Problem Solving

Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
A. 100p / (125 – p)
B. 150p / (250 – p)
C. 300p / (375 – p)
D. 400p / (500 – p)
E. 500p / (625 – p)

I found this quick solution on another site:

just take actual nos say 1 newspaper of each type was sold..

rev from A = 1, rev from B = 1.25, total rev = 2.25
r = (1/2.25) x 100 = 400/9, p = (1/2) x 100 = 50
now plug in the values for r and p in the options
option D holds good

In your question, you said that p% of revenue was from Newspaper A, but I think you mean B.

awesomeusername wrote:I found this quick solution on another site:

just take actual nos say 1 newspaper of each type was sold..

rev from A = 1, rev from B = 1.25, total rev = 2.25
r = (1/2.25) x 100 = 400/9, p = (1/2) x 100 = 50
now plug in the values for r and p in the options
option D holds good

In your question, you said that p% of revenue was from Newspaper A, but I think you mean B.

Yes, that's B. I just copied and pasted it from the original test which has such a minor mistake. Thx!

yangliu0401 wrote:Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
A. 100p / (125 – p)
B. 150p / (250 – p)
C. 300p / (375 – p)
D. 400p / (500 – p)
E. 500p / (625 – p)

assume p = 100% then r should be 100%

only B and D left.

say p = 50% then r = 50*100/(50+50*1.25) = 100/2.25 = 400/9

This possible only in D case.

Folks, a quicker way to answer this is......

Since for any given value of p and r the answer must be same.....

Take p =100 i.e the shop sold only newspaper A.

Then obviously r also will be 100.

So r = p.

Now substituting p =100 in the options , the options that gives r = p are B & D.

Now if p =50, since equal number of papers are sold, the revenue will be in the ratio of 1: 1.25 = 4:5. Hence r = 4/9(total sales)

Only D satisfies this...

More discussion regarding this question can be found here

https://www.beatthegmat.com/newspapers-a ... tml#123409