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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]

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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, 02:18, edited 2 times in total.
Added the OA
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Re: Pease help [#permalink]

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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]

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New post 01 Jun 2010, 02:43
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]

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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]

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New post 01 Jun 2010, 07:08
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]

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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]

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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 30 Jun 2013, 09:25
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]

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New post 13 Jul 2013, 23:20
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]

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New post 02 Aug 2014, 09:16
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
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 25 Nov 2014, 06:48
[...]in order to measure out the portions needed for the mixture?

How can you measure 0,75 gallons if you have only buckets of 0,5 and 1 gallons?

My answer:
2 cans of 1 gallon and 1 half can of black
1 can and a half of white
result: 4 gallons!

Unless you have an other bottle (or any thing to measure), you cannot separate 0,75 gallons!
Bunuel
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 25 Nov 2014, 07:03
plaverbach wrote:
[...]in order to measure out the portions needed for the mixture?

How can you measure 0,75 gallons if you have only buckets of 0,5 and 1 gallons?

My answer:
2 cans of 1 gallon and 1 half can of black
1 can and a half of white
result: 4 gallons!

Unless you have an other bottle (or any thing to measure), you cannot separate 0,75 gallons!
Bunuel


Please re-read the solution.

To get 2 gallons of gray paint we need \(\frac{3}{4}\) gallons of white paint and \(\frac{5}{4}\) 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.
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 09 Nov 2016, 06:19
benmtchong 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


I don't like the wording of the question! There is a possibility of two solutions here..all depends o what exactly "measure out" means to say in the question..and some information that I find is missing in the question. It should be clearly stated that one can measure out exactly as much as wanted from any can(example, one can take out 0.75 liters from a 1 liter can, and so forth). In this case, 2.5 is the correct answer. But if such thing is not possible, then we would have to work exclusively with 0.5 and 1 liter cans only, in which case, 4 will be the answer. I'm not sure if my argument is ill-founded, but please, clarify. I request Bunuel to comment and also clarify, so I don't make such comprehension mistakes if I did so.
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 22 Feb 2017, 02:40
ShashankDave wrote:
benmtchong 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


I don't like the wording of the question! There is a possibility of two solutions here..all depends o what exactly "measure out" means to say in the question..and some information that I find is missing in the question. It should be clearly stated that one can measure out exactly as much as wanted from any can(example, one can take out 0.75 liters from a 1 liter can, and so forth). In this case, 2.5 is the correct answer. But if such thing is not possible, then we would have to work exclusively with 0.5 and 1 liter cans only, in which case, 4 will be the answer. I'm not sure if my argument is ill-founded, but please, clarify. I request Bunuel to comment and also clarify, so I don't make such comprehension mistakes if I did so.


I approached this question in the same way and made the same mistake. My assumption was that we would have to pour together the whole (1 or 1/2 gallon) cans so that we can get at least 2 liters of grey paint, which gives E as a result.
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Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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New post 22 Feb 2017, 05:51
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Scyzo wrote:
ShashankDave wrote:
benmtchong 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


I don't like the wording of the question! There is a possibility of two solutions here..all depends o what exactly "measure out" means to say in the question..and some information that I find is missing in the question. It should be clearly stated that one can measure out exactly as much as wanted from any can(example, one can take out 0.75 liters from a 1 liter can, and so forth). In this case, 2.5 is the correct answer. But if such thing is not possible, then we would have to work exclusively with 0.5 and 1 liter cans only, in which case, 4 will be the answer. I'm not sure if my argument is ill-founded, but please, clarify. I request Bunuel to comment and also clarify, so I don't make such comprehension mistakes if I did so.


I approached this question in the same way and made the same mistake. My assumption was that we would have to pour together the whole (1 or 1/2 gallon) cans so that we can get at least 2 liters of grey paint, which gives E as a result.


Look at the last line of the question: what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

This clarifies that you need to find the least amount of paint that you need to buy to measure out the portions needed for 2 gallons mix.
Otherwise, it would have been mentioned that you need to use the whole can.
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Re: A certain shade of gray paint is obtained by mixing 3 parts   [#permalink] 22 Feb 2017, 05:51
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