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

Question

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. \(2 \frac{1}{2}\)

C. 3

D. \(3 \frac{1}{2}\)

E. 4

A. 2

B.  2 \frac{1}{2}

C. 3

D.  3 \frac{1}{2}

E. 4

Bunuel · Accepted Answer

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. \(2 \frac{1}{2}\)

C. 3

D. \(3 \frac{1}{2}\)

E. 4

A. 2

B.  2 \frac{1}{2}

C. 3

D.  3 \frac{1}{2}

E. 4

2 gallon of gray paint requires  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.

Bunuel · Answer

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.

sag · Answer

Doesn't  3 parts of white paint with 5 parts of black paint.  play any role... plzz explain..im missing somewhere..

thanks

sag · Answer

Thanks Bunuel.. Its crystal clear now.. now even ur 1st ans to this Q explains everything very clearly...
Thanks once again... +1...

lagomez · Answer

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

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Kriti2013 · Answer

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

tring375 · Answer

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

bhatiavai · Answer

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

ShashankDave · Answer

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.

Scyzo · Answer

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.

KarishmaB · Answer

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.

JeffTargetTestPrep · Answer

We are given that a gray pain is obtained by mixing 3 parts of white paint with 5 parts of black paint. We are also given that the paint can be purchased in one- or half-gallon cans and that the total mixture is 2 gallons. We must determine the minimum number of gallons of paint of each color needed.

Our given ratio is:

w/b = 3/5 = 1.5/2.5 = 0.75/1.25

As we can see, we need to have 0.75 gallons of white paint and 1.25 gallons of black paint in order to have 2 gallons of the mixed (i.e., gray) paint. However, in order to have the 0.75 gallons of white paint, we need to purchase 1 gallon of white paint, and in order to have the 1.25 gallons of black paint, we need to purchase 1.5 gallons of black paint. Thus, we need to purchase a total of 2.5 gallons of paint.

Answer: B

minustark · Answer

We need 2*3/8 = .75 gallons of white and 1.25 gallons of black. Plug in the options. Start from C, 3 gallons. If we buy 1 gallon of white and 2 gallons of black, we can distribute but since more than half gallons of black paint will remain, we should buy 1 one gallon of black and another half gallon of black. So, total 2 and half gallons are needed.
B is the answer

MHIKER · Answer

White: Black = 3:5, Total is 3+5=8

Required white paint=2* \frac{3}{8}   = 0.75

Required Black paint= 2* \frac{5}{8}   =1.25

Total = 0.75+1.25=2.5 or  2 \frac{1}{2}

The Answer is B

$!vakumar.m · Answer

Grey paint is obtained by mixing 3 part of White and 5 part of Black paint
say 1Gallon is G
if we mix 3G of white paint and 5G of black paint we get 8G of Grey paint
but we need only 2G of grey paint
so 2G of Grey paint = (3/4)G of white paint + (5/4)G of Black paint

but the white and black paint are available in 0.5G and 1G cans
and since we need to buy the least amount of paint 
to get 3/4 G of white paint we need to buy 1G of white paint
and to get 5/4G of black paint we need to buy 3/2 G of black paint
total 2.5G of white and black paint
Answer: B

romasharma1998 · Answer

hi,

Bunuel

is this approach correct

2 gallons =5X + 3X

x=1/4

5(1/4) =1.25 so 1 can + half can

3(1/4)= 0.75 so 1 can

total 2 1/2

RastogiSarthak99 · Answer

Whenever I see parts, i am more inclined to use fractions.

3/8 W + 5/8B = G

We need 2G

2*3/8 + 2*5/8 = 2G

6/8 W + 10/8 B

0.75W + 1.25 B

to cover 0.75 we need 1 Gallon

to cover 1.25 we need 1.5 Gallon

1 + 1.5 = 2.5

B!

A_Nishith · Answer

Let White= W & Black = B
Given, 3 Part W + 5 Part Black = 1 Part Gray
=> 3/8 W + 5/8B = 1G

=> 2*3/8 + 2*5/8 = 2G

=> 6/8 W + 10/8 B

0.75W + 1.25 B Required for 2 Gallon of Gray.

to cover 0.75 we need 1 Gallon of White Paint.

to cover 1.25 we need (1 + 1/2)= 1.5 Gallon of Black Paint.

1 + 1.5 = 2.5 . So Min. 2.5 Gallon of Paint req. to make 2 Gallon of Gray.
Ans: B

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

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

Prep Toolkit

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

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