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

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Carcass
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Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   25 May 2021, 20:03
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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

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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C
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Re: Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   26 May 2021, 00:00
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Writer with \(n+a\) stories a month

Money earned = \(na + a (a+b)\)

Writer with \(n+b\) stories a month

Money earned = \(na + b (a+b)\)

Difference = \(na + a (a+b)\) - \(na + b (a+b)\)

= \((a+b)(a-b)\)

= \(a^2 – b^2\)

Answer C
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void
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Re: Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   29 May 2021, 07:57
another merhod, given solution is bit complex for me.
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Re: Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   29 May 2021, 08:19
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Sir,

Where did you get stuck in the calculation? You can plug in numbers for \(n, a, b\)

void wrote:
another merhod, given solution is bit complex for me.
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Re: Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   29 May 2021, 08:21
rx10 wrote:
Sir,

Where did you get stuck in the calculation? You can plug in numbers for \(n, a, b\)

void wrote:
another merhod, given solution is bit complex for me.

thank s for telling :D
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Each writer for the local newspaper is paid as follows: a dollars for [#permalink] New post   30 May 2021, 01:21
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void wrote:
another merhod, given solution is bit complex for me.


Let,
a = 10
b = 5
n = 10

So, a + b = 15

For (n + a) stories he earns = n(n) + (a + b)a = 10(10) + 15(10) = 250
For (n + b) stories he earns = n(n) + (a + b)b = 10(10) + 15(5) = 175
Difference = 250 - 175 = 75

Let us check the option choices;

A. (a – b)( a + b + n) = (10 - 5)(10 + 5 + 10) = 125

B. a – b = 10 - 5 = 5

C. \(a^2 – b^2 = 10^2 - 5^2\) = 100 - 25 = 75

D. n( a – b) = 10(10 - 5) = 50

E. an + bn – an = bn = 5(10) = 50

Hence, option C
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