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
