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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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New post 26 Apr 2019, 03:18
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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



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

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New post 26 Apr 2019, 04:42
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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?
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

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

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New post 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

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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New post 14 May 2019, 19:28
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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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New post 17 May 2019, 13:54
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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

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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]

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

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New post 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.

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

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

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New post 16 Jun 2019, 03:31
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]

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New post 20 Jun 2019, 10:38
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

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

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New post 22 Oct 2019, 07:19
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

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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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Re: A paint mixture was formed by mixing exactly 3 colors of paint. By vol   [#permalink] 22 Oct 2019, 07:19
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