A certain violet paint contains 30 percent blue pigment and 70 percent

Question is not correct as there is no clear guidance that equal parts of both paints are mixed to obtain brown paint.

Well, you can confirm by using weighted avg:

Just consider the blue pigment, as it is present in both the Violet pain and Green paint

30%(violet)-------40% (avg)---------50%(green)

\(\frac{Weight of violet}{Weight of green} = \frac{(50 - 40)}{(40 - 30)} = \frac{1}{1}\)

This means equal parts of violet and green paint were mixed to form brown paint

n+n = 10gms, hence n = 5gms i.e. 5gms of Violet and 5gms of Green

Since Red pigment is present only in the Violet paint @ 70%: \(\frac{70}{100}*5 =3.5gms\)

There is an alternative way to come up with the conclusion that there must be equal amounts of green and violet paints in the mix. Since there is blue paint in both the violet and green paints, when we combine the two paints, the percentage of blue paint in the mix will be a weighted average of the percentages of blue in the violet paint and the percentage of blue in the green paint. For example, if there is twice as much violet as green in the brown mix, the percentage of blue in the violet will get double weighted. From looking at the numbers, however, 40% is exactly the simple average of the 30% blue in violet and the 50% blue in green. This means that there must be an equal amount of both paints in the mix.

Since there are equal amounts of violet and green paint in the 10 grams of brown mixture, there must be 5 grams of each. The violet paint is 70% red, so there must be (.7)(5) = 3.5 grams of red paint in the mix.

The correct answer is B.

let v=grams of violet paint
.3v+.5(10-v)=.4*10
v=5 grams
5*.7=3.5 grams of red pigment
B

\

We are given that a certain violet paint contains 30 percent blue pigment and 70 percent red pigment, and that a certain green paint contains 50 percent blue and 50 percent yellow pigment. When the violet and green paints are mixed together, they become a brown paint with 40 percent blue pigment, and the brown paint weighs 10 grams. We need to determine the weight of the red pigment contained in the 10 grams of brown paint.

To determine the weight of the red pigment in the brown paint, we need to know the weight of the violet and green paints. Since neither weight is given, we can let x be the weight of the violet paint in grams. Since the weight of brown paint (i.e., the violet and green paints mixed) is 10 grams, the weight of the green paint is 10 - x grams.

Since 30 percent of the violet paint is the blue pigment, of the x grams of violet paint, 0.3x = the weight of the blue pigment. Similarly, since 50 percent of the green paint is the blue pigment, of the 10 - x grams of green paint, 0.5(10 - x) = the weight of the blue pigment. Finally, since 40 percent of the brown paint is the blue pigment, of the 10 grams of brown paint, 0.4(10) = 4 is the weight of the blue pigment in the entire mixture. Thus, we can set up the following equation and solve for x:

0.3x + 0.5(10 - x) = 4

3x + 5(10 - x) = 40

3x + 50 - 5x = 40

-2x = -10

x = 5

Recall that x is the weight of the violet paint. Since the violet paint is 5 grams, and 70 percent of it is the red pigment, the red pigment is 0.7(5) = 3.5 grams.

Answer: B

Hi All,

As far as these types of Weighted Average questions are concerned, this one is relatively simple. While it is 'wordy', the math behind it is easier than you'll likely see on the Official GMAT.

To start, we're given the composition of two paints:

Violet paint = 30% blue and 70% red
Green paint = 50% blue and 50% yellow

After mixing a certain amount of each paint, we end up with a brown mixture that is 40% BLUE. Notice that this is the exact average of 30 and 50... meaning that we must have an equal amount of the two paints. Since the total weight of the brown mixture is 10 grams, we must have 5 grams of violet and 5 grams of green.

The question asks for the amount of RED paint in this brown mixture. Thus, we have 70% of 5 grams... (.7)(5) = 3.5 grams

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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