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A certain shade of gray paint is obtained by mixing 3 parts

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A certain shade of gray paint is obtained by mixing 3 parts [#permalink] New post 29 May 2010, 12:11
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A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

A. 2
B. 2 1/2
C. 3
D. 3 1/2
E. 4
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jun 2013, 01:18, edited 2 times in total.
Added the OA
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Re: Pease help [#permalink] New post 29 May 2010, 12:34
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overlord168 wrote:
A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

a. 2
b. 2 1/2
c. 3
d 3 1/2
e. 4


2 gallon of gray paint needs 2*\frac{3}{3+5}=2*\frac{3}{8}=\frac{3}{4} gallons of white paint and 2*\frac{5}{8}=\frac{5}{4} gallons of black paint.

To get \frac{3}{4}=0.75 gallons of white paint we should purchase at least 1 gallon of white paint;
To get \frac{5}{4}=1.25 gallons of black paint we should purchase at least 1.5 gallons of black paint.

Total: 1+1.5=2.5.

Answer: B.

Hope it helps.
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Re: Pease help [#permalink] New post 01 Jun 2010, 01:43
Doesn't 3 parts of white paint with 5 parts of black paint. play any role... plzz explain..im missing somewhere..

thanks
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Re: Pease help [#permalink] New post 01 Jun 2010, 03:10
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sag wrote:
Doesn't 3 parts of white paint with 5 parts of black paint. play any role... plzz explain..im missing somewhere..

thanks


Gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint --> total 8 parts --> white 3/8 and black 5/8 --> 2 gallon of gray paint needs 2*\frac{3}{8}=\frac{3}{4} gallons of white paint and 2*\frac{5}{8}=\frac{5}{4} gallons of black paint.

Hope it's clear now.
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Re: Pease help [#permalink] New post 01 Jun 2010, 06:08
Thanks Bunuel.. Its crystal clear now.. now even ur 1st ans to this Q explains everything very clearly...
Thanks once again... +1...
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Re: Mixture Problem [#permalink] New post 22 Jul 2010, 07:49
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TheSituation wrote:
I've been banging my head against the wall on this one... someone please give me a simple straightforward solution and assurance that it was a very difficult question lol.

A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

OA:
[Reveal] Spoiler:
B


white = 3/8
black = 5/8

Combine both and that equals 1 gallon

Multiply each by two to get 2 gallons

(3/8)*2 + (5/8)*2 = 2

(3/8)*2 = 6/8 = 3/4 = .75
(5/8)*2 = 10/8 = 5/4 = 1.25

You need .75 gallons of white but since it comes in 1/2 or 1 you need 1 gallon
You need 1.25 gallons of black but since it comes in 1/2 or 1 you need 1.5

1+1.5 = 2.5
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink] New post 13 Jun 2013, 02:09
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink] New post 30 Jun 2013, 08:25
Let one gallon be 80 liters. ( Assume smartly)

30 White +50 black = 80liters

According 2 question, we need 2 gallons i.e- 160 liters. ( multiply above equation with 2)

60W+100B=160 ltrs

Minimum gallons for 60W=1 ( 1 gallon =80 liters, 1/2=40 liters)
Minimum gallons for (80+20) B= 1+0.5=1.5
Total = 1+1.5=2.5

Ans. 2.5
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink] New post 13 Jul 2013, 22:20
Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of white & black paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 = 2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink] New post 02 Aug 2014, 08:16
The mixture is made up of 3 parts white paint and 5 parts Black paint.
Hence total is 8 parts make 2 gallons of mixture.
8x = 2(gallons) ==> x = 1/4

White paint needed = 3* 1/4 =0.75. Minimum White paint needed = 1
Black Paint needed = 5* 1/4 = 1.25 Minimum Black Paint needed = 1.5

Hence Answer = 2.5. B
Re: A certain shade of gray paint is obtained by mixing 3 parts   [#permalink] 02 Aug 2014, 08:16
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