A researcher has determined that she requires a minimum of n

Question

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?

A.\(\frac{{200n}}{{100-p}}\)

B.\(\frac{{2n}}{{100-p}}\)

C.\(\frac{{200n}}{{p}}\)

D.\(\frac{{2n(100+p)}}{{100}}\)

E.\(\frac{{2n+2np}}{{100}}\)

Show Answer

Official Answer

A

A. \frac{{200n}}{{100-p}}

B. \frac{{2n}}{{100-p}}

C. \frac{{200n}}{{p}}

D. \frac{{2n(100+p)}}{{100}}

E. \frac{{2n+2np}}{{100}}

Bunuel · Accepted Answer

Say x individuals must be surveyed.

p% of the surveyed individuals fail to respond --> the number of individuals who did NOT fail to respond =  x-x*\frac{p}{100} .
The above must be equal to 2n, so:

x-x*\frac{p}{100}=2n  -->  x(1-\frac{p}{100})=2n  -->  x=\frac{200n}{100-p} .

Answer: A.

Of course one can also use plug-in method to solve this problem.

galiya · Answer

X - #of surveyed people

(1-P)*X>=2n --> x>=2n/(1-P)

A

mvictor · Answer

suppose x is the number of people she needs to interview
out of the x, only x(100-p/100) answered.
this all is equal to n.
so n = x(100-p/100)
or x= 100n/100-p
since we need twice the number, multiply everything by 2, and get 200n/100-p.
A

musunna · Answer

Unitary method seems more comprehensible to me.

Given that p% of the surveyed individuals fail to respond.

So individual who NOT failed to respond = (100-P)%

That means,

To get (100-P) responses, 100 individual is surveyed.
For 1 response, 100 / (100-P) individual is surveyed.
For 2n responses, (100*2n) / (100-P) individual is surveyed.

Answer: (A) 200n / (100-P)

ShashankDave · Answer

The question is not hard..I got stuck because I found the wording very awkward..is the wording good enough? I'm not feeling right about this one..

DharLog · Answer

A question is a little similar to https://gmatclub.com/forum/the-price-of ... 31794.html. (the opposite similar))

testcracker · Answer

hi

how can you equate x( 1 - p/100) with 2n ..?

say, p = 10, n = 7....
now 90 people can respond, and 2n = 14

So, 14 = 90 , how come ...?

if the question used the terms "at least", it would be somewhat clear ...

thanks in advance ..

gps5441 · Answer

Plugin nos.
Let people surveyed be 100
10% of 100 surveyed do not respond=10
90 surveyed responded=the required no response for the survey to be valid.
Double is 180.
To get 180 you need 200 responders.
Plugin in n=90 and p=10 in the given expression.
1) Start from C

\frac{200n}{p}

\frac{200*90}{10} =1800=wrong.

2) Pick A (I checked all the answer choice but for sake of time and effort showing only 2 workings)

\frac{200*n}{100-p}

\frac{200*90}{100-10} =200=correct.

gmexamtaker1 · Answer

I tried to plugin numbers too and couldn't get the right answer, may I ask you something in your approach you state that 90 people is the required number of people so that the survey is valid isn't that wrong? I mean n is the minimum number those 90 are the n-p/100 + afterwards you consider the required amount to be 180, however isn't the 200 you should actually be looking for? Still, you got the right answer...

Could you please elaborate on your approach so that I can spot my mistake?

Bunuel   chetan2u  maybe you could shed some light on the problem here?

ScottTargetTestPrep · Answer

Let x = total number of people she surveys. Therefore, we have:

x(1 - p/100) = 2n

x(100 - p)/100 = 2n

x = 2n * 100/(100 - p)

x = 200n/(100 - p)

Answer: A

whatsarc · Answer

p% didnt respond means 1-p% did respond

This 1-p% should be greater than or equal to min. required responses (2n)

Put both n and p on the same side of the equation to get the solution

1-(p/100) ≥ 2n
100-p/100≥2n
2n x 100 / 100-p ≥ min requred
 200n/100-p ≥ minimum required responses

Seb2m02 · Answer

People surveyed = X
People who did not answer = pX/100
People who answered n = X - pX/100 -> n = (100X - pX)/100 -> n = X(100-p)/100

We want X, the number of people surveyed

X=100n / (100-p)

The question is 'to produce twice the minimum required number of responses' so 2 x 100n / (100-p)
Answer A

mithxrx · Answer

I don't think this a very good worded one. it should be:
' 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 WILL 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?'

The absence of will makes it sounds like a certain amount have already failed to respond and the remaining + additional should equal to 2n.

nihilveritatis · Answer

let n = 20

let p = 20%

let surveyed = 50

=> responses received = 50*0.8 = 40 
This number is 2n

Plug in the above values of n,p in the options. I started with (B) 2n/100-p which results in 40/80 but I need 4000/80 -> therefore (a) 200n/(100-p)

luisdicampo · Answer

Deconstructing the Question

Minimum required responses =  n .
We want twice that many responses, so target responses:

2n

If  p%  do not respond, then the response rate is:

100-p\%

Let  N  be the number of people surveyed.

Expected responses:

N\cdot \frac{100-p}{100}

Step-by-step

Set responses equal to the target:

N\cdot \frac{100-p}{100} = 2n

Solve for  N  by multiplying both sides by  \frac{100}{100-p} :

N = 2n\cdot \frac{100}{100-p}

N = \frac{200n}{100-p}

Answer: A

A researcher has determined that she requires a minimum of n

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A researcher has determined that she requires a minimum of n

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards