"The remaining solution will be approximately what percent sodium chloride?" means: what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/7,500*100=~6.66% of the remaining solution of 7,500 gallons.

Answer: D.

Hope it's clear.
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I have a question.

Are we supposed to assume none of the sodium chloride was evaporated from the same original 10000 Gallons.

Hence of the 500 Gallons of original Sodium Chloride wouldn't the amount of sodium chloride in the solution also decrease by the same rate as the solution without Sodium Chloride?
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Ok, I assumed that the two solutions were mixed in the same container.

Thank you Bunuel
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Bunuel, even though the answer doesn't change, I still don't grasp how WATER = SOLUTION evaporated.

I have 10,000 gallons of both: NaCl and Water.
5% of NaCl = 500 gallons so water HAS to be 9,500 gallons.

It explicitly states that 2,500 gallons of water are evaporated, thus our base reduced should be 9,500 - 2,500 = 7,000 gallons of water.

So: NaCl / (NaCl+Water) = 500/(7000+500) = 1/15 = almost 7%.

As said, the answer doesn't change but the concept behind it does.

I don´t know if the problem stem were to change a bit, maybe my explanation might help.

Just read it again, and indeed it is the same. The difference is that I separate both components first, and then subtract 2,500 from Water. You do it the other way around. It should work both ways.

As a chemical engineer, it's difficult not to follow the methodology learned over the years

Sammyh21,

Have you tried doing the math by hand? There's a pattern in the calculation that shouldn't take you too long to find; by extension, the math probably won't take you as long as you might think.

GMAT assassins aren't born, they're made,
Rich
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The remaining solution will be approximately what percent sodium chloride?

The remaining solution = 7000 gallons of water + 500 gallons of sodium chloride = 7500 gallons.

Answer: 500/7500.
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We start with 10,000 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 10,000 = 500 gallons of sodium chloride.

When 2,500 gallons of water evaporate we are left with 7,500 gallons of solution. From here we can determine what percent of the 7,500 gallon solution is sodium chloride.

(sodium chloride/total solution) x 100 = ?

(500/7,500) x 100 = ?

5/75 x 100 = ?

1/15 x 100 = ?

100/15 = 20/3 = 6 2/3 = 6.67%

Answer is D.
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Why did you take out 2500 from the 10000 gallons? The question said 2500 gallons of water, so why not 9500-2500, since 500g were sodium?

Conceptually, it helps to remember that unless told otherwise, water is assumed to have zero percent sodium chloride (or zero percent alcohol, etc.).

The prompt refers to a solution that is 5 percent sodium chloride by volume. It's part water, part sodium chloride.

To make these numbers easier to work with, divide each original volume total by 100.

Let A = 100 gallons of 5 percent (=.05) sodium chloride solution

Let B = 25 gallons of water with zero percent (=0.0) sodium chloride

Resultant solution is A - B

(Concentration A)(Volume A) - (Concentration B)(Volume B) = (Resultant concentration of A - B)(Volume of resultant solution A - B)

In the equation below, arithmetically, LHS doesn't need the second term. It's just there to show that, in weighted average terms, it is being subtracted (it evaporates).

(.05)(100) - (0.0)(25) = \(\frac{x}{100}\)(100 - 25)

5 - 0 = \(\frac{75}{100}\)x

5 = \(\frac{3}{4}\)x

\(\frac{4}{3}\)*(5) = x

x = \(\frac{20}{3}\) = 6.67

Answer D
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