Writing articles and receiving commissions

[calande]

This is taken from the Kaplan course book. There is no answer to this problem in the end of the chapter, so I tried it myself and put the answer here below, in the end of the message. I think I'm right, please correct me if I'm wrong. You can try to solve it yourself if you wish

Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month and a + b for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?

(A) (a - b)(a + b + n)
(B) a - b
(C) a² - b²
(D) n(a - b)
(E) an + bn - an

Here's how I did: Let's say the total of articles written is t. The total amount of money a writer makes is n articles × a + (t - n) × (a + b). We know there are two kinds of writers: Those who submit n + a articles, and those who submit n + b articles. Let's substitute t within the equations:

"n + a" writers make: an + (n + a - n)(a + b) dollars
"n + b" writers make: an + (n + b - n)(a + b) dollars

Let's pick numbers:

a = 10
b = 2
n = 2

And substitute:

"n + a" writers make: an + (n + a - n)(a + b) dollars
That's 20 + (10)(12) = 140 dollars

"n + b" writers make: an + (n + b - n)(a + b) dollars
That's 20 + (2)(12) = 44 dollars

In our case, "n + a" writers make 96 more dollars than "n + b" writers.

Let's find out in the answer choices. Answer choice C is a² - b², that's 100 - 4, it matches ou 96 dollar difference.

[gmatinjuly]

Hey there,

Your answer is correct but I just thought their is a simpler way to do it.

1. First n items both get paid the same, so we can eliminate that.
2. So the difference in amount will be
Difference in amount paid = difference in no of articale written * amount for each article
= (a-b) (a+b)
= a^2 - b^2

[calande]

Thanks, indeed

[gmataspirant]

a + b denotes dollars and a,b also denotes authors. Is the variables used are correct ?

I am confused . Could someone explain ?

[zacharyz]

Yes, they are reusing variables for different things.

a = dollars for the first n stories
a + b = dollars for each story about n stories

then for the equation,

n + a = number of stories from the first author
n + b = number of stories from the second author.

Looking at each author separately... You have to remember that you get paid a dollars for the each of the first n stories.
First Author
n stories at a dollars = n*a dollars
a stories at (a+b) dollars = a*(a+b) dollars (technically different things ie dollars and stories, but it just represents a number.. ie. 1 dollar for 1 story or 2 dollars for 2 stories)

So, total, he has gotten paid n*a+a*(a+b) = na + a^2 + ab

Second Author
n stories at a dollars = n*a dollars
b stories at (a+b) dollars = b*(a+b) dollars (same explanation as above)
So, total, he has been paid n*a+b*(a+b) = na + ab + b^2

Now, subtract the the second author from the first author.. both have (na), that that cancels, and both have (ab), so that cancels.. leaving

a^2 - b^2.


Per your question, yes, they are different variables, but they are the same NUMBER. This is more just for the ease of these calculations.

Hope this helps a little

[calande]

You're not the only one! I was confused in the beginning too! Welcome to the GMAT