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Mixture Prob

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by selango » Mon Aug 16, 2010 9:18 am
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
--Anand--
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by clock60 » Mon Aug 16, 2010 9:34 am
got 2,5 here
white:black=3:5
and we need 2 gal of mixture
3k+5k=2, 8k=2, k=1/4
white we need 3*1/4=3/4
black=5*1/4=5/4=1 1/4

for white only 1 gallon
for black 1 gallon +0,5 gallon
1+1+0,5=2,5
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by gmatmachoman » Mon Aug 16, 2010 10:04 am
For one unit of mixture , it needs 3 parts of white paint & 5 parts of black paint.

So white paint in 2 gallons of Mixture = (3/8 ) * 2
= 0.75 gallons
Black paint in 2 gallon mixture = 5/8 * 2
= 1.25 gallon

To get 0.75 gallon of white paint, it can be purchased only in 1 gallon can

To get 1.25 gallon of black paint , it can be purchased only in 1 + 0.5 gallon can

So total = 1+ (1+0.5)
= 2.5 gallons of paint
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by tgou008 » Wed Mar 16, 2011 10:29 am
IMO the answer is 2.5 (B)

Approach:

W: B
3: 5

Total mix needed = 2g
Units for purchase = 1g or 0.5g

3x + 5x = 2
8x = 2
x = 2/8 = 1/4

Therefore, substitute to find W and B
W = 3x = 3 (1/4) = 3/4 = 0.75g ---> therefore need to buy 1g of W paint
B = 5x = 5(1/4) = 5/4 = 1.25g ---> therefoer need to buy 1g + 0.5g of B paint = 1.5g

Total g of paint needed = 2.5g
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by force5 » Wed Mar 16, 2011 11:04 am
everyone got it correct. its 2.5 however its subject to an assumption that paint is allowed to be wasted. If however we say that the bought paint should not be wasted then he will have to buy a minimum of 4 gallons.
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by tgou008 » Wed Mar 16, 2011 11:10 am
force5 wrote:everyone got it correct. its 2.5 however its subject to an assumption that paint is allowed to be wasted. If however we say that the bought paint should not be wasted then he will have to buy a minimum of 4 gallons.
But the problem explicitly states that 2gallons is needed. If two gallons are needed, given the available purchase quantities there is always going to be wastage!
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by force5 » Wed Mar 16, 2011 12:07 pm
yes you are correct but since its a ratio question the proportion will always be a constant ( what ever the volume of paint). now if i induce that there should be no wastage of the paint. then the minimum that needs to be bought is 4 gallons. ( even if you want 2 gallons ) because less than 4 gallons will cause wastage of paint.
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by anirudhadhopate » Wed Mar 16, 2011 6:18 pm
force5 wrote:yes you are correct but since its a ratio question the proportion will always be a constant ( what ever the volume of paint). now if i induce that there should be no wastage of the paint. then the minimum that needs to be bought is 4 gallons. ( even if you want 2 gallons ) because less than 4 gallons will cause wastage of paint.
Agreed with force5. IMO answer should be E. What is OA?
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by sushantgupta » Sun May 08, 2011 11:22 am
total no of portion of paint needed = 3 + 5 = 8
total quantity needed = 2 gallon
So we need (3*2)/8 = 3/4 gallon white paint and (5*2)/8 = 5/4 gallon black paint.
Minimum Quantity of white paint = 1 gallon
Minimum Quantity of black paint = 1.5 gallon
Total = 1+ 15. = 2.5 Gallon .
So E is the answer.
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by kduncan » Tue May 24, 2011 1:44 am
IMO the answer is E.

Whilst it is possible to mix 2.5 gallons of paint and then throw the rest away, the question asks for the amount required "in order to measure out the portions needed for the mixture". Buying 1 gallon means measuring out exactly 3/4, whilst buying 1.5 galls will require 1/6 of a gallon to be poured away. Buying four gallons of paint will allow the grey to be mixed accurately, without resorting to fractions of cans.
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by mishelk » Sun Jun 19, 2011 2:15 am
We can look at the problem in two different ways...

Minimum Purchases/Gallons:
White Paint Requirement = (3/8)*2 = 3/4 = 0.75 gallons
Black Paint Requirement = (5/8)*2 = 5/4 = 1.25 gallons

If we consider purchase of minimum gallons of paint..
- 1 gallon of white paint would suffice.
- 1.5 gallons of black paint would suffice.
- Total 2.5 gallons would be needed. (B)

Direct Mixing from Gallons:
If we are to consider direct mixing from the gallons of the particular sizes (although it doesn't seems to be the least quantity of purchase)...
- White paint = 0.75 * 2 = 1.5 gallons (1 full gallon 1 half gallon)
- Black paint = 1.25 * 2 = 2.5 gallons (2 full gallons and 1 half gallon)
- Total 4 gallons would be required. From which we can easily measure and segregate 2 gallons using 2 empty full gallons. (E)

I think the answer has to be B (from the minimum gallons method) which is also costs least. The direct mixing would result in more wastage and excess spending. Also nothing was mentioned about the grey paint being directly made from the containers or measuring instruments being absent.

I go with (B).
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by winniethepooh » Sun Jun 19, 2011 2:33 am
Hey, force5 thanks for your replies!
But, what makes you say that if there should be no wastage then 4 gallons should be brought?
What is the scenario you are trying to explain?
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by amit2k9 » Sun Jun 19, 2011 3:44 am
white = 3/8 *2 = 0.75 black = 1.25.

thus 1+1+0.5= 2.5 required here.
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by mannuunnam » Sun Jun 19, 2011 11:56 am
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

Hey, I am not too sure but What about this approach ? I found option (C) more convincing this way..

Ratio is 3:5

(W)hite = 3
(B)lack = 5

Black can be written as = W+2

let x be the gallon of paint required

Wx+Bx= 2g
Wx+(Wx+2)= 2g

If, x = 1/2

then,
3(1/2) + (3*1/2+2)= 2g
3/2 +9/2 = 2g
6 = 2g
g = 3

Verify it with given 3:5

3*3/8 = 1
3*5/8 = 2

Option C ???
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by edvhou812 » Sun Jun 19, 2011 5:08 pm
White: 2/1*3/8 = 3/4 (One gallon of white paint needed)
Black: 2/1*5/8 = 5/4 = 1 1/4 (1 One gallon bucket, and 1 half gallon bucket needed)

1+1+.5 = 2.5

Answer: B
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