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

Question

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

PS16830

Bunuel · Accepted Answer

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.

Answer: A.

Hope it's clear.

SergeyOrshanskiy · Answer

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.

geno5 · Answer

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.

Answer:A

DelSingh · Answer

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

Answer is A.

KarishmaB · Answer

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. 
Answer (A)

JeffTargetTestPrep · Answer

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.

Answer A

Adityam · Answer

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

Bunuel · Answer

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.

ScottTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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...

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

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)

Answer: A

Cheers,
Brent

bagad.07 · Answer

OG Question code: PS16830

Bunuel · Answer

________________________________
Thank you! Added to the first post.

nguyenpham1309 · Answer

When they say x (for the 1st pound) > y (for each additional pound), they have a reason to say so. As many times as I have to include "the cost of first pound" by choosing to separate the package, the cost will be higher than combining them as one package (with only 1 time of including the cost of the 1st pound)

-> Eliminate D, E with a strong belief that combining the package will be the cheaper solution (and I feel happy that this is a natural logic and I do not overthink a weird situation when separating is cheaper than combining the package)

To find how much money we can save, either recognize the difference in the two methods, or plug in any numbers; whatever works well with us.

jparedes12 · Answer

I did everything right up until the subtraction of the two shipping costs.

I subtracted 2x+6y from x+7y, so I erroneously chose answer B. Can you please explain why you knew we needed to subtract x+7y from 2x+6y and not the other way around?

Thank you.

Bunuel · Answer

Shipping separately costs (2x + 6y) = (x + x + 6y), and shipping together costs (x + 7y) = (x + y + 6y). Since we are told that x > y, (x + x + 6y) > (x + y + 6y). Thus, shipping together is cheaper, and the savings are (2x + 6y) – (x + 7y) = x – y.

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

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

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