GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 03:46 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  To mail a package, the rate is x cents for the first pound

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 29 Jun 2011
Posts: 20
To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

1
16 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:46) correct 26% (02:00) wrong based on 375 sessions

HideShow timer Statistics

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..

Originally posted by miweekend on 25 Aug 2011, 09:02.
Last edited by Bunuel on 27 Jan 2012, 06:44, edited 3 times in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58313
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

5
3
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.
_________________
General Discussion
Manager  Joined: 19 Jul 2011
Posts: 89
Concentration: Finance, Economics
Schools: Duke '15
GPA: 3.9
Re: To mail a package  [#permalink]

Show Tags

4
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
_________________
Show Thanks to fellow members with Kudos its shows your appreciation and its free
Manager  Joined: 19 Jul 2011
Posts: 89
Concentration: Finance, Economics
Schools: Duke '15
GPA: 3.9
Re: To mail a package  [#permalink]

Show Tags

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
_________________
Show Thanks to fellow members with Kudos its shows your appreciation and its free
Director  Joined: 01 Feb 2011
Posts: 552
Re: To mail a package  [#permalink]

Show Tags

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

Manager  Joined: 05 Oct 2011
Posts: 150
Re: To mail a package  [#permalink]

Show Tags

2
2
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
Manager  Joined: 05 Mar 2011
Posts: 96
Re: To mail a package  [#permalink]

Show Tags

I used numbers for all the variables and got the anwer.I did not use algebra.
Intern  Joined: 29 Jun 2011
Posts: 20
Re: To mail a package  [#permalink]

Show Tags

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!!
Manager  Joined: 21 Oct 2013
Posts: 178
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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.
Intern  B
Joined: 07 Jul 2012
Posts: 29
Location: United States (IL)
Concentration: Finance, Strategy
WE: Information Technology (Consulting)
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58313
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

2
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.
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director  G
Joined: 02 Sep 2016
Posts: 649
To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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

Please correct the answer if you find an error.

It does not matter if we subtract separately from together or together from separately.

Let x=3 and y= 2 (x>y)

Separately -together= 1 (this shows that S>T and we will have a saving of 1 )

Together- Separately= -1 (this still shows that S>T and we will have a saving of 1 if we go with the together option and a loss of 1 if we go with the other option).

Therefore as the question is asking which method is cheaper and how much money is saved, we will write x-y= 3-2=1 (positive value) as saving cannot be negative.

If the question asked which method is costlier and what's the loss, then we know the answer and the loss would be 2-3= -1 (negative value as its a loss).
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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,
Rich
_________________
VP  D
Joined: 09 Mar 2016
Posts: 1232
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

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

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..

Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2
Board of Directors V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3584
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

1
dave13 wrote:
Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2

Hey dave13 ,

The highlighted text is wrong.

When you combine both, total weight = 8 pounds.

So, cost will be 2 for the 1st and 7 for the rest = 9

Thus difference between the two = 10-9=1

This is equal to x - y. Hence , A is the answer.

Does that make sense?
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

1
dave13 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

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..

Guys ,
what is the difference between answers A and C ? I chose C

I did following

let x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +6 = 8

now 10-8 = 2

Hello dave13,

I will give both the precise and the "start with easy number" approach here.

Approach #1 - Precise:

separate : (1) 3 pound package -> 1 + 2 pounds = x + 2y cents
(2) 5 pound package -> 1 + 4 pounds = x + 4y cents

total = ( x + 2y ) + ( x + 4y ) = 2x + 6y cents

combined : It will be one ( 3 + 5) = 8 pound package.

so ( 1 + 7 pound ) = x + 7y cents

The difference between the two is: combined - separate = ( x + 7y) - (2x + 6y) = y - x

since we know x > y .... y - x will be negative.

hence sending in combined is cheaper and it is cheaper by x - y cents ( negative of y - x ) Option (A)

Approach #2 - Start-with-easy-numbers: This is usually the faster method and is used by you. et x be 2 and y be 1

separately

3 pound package 2 +2 = 4
5 pound package 2 +4 = 6

total 10

combined 3 and 5 pound packages

2 +7** = 9

now 10-9 = 1 ... which is x - y ( 2 - 1 = 1)

Hope that explains everything...

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Non-Human User Joined: 09 Sep 2013
Posts: 13088
Re: To mail a package, the rate is x cents for the first pound  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: To mail a package, the rate is x cents for the first pound   [#permalink] 14 Jun 2019, 07:33
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  