3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
An alternate approach:
The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%:
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.
Let x=2 liters, y=2 liters, and z=0 liters, implying that the mixture will composed entirely of equal amounts of x and y (2 liters each).
The question stem 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
A works:
y + 3z = 2 + 3*0 = 2.
The correct answer is
A.
Last edited by GMATGuruNY on Wed Jul 10, 2013 1:12 am, edited 1 time in total.
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