Yellow paint

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leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Fri Sep 09, 2011 7:10 am

A paint mixture contains blue paint and yellow paint in a ratio of 5:2. If there are 14 liters of yellow paint in the mixture, how many more liters of yellow paint must be added to make the mixture yellow?

1. 29/3
2. 35/2
3. 47/2
4. 56
5. 60

Going mad with this problem.. Can someone solve it...

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Source: Beat The GMAT — Problem Solving | Fri Sep 09, 2011 7:10 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 09, 2011 8:00 am

leonswati wrote:A paint mixture contains blue paint and yellow paint in a ratio of 5:2. If there are 14 liters of yellow paint in the mixture, how many more liters of yellow paint must be added to make the mixture 2/3 yellow?

1. 29/3
2. 35/2
3. 47/2
4. 56
5. 60

Going mad with this problem.. Can someone solve it...

I added crucial information missing from the posted problem: after the yellow paint has been added, the mixture is to be 2/3 yellow.

B:Y = 5:2 = 35:14.
Thus, there are 35 gallons of blue paint, 14 gallons of yellow paint, and 35+14 = 49 total gallons of paint.

Since 2/3 of the new mixture is to be yellow, the 35 gallons of blue paint must be 1/3 of the new mixture:
35 = (1/3)x
x = 105.

New total - old total = 105-49 = 56.

The correct answer is D.
,

Last edited by GMATGuruNY on Fri Sep 09, 2011 8:20 am, edited 1 time in total.

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Fri Sep 09, 2011 8:14 am

B/Y=5/2

Y=14 so B=35

Total Volume=14+35=49

The current fraction of yellow paint in the total mixture=14/49

Now, a certain quantity, say x litres of yellow has to be added to make the fraction of yellow paint in the mixture equal 2/3

If the x litres of yellow is added then the fraction of yellow paint in the mixture becomes (14+x)/(49+x). As x is added to both. And this ratio equals 2/3
so (14+x)/(49+x)=2/3
Hence, x=56. Hence D

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Fri Sep 09, 2011 10:18 am

for a moment I thought what is this question asking ? 'make the solution yellow'

Thanks Mitch for adding the essential information here...

b/y = 35/14

total solution 49

let the amount added = x

therefore the equation becomes (49+x)2/3 = 14+x

solving this we get, X= 56

option D

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leonswati: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sun Aug 29, 2010 3:40 amFollowed by: 1 member; Thanked: 3 times

by leonswati » Fri Sep 09, 2011 11:14 am

wow.... thanks guys

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