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Milk Part II

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Milk Part II

by msbelasco » Mon Aug 06, 2012 7:16 pm
I actually have another question that uses milk as the subject.


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 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

y+3z

2y+3z

y+z/4

3y + z

3y + 4.5z

Thanks!
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by Anurag@Gurome » Mon Aug 06, 2012 8:08 pm
msbelasco wrote:I actually have another question that uses milk as the subject.


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 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

y+3z

2y+3z

y+z/4

3y + z

3y + 4.5z

Thanks!
[x * (1/100) + y * (2/100) + z * (3/100)] = (x + y + z) * (1.5/100)
x + 2y + 3z = 1.5x + 1.5y + 1.5z
(1.5x - x) = (2y - 1.5y) + (3z - 1.5z)
0.5x = 0.5y + 1.5z
x = y + 3z

The correct answer is A.
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by GMATGuruNY » Tue Aug 07, 2012 3:00 am
msbelasco wrote:I actually have another question that uses milk as the subject.


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 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5% grade, what is x in terms of y and z?

y+3z

2y+3z

y+z/4

3y + z

3y + 4.5z

Thanks!
Plug in 0 for ONE of the three ingredients in the mixture; then determine the required values of the OTHER TWO ingredients.

Let z=0, with the result that no Z will be in the mixture.

Since 1.5% is halfway between 1% and 2%, combining equal amounts of X (1% milkfat) and of Y (2% milkfat) will yield a mixture that is 1.5% milkfat.
Let x=2 and y=2.

The question asks for the value of x=2. This is our target.
Now we plug y=2 and z=0 into the answers to see which yields our target of 2.

Only answer choice A works:
y+3z = 2 + 3*0 = 2.

The correct answer is A.
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by truplayer256 » Tue Aug 07, 2012 12:21 pm
(0.01(x) + 0.02(y) + 0.03(z))/(x + y + z) = 0.015

0.01(x) + 0.02y + 0.03(z) = 0.015(x) + 0.015(y) + 0.015(z)

0.015(z)+ 0.005(y) = 0.005(x)

x = 200(1.5z/100 + y/200) = 3z + y

Choose A.
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