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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
