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

Answer:A

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.

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)

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

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.

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

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:

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

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

OG Question code: PS16830

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Thank you! Added to the first post.