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by alex.gellatly » Mon Apr 16, 2012 12:15 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 percent 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 ?

(A) y + 3z
(B) (y + z) / (4)
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z

Thanks in advanced
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by killer1387 » Mon Apr 16, 2012 12:31 am
alex.gellatly wrote: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 percent grade, what is x in terms of y and z ?

(A) y + 3z
(B) (y + z) / (4)
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z

Thanks in advanced
(x+2y+3z)/(x+y+z)= 1.5=3/2
solving
x= y+3z

hence A
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by GMATGuruNY » Mon Apr 16, 2012 2:48 am
alex.gellatly wrote: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 percent grade, what is x in terms of y and z ?

(A) y + 3z
(B) (y + z) / (4)
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z

Thanks in advanced
An alternate approach is to plug in values.
To make the math easy, let z=0, implying that the mixture will include NONE of the 3% grade milk.

The desired percentage (1.5%) is equal to the AVERAGE of X (1%) and Y (2%).
Thus, combining equal amounts of X and Y will yield a mixture that is 1.5% milkfat.

Let x=2, y=2 and z=0.
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 Anurag@Gurome » Mon Apr 16, 2012 2:52 am
alex.gellatly wrote: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 percent grade, what is x in terms of y and z ?

(A) y + 3z
(B) (y + z) / (4)
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z

Thanks in advanced
The concentration of milk in the mixture would be 1% * x + 2% * y + 3% * z, which is also equal to 1.5% * (x + y + z)
So, x + 2y + 3z = 1.5x + 1.5y + 1.5z
0.5y + 1.5z = 0.5x
y + 3z = x

The correct answer is A.
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