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Difficulty: 655-705 Level,    Mixture Problems,                
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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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

Final Answer:

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

Solution:

Question Stem Analysis:

We need to determine the number of gallons of green paint used,given that the paint mixture was formed by mixing 1 gallon of blue paint, an unknown amount of green paint, and 3 gallons of red paint.

Statement One Alone:

With statement one, we know that the percentages of blue paint and green paint are equal. Since 1 gallon of blue paint was used in the paint mixture, then one gallon of green paint was used. Statement one alone is sufficient.

Statement Two Alone:

With statement two, we know 60% of the total paint mixture consisted of 3 gallons of the red paint This means the total number of gallons of the paint mixture is 3 / 0.6 = 30/6 = 5. Since 1 gallon of the total is blue paint, then the remaining 5 - 3 - 1 = 1 gallon must be green paint. Statement two alone is sufficient.

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

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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
Can someone explain this question in a simple manner? Why should I consider 1 and 3 given in the last sentence of the question, as ratios?
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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 = 3∗10060=53∗10060=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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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


100%volume=x%volume+y%volume+z%volume
volume=blue+green+red
volume=(1)+green+(3)
x%volume=1
z%volume=3

(1) x = y sufic.
x%volume=1 then y%volume=1=green

(2) z = 60 sufic.
z%volume=60%volume=3…volume=3/3/5=15/3=5
volume=(1)+green+(3)…5=1+3+green…green=1

Answer (D)
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A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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Alternate Approach.

Answer is D

If Red Paint (Z) = 3 gallons and Blue Paint (X) = 1 gallons,
therefore, as Z = 60%, Blue + Green = 40%.


As 60% is 3 gallons, 20% is 1 Gallons, Hence we can say that Blue paint is 20% and thus green paint is rest i.e 20%.
Therefore Green Pain is also 1 gallons, as Blue Paint is 20% = 1 Gallon.

Originally posted by hero_with_1000_faces on 18 Dec 2019, 01:53.
Last edited by hero_with_1000_faces on 19 Jan 2021, 23:29, edited 1 time in total.
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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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


Total Paint=T
Blue Green Red
x% y% z%

x% of T=1 gallon y% of T= ? z% of T=3
(2) 60% of T=3
100% of T=5

(1)x=y therefore Amount of Blue Paint = Green Paint= 1 gallon. Sufficient.
(2) T=5 (from calculation shown above), Red Paint= 3 gallons, Green Paint=5-3(Red Paint)-1(Blue Paint)=1 gallon. Sufficient.
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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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


(1) Option gives Green = 1 specific value ; Sufficient.

(2) 3 gallon red = 60%
1 gallon blue = 20%
Rest is (100-80) = 20% is green ; sufficient.

Ans. 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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Video solution from Quant Reasoning:
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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


[/quote] A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of the yellow paint are available. [/quote]

I am unable to understand the question wording or a proper difference between the two questions, can someone help here.

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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
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lostminer wrote:
I am unable to understand the question wording or a proper difference between the two questions, can someone help here.

Sure, lostminer, I will jump in. Ratios and percents do overlap, but I would not worry so much about the difference between the questions as I would how to break down the information in each one, piece by piece.

QUESTION ONE

Quote:
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

There are three unknowns, x, y, and z, and we already know the amount of blue and red paint used, in gallons. (All the units match, so we do not need to worry about conversions.) We need to find out how many gallons of green there are in the mixture.

Statement (1): If x (blue) = y (green), then we can quickly deduce that 1 gallon of green paint was added, and we need to go no further. (We do not need to actually calculate the value of y.)

Blue - 1 gallon
Green - 1 gallon
Red - 3 gallons

Statement (1) is SUFFICIENT.

Statement (2): If z (red) = 60 percent of the mixture, then 3 gallons = 60 percent and 1 gallon (blue) must equal 20 percent, leaving only 20 percent, or 1 gallon, remaining for the green paint. Thus, Statement (2) is SUFFICIENT.

The answer must be (D).

QUESTION TWO

Quote:
A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.
(2) Exactly 10 quarts of the yellow paint are available.

The first line of the problem tells us that there are six parts that make up the mixture: 2 + 3 + 1 = 6. Yellow is represented by the 3 parts, so it will comprise 50 percent of the mixture: 3/6 parts. We need to know whether there is enough yellow to make the mixture, and to figure that out, we need to know two pieces of information:

  • How much yellow is available.
  • How many units of mixture need to be made.

Statement (1): If 20 quarts of mixture are needed, we know that 10 quarts of yellow are needed, but are 10 quarts available? Statement (1) is NOT SUFFICIENT.

Statement (2): 10 quarts of yellow are available, but how much of the mixture is needed? We have only half of the information. Statement (2) is NOT SUFFICIENT.

Together, the statements provide the two pieces of information we need, so the two statements together are sufficient, and the answer must be (C).

Again, I would not worry too much about how two different problems may share certain features or appear slightly different. Just keep track of what it is you need to answer and what information you have. If you find percents, ratios, or mixtures difficult conceptually, then I would suggest checking out the theory in posts such as the Ultimate GMAT Quantitative Megathread and ALL YOU NEED FOR QUANT ! ! ! both of which can be accessed in the Announcements section of the Quantitative main page.

Thank you for thinking to ask, and good luck with your studies.

- Andrew
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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol [#permalink]
1) If the percentages are equal so are the gallons. We know blue is one gallon, thus green is also one gallon.

2) If Z is 60/100 of the solution, and 60/100 equates to 3 gallons. Thus, we have a 5 gallon solution (our total). We already know from the stem that blue is also one gallon. Green = Total - blue - red -> 5-3-1 = 1. Equivalent to statement 1.

D is our answer.
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