prernamalhotra 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?
1) 200n / 100-p
2) 2n/100-p
3) 200n/p
4) 2n(100+p)/ 100
5) 2n+2np/100
Strategy:
Plug in values, working from the END of the problem to the BEGINNING.
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 plug n=10 and p=50 into the answers to see which yields our target of 40.
Only
A works:
200n/(100-p) = (200*10)/(100-50) = 2000/50 = 40.
The correct answer is
A.
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).
[spoiler][/spoiler][spoiler][/spoiler]
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
