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How many gallons of a 7% saline solution must be added to 4 gallons of

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How many gallons of a 7% saline solution must be added to 4 gallons of  [#permalink]

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New post 25 Jan 2017, 08:44
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How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?

A. 1
B. 4
C. 5
D. 9
E. 10

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Re: How many gallons of a 7% saline solution must be added to 4 gallons of  [#permalink]

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New post 25 Jan 2017, 08:56
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Bunuel wrote:
How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?

A. 1
B. 4
C. 5
D. 9
E. 10


x(0.07) + (0.25)(4) = (0.15)(4+x). Solving we will get x=5
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How many gallons of a 7% saline solution must be added to 4 gallons of  [#permalink]

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New post 25 Jan 2017, 09:02
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Bunuel wrote:
How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?

A. 1
B. 4
C. 5
D. 9
E. 10


This question nicely illustrates how the GMAT test-makers reward students for taking their understanding of a concept to use some number sense (rather than follow a formula).

We have 4 gallons of a 25% saline solution to start

First recognize that, IF we were to add an EQUAL volume of 7% saline solution to the 4 gallons of 25% saline solution, then the salinity of the resulting mixture would be the AVERAGE of the two solutions.
That is, if we add 4 gallons of 7% saline solution to the 4 gallons of 25% saline solution, the resulting solution will be 16% saline, since (7% + 25%)/2 = 16%.
This 16% solution is VERY CLOSE to our goal of having a 15% solution.
To get down to 15%, we must add more than 4 gallons of the weaker (less saline) solution.
However, since adding 4 gallons of the 7% solution bought us VERY CLOSE to our goal of having a 15% solution, we only need to add a LITTLE MORE THAN 4 gallons of 7% solution to reach the goal salinity of 15%.

Since only one answer choice (C) is a little more than 4, we can conclude that 5 is the correct answer.

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Re: How many gallons of a 7% saline solution must be added to 4 gallons of  [#permalink]

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New post 27 Oct 2018, 04:56
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Re: How many gallons of a 7% saline solution must be added to 4 gallons of &nbs [#permalink] 27 Oct 2018, 04:56
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