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

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, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now 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.

Algebraically:

(1% of X) + (2% of Y) + (3% of Z) must be equal to (1.5% of X+Y+Z).
Thus:
x + 2y + 3x = 1.5(x + y + z)
10x + 20y + 30z = 15x + 15y + 15z.

Since the question stem asks for the value of x, solve for x:
20y + 30z = 5x + 15y + 15z
5y + 15z = 5x
y + 3z = x.

The correct answer is A.

Thank you for detailed explanation.
I formed a correct equation.
But such questions are good and easy to solve by plugging so I tried doing it but could not.
@Mitch Hunt : How you inferred that x=y, I could not understand . Could you please elaborate?

Hi Rich

My understanding was completely the other way.
Which type of questions are the good target to solve by plugging?
As per GMATTutor, questions with in terms are a good target to solve by plugging.

eitijan wrote:Hi Rich

My understanding was completely the other way.
Which type of questions are the good target to solve by plugging?
As per GMATTutor, questions with in terms are a good target to solve by plugging.

Usually the best candidate is a word problem in which all the answer choices are variables. In those cases, you can usually pick values for each letter, then check the answers to see which matches your number.