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Three grades of milk are 1 percent, 2 percent and 3 percent

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Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] New post 16 Jun 2006, 09:17
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79% (01:52) correct 21% (02:17) wrong based on 47 sessions
Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: three-grades-of-milk-are-1-percent-2-percent-and-3-percent-fat-126122.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Oct 2012, 03:57, edited 2 times in total.
Renamed the topic, edited the question and moved to PS forum.
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 [#permalink] New post 16 Jun 2006, 10:19
X + 2Y + 3Z = 1.5(X + Y + Z)

X + 2Y + 3Z = 1.5X + 1.5Y + 1.5 Z

Add and subtract the common terms,

0.5 X = 0.5Y + 1.5Z

Divide by 0.5,

X = Y + 3 Z
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 [#permalink] New post 16 Jun 2006, 11:40
Easy one.

Total milk by adding x gallons of grade 1 , y gallons of grade 2 and z gallons of grade 3 = x/100 + 2y/100 + 3y/100

Total solution is 1.5 milk. So milk in the total solution = (x+y+z)*1.5/100

These two quantities are equal.
So x + 2y + 3z = 1.5(x+y+z). Solving this we get x = y+3z
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 [#permalink] New post 16 Jun 2006, 13:19
a. y+3z

Given that (x+y+z) is 1.5% fat, then

1.5(x+y+z) = x+2y+3z

=> 3x+3y+3z = 2x+4y+6z
=> x = y+3z
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Re: Help needed with GMATPrep question [#permalink] New post 16 Oct 2012, 21:38
Should the answer be x = y + 3z. Based on the given information, the following equation could be dervied: 1% * x + 2% * y + 3% * z = 1.5% * (x+y+z) [equation*]. Then use algebra to figure out 0.5%*x = 0.5%*y + 1.5%*z. Thus, x = y + 3z.

Let me ask you a different question based on the given information and the equation* above. If we only mix x/2 gallons of 1% grade with y/2 gallons of 2% grade and z/2 gallons of 3% grade, what would be the new mixture in terms of x and y?
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Re: Help needed with GMATPrep question [#permalink] New post 17 Oct 2012, 03:53
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Re: Help needed with GMATPrep question   [#permalink] 17 Oct 2012, 03:53
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