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

by **Guest** 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

by **RonPurewal** Wed Jul 02, 2008 3:38 am

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!

by **Guest** Sat Jul 12, 2008 2:40 am

This is from GMAT Prep software, practise test #2, question 16.

by **RonPurewal** Sat Jul 12, 2008 6:00 am

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

by **YLP1YTO** 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'

by **esledge** Mon Sep 15, 2008 1:51 pm

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.