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by GMATGuruNY » Wed Aug 19, 2015 3:21 am
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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by rommysingh » Wed Aug 19, 2015 11:00 pm
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..
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by [email protected] » Thu Aug 20, 2015 9:29 am
Hi rommysingh,

This question can be solved in a couple of different ways. TESTing VALUES will work well here, so I would take that approach. One of the 'clues' to TEST VALUES is the variables in the answer choices; notice how similar Answers A and C are though...

Those two different denominators will actually yield the SAME result when P = 50. You wouldn't necessarily notice that at first glance, but once you read the prompt and determine what "P" represents, you should be able to recognize that 100-50 is the same as 50, so using THAT Value for "P" is NOT a good idea.

If you make P some other large 'easy' percent (such as 90%), and keep N = 10, then you can work through the same steps that Mitch used to get to the correct answer.

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by nikhilgmat31 » Thu Aug 20, 2015 11:30 pm
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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by Max@Math Revolution » Fri Aug 21, 2015 7:03 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


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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by Matt@VeritasPrep » Sun Aug 23, 2015 11:18 am
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)
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