At a certain paint store "forest green"is made by mixing 4 p

Question

At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

Attachments

335E7D7D-D7E5-4247-B59E-AFF2F89D0AC0.png [ 728.25 KiB | Viewed 12570 times ]

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

EMPOWERgmatRichC · Accepted Answer

Hi All,

This question is essentially just about ratios and the average formula. You can actually do the math in a few different ways, but sometimes it's easiest to just break simple calculations down into their components:

We're told that we have 14 liters of "forest green" paint. Forest green paint is 4 parts blue paint and 3 parts yellow paint. With this information, we know that the 14 liters we currently have is....

14 liters of forest green = 8 liters blue paint + 6 liters yellow paint

"Verdant green" paint is 3 parts blue paint and 4 parts yellow paint. We're asked how many liters of YELLOW paint must be ADDED to the 14 liters of forest green paint to convert that paint into verdant green paint.

Since Verdant green paint uses the ratio of blue to yellow as B/Y = 3/4, we can use the current amount of blue paint that we have to figure out how much TOTAL yellow paint we need.

With 8 liters of blue, we can solve for TOTAL yellow:

8/Y = 3/4
3Y = 32
Y = 10 2/3 liters of TOTAL yellow paint are needed....

We currently have 6 liters of yellow paint, so we need....

10 2/3 - 6 = 4 2/3 MORE yellow paint.

Final Answer:  E

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

shalva · Answer

14 liters of "forest green" contain 8 liters of blue paint. in order to transform it into "verdant green" blue paint should become 3/7 of total paint volume (now it's 4/7)

Let's suppose we add x liters of yellow paint. Then

\frac{8}{14+x}=\frac{3}{7}

56=42+3x

x=\frac{14}{3}

dmetla · Answer

14 liter of Forset green have 8 liter of blue and 6 liter of yellow 
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is

Blue/yellow =8/(6+x) = ¾ 
Solving this we get x =14/3 and answer is 5

soundofmusic · Answer

In 14 litres of forest green there are 8L of Blue and 6L of Yellow. To convert this to Verdant green(whose ratio of mixture is 4 parts of yellow and 3 parts of blue paint)

8/(6+x) = 3/4
==> x = 14/3

But i do not find that in the choices.

KarishmaB · Answer

soundofmusic is correct.

In forest green, the ratio of Blue:Yellow is 4:3. If I have 14 lts of this paint, it means I have 8 lts of Blue in it and 6 litres of Yellow in it.

To make it Verdant Green I need to add Yellow because it has Blue:Yellow ratio of 3:4. If x lts is the amount of Yellow I need to add,
 \frac{8}{{6 + x}} = \frac{3}{4} 
 x = \frac{14}{3} = 4 \frac{2}{3}

The answer is not there in the options.

gtr022001 · Answer

Can we solve this algebraically, the thought of using ratios never occurred to me (for mixtures), I was trying to solve it algebraically and then it went downhill from there.

KarishmaB · Answer

You can use mixtures formula.

Method 2: We need to mix 14 litres of forest green(3/7 parts yellow) with yellow paint to give us verdant green (4/7 parts yellow).

Using mixtures formula:
Lets say we need x litres of yellow paint. This entire x will be yellow paint so fraction is 1.

\frac{(3/7)*14 + 1*x}{14 + x} = \frac{4}{7}

x = 14/3 litres

gracie · Answer

let y=liters of yellow to be added
(3/7)(14)+y=(4/7)(14+y)
3y=14
y=14/3 liters

JeffTargetTestPrep · Answer

We are given that we have 14 liters of forest green, which has the ratio of blue : yellow = 4x : 3x. Thus:

7x = 14

x = 2

So, we have 8 liters of blue and 6 liters of yellow. We can let y = the additional liters of yellow paint added to the 14 liters of forest green to change it to Verdant green and we can create the following equation:

(6 + y)/8 = 4/3

32 = 3(6 + y)

32 = 18 + 3y

14 = 3y

14/3 = y

Answer: E

jabhatta2 · Answer

Hello  chetan2u ,  Gladiator59 ,  generis

My question is on the blue font specifically

Should one assume that

- Blue paint to yellow paint for Forest green is 4x to 3x 
whereas 
- Blue paint to yellow paint for Verdant green is 3y : 4y

marking Blue paint to yellow paint for Verdant green as 3x : 4x WOULD BE WRONG

as the ratio's maybe different

Please let me know if my assumption is accurate

Mbahousegmat · Answer

At a certain paint store "forest green"is made by mixing 4 parts blue paint with 3 parts yellow paint."Verdant green"is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 14 liters of "forest green"to change it to "Verdant green"?

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

Attachments

335E7D7D-D7E5-4247-B59E-AFF2F89D0AC0.png [ 728.25 KiB | Viewed 12570 times ]

A. 2
B. 13/6
C. 3
D. 4
E. 14/3

chetan2u · Answer

Yes, both are different ratios and you cannot take same common ratio as x

Parvezahmed2210 · Answer

Forest Green
Blue : Yellow = 4: 3
14 litters= Blue : Yellow 8: 6

Verdant Green
Blue : Yellow 3:4

Let’s consider that X amount of yellow needs to be added

8/(6+X) = 3/4
=18+3X = 32 
X=14/3

Posted from my mobile device

Basshead · Answer

We know 14 liters of forest green consists of 8 blue, 6 yellow.

The ratio of verdant green is 4 yellow : 3 blue.

That means in our 14 liters of forest green, we need to add more yellow to get the 3/4 blue ratio.

We can make the equation:

8 / (6+x) = 3/4
18 + 3x = 32
3x = 14
x = 14/3

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

At a certain paint store "forest green"is made by mixing 4 p

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

At a certain paint store "forest green"is made by mixing 4 p

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards