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How many gallons of milk that is 10 percent butter-fat...

by AAPL » Tue Mar 20, 2018 5:14 am
How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butter-fat to obtain milk that is 20 percent butter-fat?

A. 6
B. 12
C. 14
D. 16
E. 28

The OA is B.

We can solve this PS question as follow,

10% . . . . . . . . . . . . . . . . . . . 35%
. . . . . . . . . . . . . 20% . . . . . . . . . . .
15% . . . . . . . . . . . . . . . . . . . 10%

15/10 = 2/3 -->3/2*8 = 12. Option B.

Is there another approach to this question? Can any experts help, please?
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by Brent@GMATPrepNow » Tue Mar 20, 2018 7:11 am
AAPL wrote:How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butter-fat to obtain milk that is 20 percent butter-fat?

A. 6
B. 12
C. 14
D. 16
E. 28
One option is to focus on the butter fat

We begin with 8 gallons of milk that is 35 percent butter-fat
So, the volume of butter fat = 35% of 8
= (0.35)(8)
= 2.8 gallons of butter fat (to begin)

Let x = number of gallons of milk that is 10 percent butter-fat to be added to the initial 8 gallons
The volume of butter fat = 10% of x
= 0.1x gallons of butter fat (to be added)

So, in the RESULTING mixture, we have:
Total volume of butter fat = 2.8 + 0.1x
TOTAL VOLUME of mixture = 8 + x

We want the RESULTING mixture to be 20 percent butter-fat
In other words, we want: (Total volume of butter fat)/(TOTAL VOLUME of mixture) = 20%
We can now write: (2.8 + 0.1x)/(8 + x) = 20/100
Cross multiply to get: 100(2.8 + 0.1x) = 20(8 + x)
Expand: 280 + 10x = 160 + 20x
Rearrange: 120 = 10x
Solve: x = 12

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Wed Mar 21, 2018 3:20 pm
AAPL wrote:How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butter-fat to obtain milk that is 20 percent butter-fat?

A. 6
B. 12
C. 14
D. 16
E. 28
We add x gallons of 10% butterfat milk to 8 gallons of 35% butterfat milk, and we obtain (x + 8) gallons of 20% butterfat milk. We can express this in an equation as:

0.1x + 0.35(8) = 0.2(x + 8)

0.1x + 2.8 = 0.2x + 1.6

1.2 = 0.1x

12 = x

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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