A certain painting job requires a mixture of yellow, green, and white

We can create the equation: y + g + w = 12.

We need to determine the number of quarts of green paint needed.

Statement One Alone:

The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.

We can let y + w = n and create the ratio:

g : n = x : 3x

Since our original equation is y + w + g = 12, substituting we have:

3x + x = 12

4x = 12

x = 3

The amount of green paint is 3 quarts. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.

Since we are only given the ratio of yellow to green paint and we don’t know anything about the white paint, we do not have enough information to solve. Statement two is not sufficient to answer the question.

Answer: A

Hi All,

We're told that a certain painting job requires a mixture of yellow, green, and white paint and that 12 quarts of paint are needed for the job. We're asked for the number of quarts of GREEN paint that are needed. This question can be answered with ratio-based math and TESTing VALUES.

(1) The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.

With the information in Fact 1, we have the following relationship:
(Green) : (Yellow + White) = 1 : 3

This means that for every 1 quart of green paint, we have a total of 3 quarts of yellow and white paint, so we can think of this ratio in terms of '4 quart blocks'. With 12 total quarts, we would have 3 of those blocks - meaning that we have 3 quarts of green paint and 9 quarts of yellow+white paint. The actual amounts of yellow and white paint don't matter though, since we're asked for the amount of GREEN paint and we now know that the answer must be 3.
Fact 1 is SUFFICIENT

(2) The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.

Fact 2 gives us a different ratio, but not enough to determine the exact amount of green paint....
IF....
Yellow = 3 quarts, Green = 2 quarts and White = 7 quarts, then the answer to the question is 2.
Yellow = 6 quarts, Green = 4 quarts and White = 2 quarts, then the answer to the question is 4.
Fact 2 is INSUFFICIENT

Final Answer:

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Answer: Option A

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from given info
#1
g/y+w = 1/3
so g = 1/4 * 12 ; 3
sufficeint
#2
y/g = 3/2
but total paint vol = 12 insufficient
IMO A

First, OG 2020 questions are more about logic than anything. They are bit more wordy thus, generally, take more time.

Let Y, G, and W be the amounts(quarts) of yellow, green, and white paint, respectively and we have Y+G+W=12. G=?
Most importantly, quarts suggests that its a positive integer.

1) The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.

\(\frac{G}{Y+W} = \frac{1}{3}\)
3G=Y+W
Now, Y + G + W = 12
4G=12
G=3

SUFFICIENT.

2) The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.
Y:G=3:2, but no information is given or can be inferred about the total amount of yellow and green paint combined in the mixture.
So,
Y:G:W = 3:2:7
Y:G:W = 6:4:2

INSUFFICIENT.

Answer A.

Similar question https://gmatclub.com/forum/a-certain-mi ... 43443.html

y+g+w=12

(1) \(\frac{g}{y+w}=\frac{1}{3}\)

\(⇒ 3g=y+w\)

\(⇒ g+3g=12; \)Sufficient.

(2) \(\frac{y}{g}=\frac{3}{2};\) No relation with white; Inusfficieint.

The answer is A

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Hi BrentGMATPrepNow, in St 2, y/g = 3/2. y+g+w=12 > 3+2+w=12 , W=7.
We get unique value of W and unique value of g is given. Therefore not sure why is not sufficient and what did I miss? Thanks Brent

For statement 2, you're correct to write y/g = 3/2.
However, this does not mean that y = 3 and g = 2 (it COULD be the case y = 3 and g = 2, but there are many other possible cases as well)
For example, if y = 6 and g = 4, then y/g = 6/4 = 3/2
For example, if y = 30 and g = 20, then y/g = 30/20 = 3/2
For example, if y = 45 and g = 30, then y/g = 45/30 = 3/2
.... and so on

Since the equation y/g = 3/2 does not ensure that y = 3 and g = 2, we can't take the equation y+g+w=12 and substitute values to get 3+2+w=12

Understand and thanks BrentGMATPrepNow. To clarify so this is in maths with ratio that we can't take y = 3 and g = 2 in y/g = 3/2 or only in this scenario? Thanks Brent

If we just know the ratio of two numbers (x and y), there's no way to tell what the actual values of x and y are.

Noted thanks BrentGMATPrepNow

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