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One gallon of soft drink is made of 40% orange juice and 60%

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One gallon of soft drink is made of 40% orange juice and 60%

by AAPL » Thu Jun 07, 2018 6:12 am

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One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2

The OA is A.

Let x = amount of orange juice to be added to the original one gallon, where concentration of added OJ is 100% or, in decimal form, 1

.40(1 gal) + x = .60(1 + x)

.4 + x = .6 + .6x

.4x = .2 ----> 4x = 2
x=1/2.

Has anyone another strategic approach to solve this PS question? Regards!
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by GMATGuruNY » Thu Jun 07, 2018 8:42 am
AAPL wrote:One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2
If 40% juice and 100% juice are combined in EQUAL AMOUNTS, the resulting juice concentration will be the AVERAGE of the two percents:
(40+100)/2 = 70.
Thus, if 1 gallon of soft drink (which is 40% juice) is combined with 1 gallon of pure juice (which is 100% juice), the resulting mixture will be 70% juice.
Since the resulting juice concentration must be LESS THAN 70%, the amount of added pure juice must be LESS than 1 gallon.

The correct answer is A.
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by Brent@GMATPrepNow » Thu Jun 07, 2018 8:45 am
AAPL wrote:One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2
IMPORTANT CONCEPT: when we combine EQUAL amounts of two mixtures, the concentration of the resulting mixture will be the AVERAGE of the two mixtures.
For example, if we combine 1 liter of a 10% salt solution with 1 liter of a 40% salt solution, the RESULTING solution will be 25% salt, since (10+40)/2 = 25.

So, If we take 1 gallon of soft drink with 40% orange juice and add an EQUAL amount (1 gallon) of 100% orange juice, then the resulting mixture will be 70% orange juice.
We want the resulting mixture to be 60% orange juice. So, we need to add LESS THAN 1 gallon of 100% orange juice

Check the answer choices . . . only one option (A) is less than 1 gallon.

Answer: A

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by Scott@TargetTestPrep » Fri Jun 08, 2018 10:22 am
AAPL wrote:One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2
We are given that one gallon of soft drink contains 0.4 gallons of OJ and 0.6 gallons of water. To make OJ 60%, we can let n = the number of gallons of additional OJ and create the following equation:

(0.4 + n)/(1 + n) = 0.6

0.4 + n = 0.6 + 0.6n

0.4n = 0.2

n = 1/2

Alternate Solution:

We start with 1 gallon of 40% orange juice. To it we add g gallons of 100% orange juice, yielding (1 + g) gallons of 60% orange juice. We can express this in an equation as:

1 x 0.40 + g x 1.0 = (1 + g) x 0.60

0.4 + g = 0.6 + 0.6g

0.4g = 0.2

4g = 2

g = 1/2

Answer: A

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