Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 172

To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
17 Dec 2012, 05:37
Question Stats:
75% (01:52) correct 25% (02:05) wrong based on 2113 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: 65785

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
17 Dec 2012, 05:40
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 and y cents
[#permalink]
Show Tags
13 Jan 2013, 22:54
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: 71
Location: Canada
Concentration: Accounting, Finance
GMAT Date: 09082012
GPA: 3

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
09 Jan 2013, 20:22
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



Manager
Joined: 25 Jul 2012
Posts: 64
Location: United States

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
11 Mar 2013, 17:06
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.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10784
Location: Pune, India

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
11 Mar 2013, 19:52
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 >



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
16 Jun 2016, 05:09
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
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Intern
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 and y cents
[#permalink]
Show Tags
14 May 2017, 08:15
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 xy cents B. Combined, with a saving of yx cents C. Combined, with a saving of x cents D. Separately, with a saving of xy 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: \(SeparatelyTogether=(2x+6y)(x+7y)=xy\) > as given that \(x>y\) then this difference is positive, which makes shipping together cheaper by \(xy\) cents. Answer: A. Hope it helps. Hi BB  i cannot understand why we subtracted 'Together' from 'Separately' and not 'Separately' from 'Together'. Can you please help



Math Expert
Joined: 02 Sep 2009
Posts: 65785

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
14 May 2017, 08:57
Adityam wrote: 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 xy cents B. Combined, with a saving of yx cents C. Combined, with a saving of x cents D. Separately, with a saving of xy 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: \(SeparatelyTogether=(2x+6y) (x+7y)=xy\) > as given that \(x>y\) then this difference is positive, which makes shipping together cheaper by \(xy\) cents.Answer: A. Hope it 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)=xy. Hope it's clear. P.S. This is explained in highlighted part of my post above.
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11394
Location: United States (CA)

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
18 May 2017, 19:03
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 xy cents B. Combined, with a saving of yx cents C. Combined, with a saving of x cents D. Separately, with a saving of xy 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 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 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
_________________
★
★
★
★
★
250 REVIEWS
5STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
01 Mar 2018, 12:34
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 3pound package would cost 3 + 2(2) = 7 cents A 5pound package would cost 3 + 4(2) = 11 cents An 8pound 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 05 Sep 2016
Posts: 24
Location: Bangladesh
Concentration: Accounting, Finance
GPA: 3.98
WE: Education (Education)

To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
13 Apr 2020, 10:08
Given x>y. Let x =2 and y =1. Hence, First pound costs 2 cents and additional each pound 1 cent. So, 3pound package costs = 2 + (31)1= 4 cents 5pound package costs = 2+ (51)1 =6 cents If combined (3+5)=8pound package costs =2 + (81)1=9 cents So, Mailing combined package save =(4+6)9= 1 cent. Ans. A combined and save 'xy' cents i.e., 21 =1 cent
_________________



Intern
Joined: 10 Apr 2019
Posts: 10
Location: India
GPA: 3.7

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
13 Apr 2020, 10:57
hi.
Case 1 : Seperately > we get X+2Y and X+4Y .So, the total expenditure for that person is 2X +6Y.
Case 2: Combined > We get X+7Y .
To find the difference , we need to bring the two equation to common platform . 2X +6Y = X+(X+6Y) X+7Y = (X+6Y)+Y.
As the condition is X>Y , we can understand that Combined is the best method to send the package. The amount he is going to save is XY from the above two equations . So, combined with the savings of XY



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4987
Location: Canada

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
12 May 2020, 08:59
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 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 3pound packageWe pay x cents for the first pound, and then y cents for each of the 2 additional pounds. Total cost = x + y + y = x + 2yCost of 5pound packageWe 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 + 4yTOTAL cost = ( x + 2y) + ( x + 4y) = 2x + 6y Now let's see what happens when we COMBINE the two packages into an 8pound package Cost of 8pound packageWe 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 + 7yWe're told that x > y. So let's use this information. Take: 2x + 6y and rewrite it as (x + 6y) + xTake: x + 7y and rewrite it as (x + 6y) + yBoth 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) + xIn other words, x + 7y is less than 2x + 6yIn 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
_________________
If you enjoy my solutions, you'll love my GMAT prep course.



NonHuman User
Joined: 09 Sep 2013
Posts: 15595

Re: To mail a package, the rate is x cents for the first pound and y cents
[#permalink]
Show Tags
03 Jun 2020, 10:24
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 and y cents
[#permalink]
03 Jun 2020, 10:24




