To mail a package, the rate is x cents for the first pound : GMAT Problem Solving (PS)
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# To mail a package, the rate is x cents for the first pound

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

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25 Aug 2011, 08:02
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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 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

hi there.. could anyone pls help to explain what does it mean by ".......saving of x-y cents, y-x cents" pls?I have difficult understand it..
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jan 2012, 05:44, edited 3 times in total.
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Re: To mail a package [#permalink]

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25 Aug 2011, 08:13
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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.
This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents

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?

Separately cost:
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y

Combined cost:
8 pounds: x+7y

So we are saving:
(2X+6y) - x+7y
= x-y cents

Combined is cheaper as we maximise y and minimize x.
1) Combined, with a saving of x-y cents
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Re: To mail a package [#permalink]

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25 Aug 2011, 08:42
miweekend wrote:
nammers wrote:
To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x>y.
This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents

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?

Separately cost:
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y

Combined cost:
8 pounds: x+7y

So we are saving:
(2X+6y) - x+7y
= x-y cents

Combined is cheaper as we maximise y and minimize x.
1) Combined, with a saving of x-y cents

thank you nammer.

I saw you are using (Separate Cost) - (Combined Cost).
So it is (2x+6y) - (x+7y) = 2x + 6y - x - 7y = x-y <--- it makes sense here to conclude answer is A.

However, if we try using (Combined Cost) - (Separate Cost). isn't it ended up as Answer (B)

(x+7y) - (2x+6y) = x + 7y - 2x - 6y = -x+y which is a y-x

-> Combined, with a saving of y-x cents

I'm stuck here..

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

It is the other way round as we are calculating saving
You save
2x+6y
And spend
x+7y
Therefore you save in total
2x+6y -(x +7y) = x-y
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Re: To mail a package [#permalink]

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25 Aug 2011, 15:30
another way is you can think this as follows

2x+6y vs x+7y

= x+6y+x vs x+6y+y

now we can clearly see x on the LHS and y on the right hand side is the only difference.

also its mentioned in the question that x>y

so the LHS must be greater than RHS. (or RHS < LHS)

In other words x+7y is cheaper than 2x+6y. Find out the difference by subtracting the smaller from the larger.

so combined is cheaper by 2x+6y-(x+7y) = x-y

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Re: To mail a package [#permalink]

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21 Nov 2011, 12:18
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Another way of solving this problem is using numbers in place of x and y
choose $$x = 3$$ and $$y = 2$$ as $$x>y$$

Shipping separately :
3 lb Package: $$3 + 2 *2 = 7$$
5 lb package: $$3 + 4*2 = 11$$
Total cost: 18 lbs

Shipping combined:
Cost = 3 + 7 * 2 = 17 lbs

So shipping combined is cheaper it is cheaper by 1cent(i.e 3-2 or x-y)

Looking at the answer choices - A
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Re: To mail a package [#permalink]

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30 Nov 2011, 22:32
I used numbers for all the variables and got the anwer.I did not use algebra.
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Re: To mail a package [#permalink]

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27 Jan 2012, 05:30
Spidy001 wrote:
another way is you can think this as follows

2x+6y vs x+7y

= x+6y+x vs x+6y+y

now we can clearly see x on the LHS and y on the right hand side is the only difference.

also its mentioned in the question that x>y

so the LHS must be greater than RHS. (or RHS < LHS)

In other words x+7y is cheaper than 2x+6y. Find out the difference by subtracting the smaller from the larger.

so combined is cheaper by 2x+6y-(x+7y) = x-y

thank you! Finally I got it now!!
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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27 Jan 2012, 05:55
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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

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

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03 Oct 2013, 07:25
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Re: To mail a package, the rate is x cents for the first pound [#permalink]

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16 Jun 2014, 02:29
Easiest way to do it imho is picking numbers for x and y. E.g. pick 2 $for x and 1$ for y. Then you see that

separately: first package : 3 pounds, hence x +y +y +y = 4 $second package: 5 pounds, hence x +y +y +y +y = 6$
totals 10 $combined: 8 pounds: x +y +y +y +y +y +y +y = 9$

Now you see that you save 1 $if you send the package combined. And 1$ equals 2$(x)-1$(y), hence it's A.
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25 Jun 2015, 09:26
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30 Jul 2016, 15:00
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