I am having difficulties on how to approach this problem:
Would appreciate a little help, and if you have a couple of similar problems I can practice on.
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Thanks in advance
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The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%: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
Hi GMATGuruGMATGuruNY wrote:The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%: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
(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.
Hi Rich[email protected] wrote:Hi lucas211,
This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions.
First, translate the equation:
[(.01x) + (.02y) + (.03z)] / {x + y + z] = .015
.01x + .02y + .03z = .015x + .015y + .015z
Let's multiply everything by 1000 to get rid of the decimals....
10x + 20y + 30z = 15x + 15y + 15z
5y + 15z = 5x
y + 3z = x
Final Answer: A
GMAT assassins aren't born, they're made,
Rich