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A certain retailer decided to raise its prices by p%. When, as a resul

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A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]

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New post 17 Feb 2017, 02:03
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A certain retailer decided to raise its prices by p%. When, as a result, its sales dropped by q%, the retailer found that its total revenue was unchanged. Which of the following correctly expresses q in terms of p?

A. p
B. 1/p
C. p/(1−p)
D. 100/(100+p)
E. 100p/(100+p)
[Reveal] Spoiler: OA

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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]

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New post 17 Feb 2017, 03:23
i dont know easy way, but i calculated this way:
lets say begining number of sales number was 10 and sales price was 10 so total sales was 100
after P% increase lets say 20% price became 12
but total sales did not changed so was still 100
so number of items sold was aprox 8.3. ( bad numbers i know) :)
so drop q% was aprox 16.6%

if we subs. numbers from answers we will get E
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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]

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New post 22 Feb 2017, 01:01
these kind of problems can be solved easily by plug in some no. and whenever we see variables in questions the easy way to tackle them by plugging in no. for this we can take some easy no such as let's say revenue=sales(#of products)*price
now initial revenue was 300=30*10 and now after increasing price which is P by 50% we get price =45*q=300 and solving for q we get 20/3 and to calculate declining % we do 1-20/3=10/30*100 that 100/3 so q is =100/3% now we can substitute these values in options , that only option E provides 100/3 hence answer must be E
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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]

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New post 22 Feb 2017, 01:12
Bunuel wrote:
A certain retailer decided to raise its prices by p%. When, as a result, its sales dropped by q%, the retailer found that its total revenue was unchanged. Which of the following correctly expresses q in terms of p?

A. p
B. 1/p
C. p/(1−p)
D. 100/(100+p)
E. 100p/(100+p)


Let, 100 is increased by 25% (p%) so it becomes 125

Now we need to decrease it by 20% (q%) to bring it to the same level i.e. 100

So, p=25 and q=20 satisfies the requirement. Verify the options

A. p This is not equal to q hence INCORRECT
B. 1/p = 1/25 This is not equal to q hence INCORRECT
C. p/(1−p)= 25/(1-25) This is not equal to q hence INCORRECT
D. 100/(100+p) = 100/(100+25) This is not equal to q hence INCORRECT
E. 100p/(100+p) = 100*25/(100+25) = 20 This is equal to q hence CORRECT

Answer: Option E
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Re: A certain retailer decided to raise its prices by p%. When, as a resul [#permalink]

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New post 23 Feb 2017, 09:29
Bunuel wrote:
A certain retailer decided to raise its prices by p%. When, as a result, its sales dropped by q%, the retailer found that its total revenue was unchanged. Which of the following correctly expresses q in terms of p?

A. p
B. 1/p
C. p/(1−p)
D. 100/(100+p)
E. 100p/(100+p)


We can let n = number of items and x = price per item.

Since the price was raised by p%, the sales dropped by q%, and revenue remained the same, we have:

nx = [1+(p/100)]x * [(1-(q/100)]n

1 = [(100+p)/100][(100-q)/100]

1 = (100+p)(100-q)/10,000

10,000 = 10,000 + 100p - 100q - pq

100q + pq = 100p

q(100 + p) = 100p

q = 100p/(100 + p)

Answer: E
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Re: A certain retailer decided to raise its prices by p%. When, as a resul   [#permalink] 23 Feb 2017, 09:29
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