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To mail a package, the rate is x cents for the first...

by swerve » Sun Jan 28, 2018 7:02 am

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To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

A. Combined, with a savings of x - y cents
B. Combined, with a savings of y - x cents
C. Combined, with a savings of x cents
D. Separately, with a savings of x - y cents
E. Separately, with a savings of y cents

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by [email protected] » Sun Jan 28, 2018 12:26 pm
Hi swerve,

We're told that to mail a package, the rate is X cents for the first pound and Y cents for each additional pound, where X > Y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. We're asked which method is cheaper and how much money is saved. This question can be solved by TESTing VALUES.

IF... X=3, Y=2, then the cost to ship the two packages would be:
Together = 5 pounds = 1(3) + 4(2) = 11 cents
Separate = 3 pounds = 1(3) + 2(2) = 7 cents and 2 pounds = 1(3) + 1(2) = 5 cents --> total = 12 cents

Thus, when we use X=3 and Y=2, we're looking for an answer that says 'together' and the savings will be 1 cent. There's only one answer that matches...

Final Answer: A

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Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Fri Jul 12, 2019 6:01 pm
swerve wrote:To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

A. Combined, with a savings of x - y cents
B. Combined, with a savings of y - x cents
C. Combined, with a savings of x cents
D. Separately, with a savings of x - y cents
E. Separately, with a savings of y cents
We can solve this problem by first creating expressions for the given information. We know that the rate is x cents for the first pound and y cents for each pound after the first. This can be written as:

x + y(t - 1), where t is the number of pounds of the package. Let's first determine the cost of mailing the two packages separately. We start with the 3-pound package:

x + y(3 - 1)

x + y(2)

x + 2y

Next we can determine the cost of mailing the 5-pound package:

x + y(5 - 1)

x + y(4)

x + 4y

Thus, the total cost of mailing the two individual packages separately is:

x + 2y + x + 4y = 2x + 6y

Now let's determine the cost of mailing the two packages if they are combined as one package. The combined package would weigh 8 pounds, and its shipping cost would be:

x + y(8 - 1)

x + y(7)

x + 7y

We are given that x > y, and so we see that mailing the packages individually is more costly than mailing them as one combined package. We now need to determine the difference in cost between the two mailing options:

2x + 6y - (x + 7y)

2x + 6y - x - 7y

x - y

Thus, the savings is (x - y) cents when the packages are shipped as one combined package.

Answer: A

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Re: To mail a package, the rate is x cents for the first...

by Brent@GMATPrepNow » Tue May 12, 2020 9:02 am
swerve wrote: ↑
Sun Jan 28, 2018 7:02 am
 To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

A. Combined, with a savings of x - y cents
B. Combined, with a savings of y - x cents
C. Combined, with a savings of x cents
D. Separately, with a savings of x - y cents
E. Separately, with a savings of y cents
To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y.
Cost of 3-pound package
We pay x cents for the first pound, and then y cents for each of the 2 additional pounds.
Total cost = x + y + y = x + 2y

Cost of 5-pound package
We pay x cents for the first pound, and then y cents for each of the 4 additional pounds.
Total cost = x + y + y + y + y = x + 4y

TOTAL cost = (x + 2y) + (x + 4y) = 2x + 6y
-------------------------

Now let's see what happens when we COMBINE the two packages into an 8-pound package
Cost of 8-pound package
We pay x cents for the first pound, and then y cents for each of the 2 additional pounds.
Total cost = x + y + y + y + y + y + y + y = x + 7y
-------------------------

Which method is cheaper, and how much money is saved?
We must determine which value is less: 2x + 6y or x + 7y
We're told that x > y. So let's use this information.

Take: 2x + 6y and rewrite it as (x + 6y) + x
Take: x + 7y and rewrite it as (x + 6y) + y
Both quantities have (x + 6y) in common. So those values are equal.
Since x > y, we know that (x + 6y) + y is less than (x + 6y) + x
In other words, x + 7y is less than 2x + 6y
In other words, the packages COMBINED is the cheaper option.

Determine the savings, we'll subtract the cheaper cost from the more expensive cost.
In other words: savings = (2x + 6y) - (x + 7y) = x - y (cents)

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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