A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?
Since the GMAT would provide answer choices, we can plug in values.nidhis.1408 wrote:A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?
If n=10 responses are required, then twice the minimum = 20.
If p=50% of the individuals fail to respond, then 40 individuals must be surveyed to yield 20 responses.
The question stem asks for the number of individuals who must be surveyed: 40.
This is our target.
Now we plug n=10 and p=50 into the answers to see which yields our target of 40.
Answer choice: 200n/(100-p)
200n/(100-p) = (200*10)/(100-50) = 2000/50 = 40.
Algebraically:
Let the number interviewed = i.
Since p% don't respond, the number who don't respond = (p/100)i.
Thus, the number who DO respond = i - (p/100)i.
Since this result must be equal to 2n -- twice the minimum number of required responses -- we get:
i - (p/100)i = 2n
i(1 - p/100) = 2n
i*(100-p)/100 = 2n
i = 200n/(100-p).
