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GMAT PREP PS question

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alex.gellatly GMAT Destroyer! Default Avatar
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GMAT PREP PS question Post Mon Apr 16, 2012 1:15 am
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    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

    Thanks in advanced

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    Post Mon Apr 16, 2012 1:31 am
    alex.gellatly wrote:
    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

    Thanks in advanced
    (x+2y+3z)/(x+y+z)= 1.5=3/2
    solving
    x= y+3z

    hence A

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    Post Mon Apr 16, 2012 3:48 am
    alex.gellatly wrote:
    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

    Thanks in advanced
    An alternate approach is to plug in values.
    To make the math easy, let z=0, implying that the mixture will include NONE of the 3% grade milk.

    The desired percentage (1.5%) is equal to the AVERAGE of X (1%) and Y (2%).
    Thus, combining equal amounts of X and Y will yield a mixture that is 1.5% milkfat.

    Let x=2, y=2 and z=0.
    The question asks for the value of x=2. This is our target.

    Now we plug y=2 and z=0 into the answers to see which yields our target of 2.

    Only answer choice A works:
    y+3z = 2 + 3*0 = 2.

    The correct answer is A.

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    Post Mon Apr 16, 2012 3:52 am
    alex.gellatly wrote:
    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

    Thanks in advanced
    The concentration of milk in the mixture would be 1% * x + 2% * y + 3% * z, which is also equal to 1.5% * (x + y + z)
    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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