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Three Grades of milk are 1 percent, 2 percent and 3 percent

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Guest
 Post subject: Three Grades of milk are 1 percent, 2 percent and 3 percent
 Post Posted: Mon Jun 30, 2008 12:05 am 
Three Grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z

1. y+ 3z
2. y+z/4
3. 2y+3z
4. 3y + z
5. 3y + 4.5z
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RonPurewal
 Post subject:
 Post Posted: Wed Jul 02, 2008 3:38 am 
Offline
ManhattanGMAT Staff


Posts: 7146
please post the source of this problem (per forum rules). if the source isn't posted within the next few days, we'll have to remove the thread.

this rule has always been important, but i'm sure you can understand its importance even more now that this whole scoretop scandal has broken.

sources! please! thank you!
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Guest
 Post subject:
 Post Posted: Sat Jul 12, 2008 2:40 am 
This is from GMAT Prep software, practise test #2, question 16.
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RonPurewal
 Post subject:
 Post Posted: Sat Jul 12, 2008 6:00 am 
Offline
ManhattanGMAT Staff


Posts: 7146
the easiest way to do this is to pick numbers. in fact, you can pick numbers on ALL problems whose question prompts feature the words "in terms of", because such problems, by definition, work with any given values of those variables.

let's pick easy numbers: y = 2, z = 4. (these aren't totally random. the choice for y is essentially random, but z has been deliberately chosen so that #2 and #5 will be integers.)

then we have:
x gallons of 1% = 0.01x gallons of fat
2 gallons of 2% = 0.02(2) = 0.04 gallons of fat
4 gallons of 3% = 0.03(4) = 0.12 gallons of fat
total fat = 0.01x + 0.04 + 0.12 = (0.01x + 0.16) gallons
total volume = x + 2 + 4 = (x + 6) gallons

so:
(0.01x + 0.16)/(x + 6) = 0.015
multiply by 100 ----- (x + 16)/(x + 6) = 1.5
multiply through by (x + 6) ----- x + 16 = 1.5x + 9
7 = 0.5x
14 = x

check the answer choices with y = 2, z = 4:
a: 14
b: 3
c: 16
d: 10
e: 24

a wins
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YLP1YTO
 Post subject:
 Post Posted: Tue Jul 15, 2008 5:45 pm 
There is another way I did it is,

1x+2y+3z = 1.5(x+y+z)
x+2y+3z = 1.5x+1.5y+1.5z
1.5x-x = 2y-1.5y+3z-1.5z
0.5x=0.5y+1.5z (divide by 0.5 on all sides)
x=y+3z

So answer is 'A'
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esledge
 Post subject:
 Post Posted: Mon Sep 15, 2008 1:51 pm 
Offline
ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
That method works, too. Thanks YLP1YTO. Also, I am going to move this thread to the GMATPrep folder. Everyone please read the posting guidelines and put things in the appropriate folders.

_________________
Emily Sledge
Instructor
ManhattanGMAT
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