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# A certain mixture of paint requires blue, yellow, and red paints in

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A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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26 Jun 2017, 02:07
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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.
[Reveal] Spoiler: OA

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26 Jun 2017, 09:26
I - states How much We need of yellow.
II - states How much We have of yellow.

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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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26 Jun 2017, 10:02
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Red and blue sufficient
Yellow is sufficient?
R:b:y =2:1:3
Yellow is 50% of total$$\frac{3}{6}$$

(1) Exactly 20 quarts of the mixture are needed.
States 10 quarts of yellow paint is needed
Available quantity of yellow is unknown
NS
(2) Exactly 10 quarts of the yellow paint are available
Required quantity is unknown
Available quantityof yellow paint is 10 quarts
NS

St 1+2 : 10 quarts of yellow paint is required and available
Option C
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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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26 Jun 2017, 11:59
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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.

given : 2x + 3x + x = 6x

st[1] = 6x = 20 or x = $$\frac{10}{3}$$ : we do not know if we have this much Yellow paint==> Hence not sufficient

st[1] = ok so we have in total 10 quarts of yellow paint : we do not know what is the final mixture amount, if it is 60 then Yellow is sufficient but if the needed mixture is 120 then we will need 20 quarts of yellow which w do not have ==> hence not sufficient

st[1] + st[2] tells we need $$\frac{10}{3}$$ of yellow == which is less than the total yellow so its sufficient
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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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26 Jun 2017, 22:06
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Bunuel wrote:
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.

Blue : Yellow : Red = 2 : 3 : 1

We need to find the amount of Yellow paint required. On the ratio scale, it is 3 parts and the other two combined are 2 + 1 = 3 parts. So half of the mix must be yellow paint.

To find whether we have enough yellow, we need two things - how much yellow we have and how much mix we need.
Both statements together answer these questions and are hence sufficient.

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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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24 Jul 2017, 11:07
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Bunuel wrote:
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.

Target question: Is there enough of the yellow paint to make the desired amount of the mixture?

Statement 1: Exactly 20 quarts of the mixture are needed.
Since the ratio of blue : yellow : red = 2 : 3 : 1, we can conclude that we need:
20/3 quarts of blue paint
10 quarts of yellow paint
20/6 quarts of red paint
Since we don't know how much yellow paint is available, we cannot answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: Exactly 10 quarts of the yellow paint are available.
In this case, we don't know the VOLUME of mixed paint are needed. Consider these two cases:
Case a: we need 6 quarts of the mixed paint, which means we need 2 quarts of blue paint, 3 quarts of yellow paint and 1 quarts of red paint. In this case, there IS enough yellow paint
Case b: we need 600 quarts of the mixed paint, which means we need 200 quarts of blue paint, 300 quarts of yellow paint and 100 quarts of red paint. In this case, there is NOT enough yellow paint
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that we NEED 10 quarts of yellow paint
Statement 2 tells us that we HAVE 20 quarts of yellow paint
So, YES, there IS enough yellow paint
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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08 Aug 2017, 08:12
Bunuel wrote:
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.

b:y:r = 2:3:1
=> b = 2x
=> y = 3x
=> r = x
Total = 6x => y is half of total.
y - available = required ?

1) 20 Quartz needed => 10 Quartz of yellow needed
Yellow available ?
Insufficient

2) 10 Quartz of yellow available
Yellow needed ?
Insufficient.

1+2)
10 Needed = 10 Required.
Sufficient.
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Re: A certain mixture of paint requires blue, yellow, and red paints in [#permalink]

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15 Nov 2017, 17:22
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Bunuel wrote:
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.

We are given the ratio:

blue : yellow : red = 2x : 3x : x

We need to determine if there is enough yellow paint available to allow the ratio to hold true.

Statement One Alone:

Exactly 20 quarts of the mixture are needed.

We can create the following equation:

2x + 3x + x = 20

6x = 20

x = 20/6 = 10/3

Thus, we see that 3 x 10/3 = 10 quarts of yellow paint are needed. However, since we do not know how much yellow paint is available, statement one alone is not sufficient to answer the question.

Statement Two Alone:

Exactly 10 quarts of the yellow paint are available.

Since we do not know how many quarts of paint are needed, we cannot answer the question. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements together, we see that we need 10 quarts of yellow paint and we have exactly 10 quarts of yellow paint available. Thus, we have enough yellow paint.

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Re: A certain mixture of paint requires blue, yellow, and red paints in   [#permalink] 15 Nov 2017, 17:22
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