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# A paint mixture was formed by mixing exactly 3 colors of paint. By vol

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A paint mixture was formed by mixing exactly 3 colors of paint. By vol  [#permalink]

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26 Apr 2019, 03:18
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65% (hard)

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54% (01:58) correct 46% (01:37) wrong based on 125 sessions

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A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?

(1) x = y
(2) z = 60

DS24751.01
OG2020 NEW QUESTION

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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol  [#permalink]

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26 Apr 2019, 04:42
A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?
So, x%:y%:z%=1:y%:3

(1) x = y
So the volume of green paint is of same % as blue, so green is also 1 gallon.

(2) z = 60
x%:y%:z%=1:y%:3......... x%:y%:60%=1:y%:3
If 60% is 3, total = $$\frac{3*100}{60}=5$$
So green= total-blue-red=5-3-1=1 gallon

D
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol  [#permalink]

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27 Apr 2019, 09:31
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[quote="Bunuel"]A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?

(1) x = y
(2) z = 60

Target question: How many gallons of green paint were used?

Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used.
In other words, we have:
1 gallon of BLUE paint representing x% of the mixture
3 gallons of RED paint representing z% of the mixture
? gallons of GREEN paint representing y% of the mixture

Statement 1: x = y
In other words, BLUE paint and GREEN paint comprise the same PERCENTAGE of volume in the mixture
This means the volume of BLUE paint in the mixture = the volume of GREEN paint in the mixture
Since we know there's 1 gallon of BLUE paint in the mixture, we must also have 1 gallon of GREEN paint in the mixture
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 60
In other words, RED paint comprises 60% of the mixture
In other words, 3 gallons of RED paint = 60% of the mixture's TOTAL volume
It also means that 1 gallon of BLUE paint = 20% of the mixture's TOTAL volume
This means the REMAINING 20% of the mixture must be GREEN paint.
We already know that 1 gallon = 20% of the mixture
So, we must also have 1 gallon of GREEN paint in the mixture
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol  [#permalink]

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14 May 2019, 19:28
1
Hi All,

We're told that a paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was X% blue paint, Y% green paint, and Z% red paint and exactly 1 gallon of BLUE paint and 3 gallons of RED paint were used. We're asked for the number of gallons of green paint that were used. This question is built around 'System math' and has a great, built-in math shortcut that we can take advantage of....

To start, since there are only 3 colors in the mixture - and each color represents a certain percentage of the total, we can create the following equation:
X + Y + Z = 100.

In addition, we know exactly how much blue paint and red paint were used, so we can create a second equation (based around the percentages) - we used 3 times the amount of RED paint as BLUE paint, so...
Z = 3X

We now have 3 variables and 2 unique equations. If we have a third unique equation, then we'll have a System of equations and can solve for all 3 variables - meaning that we COULD answer the question that's asked (and without actually having to do all of that math).

(1) X = Y

Fact 1 gives us a third unique equation, so COULD determine the amount of green paint.
Fact 1 is SUFFICIENT

(2) Z = 60

Fact 2 also gives us a third unique equation, so COULD determine the amount of green paint.
Fact 2 is SUFFICIENT

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern Joined: 14 Apr 2017 Posts: 44 Location: Hungary GMAT 1: 690 Q50 V34 GMAT 2: 760 Q50 V42 GMAT 3: 700 Q50 V33 WE: Education (Education) Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink] ### Show Tags 17 May 2019, 13:54 1 Bunuel wrote: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used? (1) x = y (2) z = 60 DS24751.01 OG2020 NEW QUESTION Let $$B$$, $$G$$, and $$R$$, be the amounts of blue, green, and red paint used, respectively. We know that $$x+y+z=100$$ and $$B:G:R=x:y:z=1:G:3$$. The original question: $$G=?$$ 1) We know that $$x=y$$. $$x:y=1:1 \implies \frac{1}{1}=\frac{1}{G} \implies G=1$$ Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient 2) We know that $$z=60$$. $$\frac{z}{x+y}=\frac{3}{1+G}$$ $$\frac{60}{40}=\frac{3}{1+G}$$ Thus, we could get a unique value to answer the original question. $$\implies$$ Sufficient Answer: D _________________ Manager Joined: 27 Nov 2015 Posts: 100 Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink] ### Show Tags 18 May 2019, 00:25 i dont understand how "if the BLUE paint and GREEN paint comprise the same PERCENTAGE of volume in the mixture then this means the volume of BLUE paint in the mixture = the volume of GREEN paint in the mixture" can someone kindly explain this more please EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14198 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink] ### Show Tags 18 May 2019, 10:05 rnn wrote: i dont understand how "if the BLUE paint and GREEN paint comprise the same PERCENTAGE of volume in the mixture then this means the volume of BLUE paint in the mixture = the volume of GREEN paint in the mixture" can someone kindly explain this more please Hi rnn, The prompt tells us "by volume, the mixture was X% blue paint, Y% green paint, and Z% red paint." This means that the mixture is made up of just these 3 colors and each color represents a certain amount of the total. IF two of the percentages are EQUAL, then the amount of paint of those 2 colors is also EQUAL. For example: If... the mixture is 10 total gallons and is 20% blue, 20% green and 60% red, then we have.... 2 gallons of blue, 2 gallons of green and 6 gallons of red. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol  [#permalink]

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19 May 2019, 02:17
Hi Rich,

Thanks for the response. I was thinking the following.

1 gallon of BLUE paint representing x% of the mixture => $$\frac{xB}{100}=1$$
3 gallons of RED paint representing z% of the mixture => $$\frac{zR}{100}=3$$
? gallons of GREEN paint representing y% of the mixture => $$\frac{yG}{100}=?$$

Now even if i replace y with x in $$\frac{yG}{100}=?$$, I will still not be able to get the answer. I will have $$\frac{G}{B}$$, which is useless.

Kindly let me know where I am going wrong with this approach.

Thanks
Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol   [#permalink] 19 May 2019, 02:17
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