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A company pays project contractors a rate of "a" dollars for

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A company pays project contractors a rate of "a" dollars for [#permalink] New post 18 Jun 2011, 03:31
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A company pays project contractors a rate of "a" dollars for the first hour and "b" dollars for each additional hour after the first, where a > b.

In a given month, a contractor worked on two different projects that lasted 2 and 4 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?

A) Per month, with savings of $(a + b)
B) Per month, with savings of $(a - b)
C) The two options would cost an equal amount.
D) Per project, with savings of $(a + b)
E) Per project, with savings of $(a - b)
[Reveal] Spoiler: OA
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Re: Interesting P.S question [#permalink] New post 18 Jun 2011, 04:27
Per Project, company will pay as follows:
For 2 hours work = a+b
For 4 hours work = a+3b
Total = 2a+4b

Per Month, company will pay for 6 hours work = a+5b

Total per contract - total per month
2a+4b - (a+5b)
a-b
Since a>b Amount 2a+4b(per contract amount) > a+5b (per project amount) by a-b.

Hence per month payment will be cheaper by a-b .

OA B
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Re: Interesting P.S question [#permalink] New post 18 Jun 2011, 05:04
guygmat wrote:
A company pays project contractors a rate of "a" dollars for the first hour and "b" dollars for each additional hour after the first, where a > b.

In a given month, a contractor worked on two different projects that lasted 2 and 4 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?

A) Per month, with savings of $(a + b)
B) Per month, with savings of $(a - b)
C) The two options would cost an equal amount.
D) Per project, with savings of $(a + b)
E) Per project, with savings of $(a - b)


If per project:
2 hours-> Payment=a+b
4 hours-> Payment=a+3b
Total = a+b+a+3b=2a+4b=a+a+4b-----------------1

Monthly;
6 hours-> Payment=a+5b=a+4b+b-----------------2

Comparing 1 and 2; a+4b gets canceled and we know, a>b; thus 1 is more expensive payment option for the company.

Q: Which arrangement would be cheaper for the company and how much would the company save?
Ans: Monthly payment would be cheaper.
How much is "a" greater than "b"; "a-b", which is saving for the company.

Ans: "B"
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Re: Interesting P.S question [#permalink] New post 18 Jun 2011, 07:16
guygmat wrote:
A company pays project contractors a rate of "a" dollars for the first hour and "b" dollars for each additional hour after the first, where a > b.

In a given month, a contractor worked on two different projects that lasted 2 and 4 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?

A) Per month, with savings of $(a + b)
B) Per month, with savings of $(a - b)
C) The two options would cost an equal amount.
D) Per project, with savings of $(a + b)
E) Per project, with savings of $(a - b)


I will plug in
a= 10, b = 5
if its per month = 6 hrs = 10+5(5hrs) = 35
per project = 2 hrs + 4 hrs = 10+5(1hr) +(10+5(4hrs))= 15+25= 40

so per month is cheaper and saving is 40 - 35 = 5 , which is a-b
hence B
Re: Interesting P.S question   [#permalink] 18 Jun 2011, 07:16
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