BTGModeratorVI wrote: ↑

Tue May 12, 2020 2:18 pm

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

Answer: C

Solution:

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) = na + a^2 + ab 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) = na + ab + b^2 dollars.

Now that we have the earnings of each writer, we simply need to determine the difference between the two.

na + a^2 + ab - (na + ab + b^2)

na + a^2 + ab - na - ab - b^2

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

BTGModeratorVI wrote: ↑

Tue May 12, 2020 2:18 pm

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

Answer: C
Source: Kaplan

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
Scott (above) has 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: [spoiler=]C[/spoiler]

Cheers,
Brent