A certain brand of house paint must be purchased either in

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

A certain brand of house paint must be purchased either in

by BTGmoderatorDC » Mon Dec 23, 2019 7:31 pm

A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

OA C

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Mon Dec 23, 2019 7:31 pm

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Dec 23, 2019 10:17 pm

BTGmoderatorDC wrote:A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

OA C

Source: Official Guide

Color composition: Blue : White : Total
Ratio (gallons) = 3 : 2 : (3 + 2)
Ratio (gallons) = 3 : 2 : 5;

It is given that the total is 5 gallons, thus,

Ratio (gallons) = (3*3/5) : (3*2)/5 : 3/5
Actual ratio (gallons) = 1.8 : 1.2 : 3

Calculating the minimum value for the purchase:

For blue 1.8 gallons => 2 gallon => $18 * 2 = $36
For white 1.2 gallons => 1 gallon + 0.2*4 = 0.8 quart => 1 gallon + 1 quart=> $18 + $12 = $30

Least amount of money needed = $18 + $30 = $66

The correct answer: C

Hope this helps!

-Jay
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SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

by SampathKp » Tue Dec 24, 2019 2:02 pm

BTGmoderatorDC wrote:A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

Given that 1 gallon of mixture of paint has Blue colour in 3/5 proportion and White colour in 2/5 proportion.

The painter needs 3 gallons of mixture of paint i.e he need 3*3/5 of blue paint and 3*2/5 of white paint.

i.e A painter needs 1.8 gallons of blue paint and 1.2 gallons of white paint.
Blue paint = 1.8 Gallons , 2 gallons of paint is $36. 1 gallon +2 quarts of paint is $18+$24 = $42.
White paint = 1.2 gallons , 1 gallon + 1 quart of paint is enough $18+$12 = 30

The least amount a painter needs to spend to get 3 gallons of paint containing 3 blue and 2 white parts is $ 66

Answer is C

OA C

Source: Official Guide

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8089; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: A certain brand of house paint must be purchased either in

by Scott@TargetTestPrep » Mon Jan 13, 2020 2:26 pm

BTGmoderatorDC wrote: ↑
Mon Dec 23, 2019 7:31 pm
A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?

(4 quarts = 1 gallon)

A. $54
B. $60
C. $66
D. $90
E. $144

OA C

Source: Official Guide

Since 3 gallons = 12 quarts, we can create the equation:

3x + 2x = 12

5x = 12

x = 12/5 = 2.4.

So the painter needs 4.8 quarts = 1 gallon and 0.8 quarts of white paint and 7.2 quarts = 1 gallon and 3.8 quarts of blue paint.

However, the white paint must be purchased in 1-gallon cans and 1-quart cans, so the cheapest cost of the white paint is 18 + 12 = 30 dollars. One the other hand, the blue paint is cheaper when purchased in two 1-gallon cans (instead of one 1-gallon can and four 1-quart cans), so the cheapest cost of the blue paint is 2 x 18 = 36 dollars.

Therefore, the minimum expenditure for the two colors of paint is 30 + 36 = 66 dollars.

Answer: C

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