test 37 #10

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

test 37 #10

by dunkin77 » Sun Apr 29, 2007 5:23 pm

. 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, respactively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved ?
(A) Combined, with a saving of x – y cents
(B) Combined, with a saving of y – x cents
(C) Combined, with a saving of x cents
(D) Separately, with a saving of x – y cents
(E) Separately, with a saving of y cents

Hi,

I though the answer was C) but turned out to be A)..... Can you help?

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Source: Beat The GMAT — Problem Solving | Sun Apr 29, 2007 5:23 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pm; Location: Silicon valley, California; Thanked: 30 times; Followed by:1 members

Re: test 37 #10

by jayhawk2001 » Sun Apr 29, 2007 6:36 pm

dunkin77 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, respactively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved ?
(A) Combined, with a saving of x – y cents
(B) Combined, with a saving of y – x cents
(C) Combined, with a saving of x cents
(D) Separately, with a saving of x – y cents
(E) Separately, with a saving of y cents

Hi,

I though the answer was C) but turned out to be A)..... Can you help?

Cost for 3 pound package = x + 2y
Cost for 5 pound package = x + 4y
Cost for 8 pound package = x + 7y

Now, adding first 2 we get 2x + 6y which is > x+7y since x > y

So, combined is cheaper. Difference in price = 2x + 6y - x - 7y = x - y

Hence A

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Mon Apr 30, 2007 12:35 am

x>y...Hence obviously it makes better sense to combine the two packages
For the first 1 pound charge = x cents
For the rest of the 7 pounds charge = 7y cents
Therefore total = x+7y

If sent seperately
3 pounds charges = x + 2y
5 pound package charges = x + 4y
Therefore total = 2x + 6y

Hence savings = 2x + 6y - x - 7y
= x - y where x>y

Choice A

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon May 20, 2019 6:17 pm

dunkin77 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, respactively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved ?
(A) Combined, with a saving of x ï¿½ y cents
(B) Combined, with a saving of y ï¿½ x cents
(C) Combined, with a saving of x cents
(D) Separately, with a saving of x ï¿½ y cents
(E) Separately, with a saving 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), in which 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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