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47) Three grades of milk: 1%, 2%, and 3% fat by volume. X ga

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by varun289 » Sun May 05, 2013 8:33 pm
47) 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 + 4z
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by Atekihcan » Sun May 05, 2013 9:04 pm
One of the most discussed problems in this forum...

https://www.beatthegmat.com/grade-of-milk-t226167.html
https://www.beatthegmat.com/mixture-of-f ... 24194.html
https://www.beatthegmat.com/gmat-prep-ps ... 10269.html
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by fifafreak » Mon May 06, 2013 6:18 am
varun289 wrote:47) 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 + 4z
Let the volumes be X Y and Z.
While Mixing : X+2Y+3Z = fat content.
After Mixing : 1.5(X+Y+Z) = fat content.
equating these 2 we get :
X=Y+3Z.

Ans. A
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by Brent@GMATPrepNow » Mon May 06, 2013 6:25 am
varun289 wrote:47) 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 + 4z
Let's start with a word equation and slowly turn it into an algebraic expression:

Total fat in mixture = 1.5% of (x+y+z)
(1% of x) + (2% of y) + (3% of z) = 0.015(x+y+z)
0.01x + 0.02y + 0.03z = 0.015x + 0.015y + 0.015z
Multiply both sides by 100: 1x + 2y + 3z = 1.5x + 1.5y + 1.5z
Simplify: 0.5y + 1.5z = 0.5x
Multiply both sides by 2: y + 3z = x

Answer = A

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by hutch27 » Mon May 27, 2013 2:10 pm
What are some other problems that are similar to this? Can an expert post a few?
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by deepsea13 » Tue May 28, 2013 2:47 am
Answer: A

Explanation: We know that the total fat in the mixture is: 1.5% of x+y+z

Now the mixture: 0.01x + 0.02y + 0.03z = 0.0015(x+y+z)

We need to know what x is in terms of y and z. So, we take the y and z terms to the LHS and x terms to the RHS. This gives us,

0.005y + 0.015z = 0.005x

From the above, we can see that:
y=x=3z (0.005 x 3 = 0.015)

SO, re-writing the equation gives us: y + 3z = x
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