Akansha wrote:Three grades of milk: 1%, 2%, and 3% fat by volume. X gallons of 1%, y gallons
of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. 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
OA is A
X=1% milkfat.
Y=2% milkfat.
If equal amounts of X and Y are combined, the percentage of milkfat in the resulting mixture will be the average of the two percentages above:
(1% + 2%)/2 = 1.5%.
To illustrate:
Let X = 200 liters and Y = 200 liters.
Milkfat in X = .01*200 = 2.
Milkfat in Y = .02*200 = 4.
Total milkfat = 2+4 = 6.
Total volume = 200+200 = 400.
Percentage of milkfat = 6/400 = (1.5)/100 = 1.5%.
Thus, the correct answer must work when equal amounts of X and Y are combined.
Plug in X=2, Y=2, Z=0.
This represents a mixture consisting of equal amounts of X and Y, with no Z.
Since equal amounts of X and Y are being combined, the resulting mixture will be 1.5% milkfat, as illustrated above.
The question asks for the value of X.
Given the values above, 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.
Last edited by GMATGuruNY on Fri Jun 17, 2011 10:30 am, edited 1 time in total.
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