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  • Ugly Mixture Problem – GMAT Quant Prep

    A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

    (A) 2
    (B) 2 1/2
    (C) 3
    (D) 3 1/2
    (E) 4

    Answer is B. Let me walk you through.

    This is a mixture problem.

    Step 1) "A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. "

    You should think: 3 parts white, 5 parts black. That means total there’s 8 parts.

    More specifically, 3/8 of the mixture is white stuff and 5/8 of the mixture is black stuff.

    Step 2) "If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans"

    OK. So we know the mixture 2 gallons. How much of these 2 gallons is white stuff and how much of these 2 gallons is black stuff? Of course the white and black stuff must add up to equal 2 gallons.

    Well, we know 3/8 of the mixture is white stuff. And the entire mixture is 2 gallons.

    So 3/8 of the 2 gallons = 3/8 * 2 = 6/8 = 3/4 = .75 of a gallon is white stuff

    Likewise 5/8 of the 2 gallons or 5/8 * 2 = 10/8 = 5/4 = 1.25 of the gallon is black stuff

    Step 3) " individual colors can be purchased only in one-gallon or half- gallon cans"

    What does this mean? Well, it means that the .75 needs to be rounded up to 1 gallon

    And it means the 1.25 gallon needs to be rounded up to 1.5 gallons (a 1 gallon tank and a half gallon tank)

    Combine the 1 gallon of white + 1.5 gallon of black = 2.5 total gallons = Answer (B) !!!

    Hope that helps!

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    7 responses to “Ugly Mixture Problem – GMAT Quant Prep”


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    1. Kris J

      I have a doubt with this solution.

      If B is thee answer, then the amount of white in the resulting mix will be 1/2.5, and the black will be 1.5/2.5. The ratio between white and black should be 3:5 as per the problem. But (1/2.5): (1.5/2.5) is not 3:5, its 2:3. So, then B is not the right answer, right?

      I am thinking E is the answer, as the smallest quantity of white that can be bought is (3*.5)G = 1.5G of white. And smallest quantity of black that can be bought is (5*0.5) = 2.5G of black. Total: 4G of paint – is that right?


    2. The logic is that you have to buy either half or 1 gallon cans but you don’t have to use all of the content of the can.


    3. Yes, the logic is you can onlhy buy either half gallon or full gallon but you don’t need to use all of it. So if you use a quarter gallon, you will need to buy a half gallon.
      If you use 3/4 gallon, you will need to buy a full gallon.

      You cannot just multiply (3*.5) and (5*.5) as Kris suggests above. You must round your calculations to the nearest 50 cent multiple at the very end of your calculations–not the beginning.

    4. jerry

      hi.so which choice is true?e or b?


    5. Jerry,
      Please look at the top of my response–the answer is B.
      Zeke


    6. Hi, just doing some browsing for my Michigan 4g site. Can't believe the amount of information out there. Not quite what I was looking for, but good site. Take care.

    7. JANICE

      GREAT EXPLAINATION~!!

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About Zeke Lee
Zeke Lee is the "98th %ile in 2 weeks" guy from Stanford who teaches MBA candidates how to think efficiently on the GMAT and how to study less, but score more... [more]
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