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).
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Hi,
There are two terms that give value of 40
option A & Option C....so i dont know if it works like that


How would I know what numbers to pic. Like how can I assume numbers and percentages...what question trigger should I see to know that i can assume more than one number...plz help..

we can do it in simple way as

lets say total number of persons to be surveryed = T

twice minimum of respondents = 2n

(1 - p/100) T = 2n

(100- p) *T = 200n

T = 200n/(100-p)

Answer A

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If we note the overall number of individuals that participate in the survey as 100x, p% of 100x = px, and since the rest are double that number 2n + px = 100x. 2n = (100-p)x, and x = 2n/(100-p). Since the problem asks for 100x, 100x=100*2n/(100-p)=200n/(100-p) and therefore A is the answer.


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Let's say we survey x people. We know that p% of them won't respond, but (100 - p)% will.

Our researcher wants to get 2n responses, so

(number surveyed) * (percent who respond) = 2n, or

x * (100 - p)% = 2n, or

x * (100 - p)/100 = 2n, which simplifies to

x * (100 - p) = 200n, or

x = (200n) / (100 - p)