grade of milk

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seamaster1: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Wed Dec 19, 2012 8:17 pm

grade of milk

by seamaster1 » Fri Apr 26, 2013 11:13 pm

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
Someone please help why a is correct

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Source: Beat The GMAT — Problem Solving | Fri Apr 26, 2013 11:13 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 am; Location: Delhi, India; Thanked: 344 times; Followed by:86 members

by Anju@Gurome » Fri Apr 26, 2013 11:14 pm

seamaster1 wrote: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?

The concentration of milk in the mixture = 1% of x + 2% of y + 3% of z = (x + 2y + 3z)/100
Also, the concentration of milk in the mixture = 1.5% of (x + y + z) = (1.5)*(x + y + z)/100

So, x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5y + 1.5z = 0.5x
--> y + 3z = x

The correct answer is A.

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Quant Expert, Gurome

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GMAT/MBA Expert

Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 am; Location: Delhi, India; Thanked: 344 times; Followed by:86 members

by Anju@Gurome » Fri Apr 26, 2013 11:23 pm

As the answer choices include variables, we can plug numbers for variables to solve this problem.

Let us assume z = 0.
So, we are mixing only 1% milk and 2% milk (we are not mixing 3% milk).
Now, the final concentration of the mixture of milk is 1.5% which is exactly midway between 1% and 2%.

So, in the final mixture, the amount of 1% milk must be equal to the amount of 2% milk.
--> x = y

Now, plug z = 0 in the answer choices and check which one of them gives x = y.

Only option A works.