Each writer for the local newspaper is paid as follows: a dollars for

Question

Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month, and a + b dollars 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. a^2 – b^2
D. n( a – b)
E. an + bn – an

A. (a – b)( a + b + n) 
B. a – b
C. a^2 – b^2 
D. n( a – b) 
E. an + bn – an

BrentGMATPrepNow · Accepted Answer

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach. 
The two posters above have solved the question algebraically, so let's use the  INPUT-OUTPUT approach .

Choose some values for the variables...
a = 3 (so, $3 for each of the first n stories)
n = 5 (so, $3 for each of the first 5 stories)
b = 1 (the number of additional stories beyond 5 stories)
a+b = 3+1 = 4 (so, $4 for each story beyond 5 stories)

Writer who submits n + a stories in a month 
In other words, writer who submits 5 + 3 stories in a month
So, TOTAL payment = (5 stories)($3 per story) + (3 stories)($4 per story) = 15 + 12 = $27

Writer who submits n +b stories in a month 
In other words, writer who submits 5 + 1 stories in a month
So, TOTAL payment = (5 stories)($3 per story) + (1 story)($4 per story) = 15 + 4 = $19

How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?   
$27 - $19 =  $8

So, when  a = 3, n = 5 and b = 1 , the answer to the question is  $8 
In other words, when we INPUT  a = 3, n = 5 and b = 1 , the OUTPUT is  8

Now we'll test each answer choice by plugging in  a = 3, n = 5 and b = 1  to see which one yields an OUTPUT of  8

A. ( 3  –  1 )(  3  +  1  +  5 ) =  18  (no match...ELIMINATE)
B.  3  –  1  =  2  (no match...ELIMINATE)
C.  3 ^2 –  1 ^2 =  8  (a match...KEEP)
D.  5 (  3  –  1 ) =  10  (no match...ELIMINATE)
E. ( 3 )( 5 ) + ( 1 )( 5 ) – ( 3 )( 5 ) =  5  (no match...ELIMINATE)

Answer:  C

Cheers, 
Brent

CounterSniper · Answer

total earned for n+a stories =a + a(a+b)
total earned for n+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
 =(a+b)(a-b) =a^2-b^2

GMATinsight · Answer

Money earned by a writer who submits n + a stories in a month

a*n + (a+b)*a

Money earned by a writer who submits n + b stories in a month

a*n + (a+b)*b

Difference in their earnings =   -   = (a+b)(a-b) = a^2 - b^2

Answer: option C

ScottTargetTestPrep · Answer

We will calculate the earnings of the writers separately. 
 
The writer who writes n + a stories:
 
For the first n stories, the writer makes a dollars each, earning na dollars in total. For the remaining (n + a) - n = a stories, the writer makes a + b dollars each, earning a(a + b) dollars in total. Thus, for the n + a stories, this writer makes na + a(a + b) dollars.
 
The writer who writes n + b stories:
 
Similar to the previous case, this writer makes na dollars for the first n stories. For the remaining (n + b) - n = b stories, which earn a + b dollars each, this writer makes b(a + b) dollars. In total, the writer makes na + b(a + b) dollars.
 
Now that we have the earnings of each writer, we simply need to determine the difference between the two. 
 
na + a(a + b) -  
 
na + a(a + b) - na - b(a + b)
 
a(a + b) - b(a + b)
 
(a - b)(a + b) = a^2 - b^2
 
The writer who writes n + a stories makes a^2 - b^2 dollars more than the writer who writes n + b stories.
 
Answer: C

Jainam24 · Answer

My approach to solving is as below:
 We know that for n stories both will earn the same amount. Thus our focus is on the remaining part i.e. a stories of the first writer and b stories of the second writer  
Lets call the writer who sumbits n+a stories as X and the writer who sumbits n+b stories as Y 
Y's earnings: a*(a+b)=a^2+ab
X's earnings: b*(a+b)=b^2+ab
How many more dollars=difference=a^2+ab-b^2-ab=a^2-b^2
Hence option C is the ans

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