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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] New post 17 Dec 2012, 05:37
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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 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
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 17 Dec 2012, 05:40
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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 8-pound package costs 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.

Answer: A.

Hope it's clear.
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 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 x-y

Solved in 1min 45 secs so is approachable this way and may seem easier than algebraically, cheers.

Answer:A
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 13 Jan 2013, 22:54
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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 x-y as you are only saving on the first pound.

No need to do any algebra, nor to plug in any numbers.
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 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 x-y

Answer is A.
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 11 Mar 2013, 19:52
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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 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)
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 10 Jan 2014, 01:38
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 8-pound package costs 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.

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
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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 10 Jan 2014, 02:19
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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 8-pound package costs 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.

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.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: To mail a package, the rate is x cents for the first pound [#permalink] New post 12 Jan 2014, 19:57
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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.
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Re: To mail a package, the rate is x cents for the first pound   [#permalink] 12 Jan 2014, 19:57
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