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## Rate problem

datonman Senior | Next Rank: 100 Posts
Joined
28 May 2014
Posted:
53 messages
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1 members

#### Rate problem

Wed Nov 12, 2014 12:56 pm
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

Mathsbuddy Master | Next Rank: 500 Posts
Joined
08 Nov 2013
Posted:
447 messages
Followed by:
1 members
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Fri Nov 14, 2014 6:33 am
Package A: 3 lb = 1 lb + 2 lb, so cost A = x + 2y
Package B: 5 lb = 1 lb + 4 lb, so cost B = x + 4y

Therefore Separately, cost S = A + B = 2x + 6y

Combined: 8 lb = 1 lb + 7 lb, cost C = x + 7y

As x > y, we could say that x = y + t (where x,y,t > 0)

So, S = 2(y + t) + 6y = 8y + 2t
and C = y + t + 7y = 8y + t

Therefore C < S with difference = t = x - y
So COMBINED is cheaper by (x - y)

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9293 messages
Followed by:
477 members
2867
GMAT Score:
800
Wed Nov 12, 2014 8:27 pm
Hi datonman,

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 numbersâ€¦.
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

_________________
Contact Rich at Rich.C@empowergmat.com

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