May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 174

To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
17 Dec 2012, 06:37
Question Stats:
76% (01:54) correct 24% (02:04) wrong based on 1388 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 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
17 Dec 2012, 06:40
Walkabout 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 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 8pound package costs \(1x+7y\) (x cents for the first pound and y cents for the additional 7 pounds); Difference: \(SeparatelyTogether=(2x+6y)(x+7y)=xy\) > as given that \(x>y\) then this difference is positive, which makes shipping together cheaper by \(xy\) cents. Answer: A. Hope it's clear.
_________________




Manager
Joined: 12 Jan 2013
Posts: 56
Location: United States (NY)
GPA: 3.89

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
13 Jan 2013, 23:54
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 \(xy\) as you are only saving on the first pound. No need to do any algebra, nor to plug in any numbers.
_________________
Sergey Orshanskiy, Ph.D. I tutor in NYC: http://www.wyzant.com/Tutors/NY/NewYork/7948121/#ref=1RKFOZ




Manager
Joined: 05 Dec 2011
Posts: 76
Location: Canada
Concentration: Accounting, Finance
GMAT Date: 09082012
GPA: 3

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
09 Jan 2013, 21:22
Walkabout 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 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 xy Solved in 1min 45 secs so is approachable this way and may seem easier than algebraically, cheers. Answer:A
_________________
Thanks = +1 Kudos Study from reliable sources!! Thursdays with Ron: http://www.manhattangmat.com/thursdayswithron.cfmGmat Prep Questions: CR http://gmatclub.com/forum/gmatprepsc105446.html SC http://gmatclub.com/forum/gmatprepsc105446.html



Manager
Joined: 25 Jul 2012
Posts: 66
Location: United States

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
11 Mar 2013, 18:06
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 xy Answer is A.
_________________
If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9238
Location: Pune, India

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
11 Mar 2013, 20:52
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 xy
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)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 12 Jan 2013
Posts: 145

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
10 Jan 2014, 02:38
Bunuel wrote: Walkabout 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 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 8pound package costs \(1x+7y\) (x cents for the first pound and y cents for the additional 7 pounds); Difference: \(SeparatelyTogether=(2x+6y)(x+7y)=xy\) > as given that \(x>y\) then this difference is positive, which makes shipping together cheaper by \(xy\) cents. Answer: A. Hope it's clear. I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y)  (2x+6y) = y  x\), so I went with B My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately  Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together  Separately? Thank you



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
10 Jan 2014, 03:19
aeglorre wrote: Bunuel wrote: Walkabout 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 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 8pound package costs \(1x+7y\) (x cents for the first pound and y cents for the additional 7 pounds); Difference: \(SeparatelyTogether=(2x+6y)(x+7y)=xy\) > as given that \(x>y\) then this difference is positive, which makes shipping together cheaper by \(xy\) cents. Answer: A. Hope it's clear. I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y)  (2x+6y) = y  x\), so I went with B My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately  Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together  Separately? Thank you Please read the red part in the solution you are quoting. Hope it helps.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9238
Location: Pune, India

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
12 Jan 2014, 20:57
aeglorre wrote:
I came to this conclusion: \((2x+6y) = (x+7y)\), but obviously nothing tells us that posting in one 8 pound package is EQUAL to posting separately, actually the question even implies there's a difference.. But anyways, my calculations with the above in mind ended up in: \((x+7y)  (2x+6y) = y  x\), so I went with B
My question is: For questions like these, what is it that makes you "know" that the difference we are supposed to calculate is Separately  Together? That subtraction is not very immediately intuitive to me, why would we for instance not go the other way: Together  Separately?
Thank you
I would like to further point out here that since you are given that x > y, when you get the answer as y  x, you should realize that this will be negative. But money saved must be positive so Separately must be higher than Together and you are required to find Separately  Together. Also, Separately = 2x + 6y Together = x + 7y Separately has an x instead of a y and since x is higher, Separately is higher than Together.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 10 Mar 2013
Posts: 495
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
30 May 2015, 06:00
Together: x + 7y Separately: x + 2y + y + 4y = 2x + 6y to send the package together will be cheaper because x>y (If Separately we have one x more and one y less, but we know that x>y) > 2x+6y  x 7y = xy (A)
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
16 Jun 2016, 06:09
Walkabout 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 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 3pound package: x + y(3 – 1) x + y(2) x + 2y Next we can determine the cost of mailing the 5pound 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
_________________
5star rated online GMAT quant self study course 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.



VP
Joined: 09 Mar 2016
Posts: 1283

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
14 Apr 2018, 04:00
Walkabout 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 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 Can someone give me an example in which C would be correct answer and not A ? just confused choosing between A and C



NonHuman User
Joined: 09 Sep 2013
Posts: 11010

Re: To mail a package, the rate is x cents for the first pound
[#permalink]
Show Tags
12 May 2019, 13:01
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]
12 May 2019, 13:01






