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Manager  Joined: 02 Dec 2012
Posts: 172
To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 75% (01:52) correct 25% (02:05) wrong based on 2113 sessions

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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
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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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

Shipping separately costs $$1x+2y$$ for the 3 pounds package (x cents for the first pound and y cents for the additional 2 pounds) plus $$1x+4y$$ for the 5 pounds package (x cents for the first pound and y cents for the additional 4 pounds), so total cost of shipping separately is $$(x+2y)+(x+4y)=2x+6y$$;

Shipping together in one 8-pound package costs $$1x+7y$$ (x cents for the first pound and y cents for the additional 7 pounds);

Difference: $$Separately-Together=(2x+6y)-(x+7y)=x-y$$ --> as given that $$x>y$$ then this difference is positive, which makes shipping together cheaper by $$x-y$$ cents.

Hope it's clear.
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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The actual weight of the packages is irrelevant, so long as both weights are positive integers.

Even if the packages weighed 1234 pounds and 5678 pounds, you would still get $$x-y$$ as you are only saving on the first pound.

No need to do any algebra, nor to plug in any numbers.
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Manager  Joined: 05 Dec 2011
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GMAT Date: 09-08-2012
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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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

Back solve and plug in numbers:
x>y
x=4
y=3
A=3lbs, B=5lbs
A=4+3*2=10
B=4+3*4=16 Individually =$26 Together=4+7*3=25 Combined is cheaper and by looking at the answers you can get$1 x-y

Solved in 1min 45 secs so is approachable this way and may seem easier than algebraically, cheers.

Manager  Joined: 25 Jul 2012
Posts: 64
Location: United States
Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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1
For me, picking numbers helped the most and talking myself through this question.

x cents for the first pound and y cents for each additional pound

The rule is x>y

(obviously because usually when someone tries to give you a deal they say "buy this thing and get the 2nd thing for a cheaper amount!")

Pick some easy numbers:
x=10 cents
y=5 cents

Given: two packages that are 3 pounds and 5 pounds
Question: What method (combined or separately) is cheaper and how much is saved?

Sending out separate packages:

3 pound package:
1(first cent per pound x) + 2(additional cents per pound y)
1(10)+2(5) = 20

5 pound package:
1(first cent per pound x)+4(additional cents per pound y)
1(10)+4(5) = 30

30+20 = 50

Sending the two packages combined:

Two packages are: 3 pounds + 5 pounds = 8 pounds

8 pound package:
1(first cent per pound x)+7(additional cents per pound y)
1(10) + 7(5) = 45

What's cheaper and by how much?

We realize that the combined (45) is cheaper than the separate(50) package.

It's cheaper by 5 cents or x-y

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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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DelSingh wrote:
For me, picking numbers helped the most and talking myself through this question.

x cents for the first pound and y cents for each additional pound

The rule is x>y

(obviously because usually when someone tries to give you a deal they say "buy this thing and get the 2nd thing for a cheaper amount!")

Pick some easy numbers:
x=10 cents
y=5 cents

Given: two packages that are 3 pounds and 5 pounds
Question: What method (combined or separately) is cheaper and how much is saved?

Sending out separate packages:

3 pound package:
1(first cent per pound x) + 2(additional cents per pound y)
1(10)+2(5) = 20

5 pound package:
1(first cent per pound x)+4(additional cents per pound y)
1(10)+4(5) = 30

30+20 = 50

Sending the two packages combined:

Two packages are: 3 pounds + 5 pounds = 8 pounds

8 pound package:
1(first cent per pound x)+7(additional cents per pound y)
1(10) + 7(5) = 45

What's cheaper and by how much?

We realize that the combined (45) is cheaper than the separate(50) package.

It's cheaper by 5 cents or x-y

Number plugging is a great technique. Though, it will be good if you understand the logic too. You could save yourself some time and energy.

Cost of first pound - x cents
Cost of every additional pound - y cents
x > y
So first pound is costlier than every subsequent pound.
Two packets - 3 pounds, 5 pounds

If I have 8 pounds, I should send them together so that there is only one expensive 'first pound'. If I send them separately, I will have two expensive 'first pounds'.
After putting 3 pounds in the packet, if I continue to put the 4th pound in the same packet, I save money on it because it is not the expensive 'first pound' which costs x cents but rather the fourth pound which costs only y cents. The rest of the 4 pounds go as the same y cents rate whether they are sent separately or together.
So the only saving when I send them together is x - y on the fourth pound of the combined packet.
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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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

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 individual 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 for the two individual packages (if they are mailed separately) is:

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

Now let's determine the cost of 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.

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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Bunuel wrote:
miweekend 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 seperately 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

If we ship two packages separately it'll cost: $$1x+2y$$ for the 3 pounds package (x cents for the first pound and y cents for the additional 2 pounds) plus $$1x+4y$$ for the 5 pounds package (x cents for the first pound and y cents for the additional 4 pounds), so total cost of shipping separately is $$(x+2y)+(x+4y)=2x+6y$$;

If we ship them together in one 8pound package it'll cost: $$1x+7y$$ (x cents for the first pound and y cents for the additional 7 pounds);

Difference: $$Separately-Together=(2x+6y)-(x+7y)=x-y$$ --> as given that $$x>y$$ then this difference is positive, which makes shipping together cheaper by $$x-y$$ cents.

Hope it helps.

Hi BB - i cannot understand why we subtracted 'Together' from 'Separately' and not 'Separately' from 'Together'. Can you please help
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Posts: 65785
Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Bunuel wrote:
miweekend 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 seperately 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

If we ship two packages separately it'll cost: $$1x+2y$$ for the 3 pounds package (x cents for the first pound and y cents for the additional 2 pounds) plus $$1x+4y$$ for the 5 pounds package (x cents for the first pound and y cents for the additional 4 pounds), so total cost of shipping separately is $$(x+2y)+(x+4y)=2x+6y$$;

If we ship them together in one 8pound package it'll cost: $$1x+7y$$ (x cents for the first pound and y cents for the additional 7 pounds);

Difference: $$Separately-Together=(2x+6y) -(x+7y)=x-y$$ --> as given that $$x>y$$ then this difference is positive, which makes shipping together cheaper by $$x-y$$ cents.

Hope it helps.

Hi BB - i cannot understand why we subtracted 'Together' from 'Separately' and not 'Separately' from 'Together'. Can you please help

First of all, I'm not bb. bb is completely different person. I'm Bunuel.

Next, the question asks which method is cheaper?

Shipping separately costs (2x+6y) = (x + x + 6y) and shipping together costs (x+7y) = (x + y + 6y). Since we are told that x>y, then (x + x + 6y) > (x + y + 6y), thus shipping together is cheaper and this way we are saving (2x+6y) -(x+7y)=x-y.

Hope it's clear.

P.S. This is explained in highlighted part of my post above.
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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miweekend 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 seperately 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

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.

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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Hi All,

This question can be solved in a couple of different ways, but it's perfect for TESTing VALUES.

We're told that X > Y so let's use:

X = 3 cents for the first pound
Y = 2 cents for each additional pound

With these numbers….
A 3-pound package would cost 3 + 2(2) = 7 cents
A 5-pound package would cost 3 + 4(2) = 11 cents

An 8-pound package would cost 3 + 7(2) = 17 cents

So mailing them separately costs 18 cents total, while mailing them combined costs 17 cents total.

We're asked which option would be cheaper and by how much. We know that mailing the packages combined is cheaper, so we just need to plug in X = 3 and Y = 2 into the first 3 answers and confirm that only one of them gives us an answer of 1 cent...

GMAT assassins aren't born, they're made,
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To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Given x>y. Let x =2 and y =1. Hence, First pound costs 2 cents and additional each pound 1 cent.
So, 3-pound package costs = 2 + (3-1)1= 4 cents
5-pound package costs = 2+ (5-1)1 =6 cents
If combined (3+5)=8-pound package costs =2 + (8-1)1=9 cents
So, Mailing combined package save =(4+6)-9= 1 cent.
Ans. A- combined and save 'x-y' cents i.e., 2-1 =1 cent
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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hi.

Case 1 : Seperately --> we get X+2Y and X+4Y .So, the total expenditure for that person is 2X +6Y.

Case 2: Combined --> We get X+7Y .

To find the difference , we need to bring the two equation to common platform .
2X +6Y = X+(X+6Y)
X+7Y = (X+6Y)+Y.

As the condition is X>Y , we can understand that Combined is the best method to send the package. The amount he is going to save is X-Y from the above two equations .
So, combined with the savings of X-Y
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Re: To mail a package, the rate is x cents for the first pound and y cents  [#permalink]

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Top Contributor
1
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 are cheaper.

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)

Cheers,
Brent
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_________________ Re: To mail a package, the rate is x cents for the first pound and y cents   [#permalink] 03 Jun 2020, 10:24

# To mail a package, the rate is x cents for the first pound and y cents  