination or 1 or both of price or speed. Lets assume they only choose one of the other in order to maximize.

42% - 16% = 26% choose stability only.
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by netcaesar » Mon Sep 07, 2009 1:29 pm
Your answer is correct.
Can you explain why did you substract 30+x?
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by tom4lax » Mon Sep 07, 2009 1:44 pm
sure, formula for 3 overlapping sets:

100% = (A+B+C) - (AB + BC + AC) - 2(ABC)

A+B+C is straight forward. But then you need to subtract by # of people who were in the overlapping sets so that they arent double and triple counted. We know the 30, but we dont know how many mentioned stability and one of the others (this is the x). In order to maximize, we assume that none of the categories were mentioned 3 times. So 30 + x is the amount of ppl who mentioned more than one category. One we find x, we subtract from how many mentioned stability overall.
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