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# A tank contains 10,000 gallons of a solution that is 5

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A tank contains 10,000 gallons of a solution that is 5 [#permalink]  20 Dec 2012, 05:23
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A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?

(A) 1.25%
(B) 3.75%
(C) 6.25%
(D) 6.67%
(E) 11.7%
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  20 Dec 2012, 05:25
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A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?

(A) 1.25%
(B) 3.75%
(C) 6.25%
(D) 6.67%
(E) 11.7%

"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.

Hope it's clear.
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  08 Mar 2013, 23:09
A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?

(A) 1.25%
(B) 3.75%
(C) 6.25%
(D) 6.67%
(E) 11.7%

5% of 10,000 = 500.

required %age = 500 * 100/7500 = 6.67%
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  30 Jun 2013, 20:12
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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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  30 Jun 2013, 21:30
Expert's post
hfbamafan wrote:
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?

We are told that from 10,000 gallons of a solution, evaporated 2,500 gallons of water. So, salt did not evaporate.

If it were the way you suggest (if salt evaporated at the same rate as the water) then the answer would simply be 5%.
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  30 Jun 2013, 21:51
Bunuel wrote:
hfbamafan wrote:
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?

We are told that from 10,000 gallons of a solution, evaporated 2,500 gallons of water. So, salt did not evaporate.

If it were the way you suggest (if salt evaporated at the same rate as the water) then the answer would simply be 5%.

Ok, I assumed that the two solutions were mixed in the same container.

Thank you Bunuel
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  01 Jul 2014, 06:23
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  02 Jul 2014, 01:54
This is a inverse proportional problem.

With the salt quantity remaining constant, if the water decreases, it means the percentage of salt increases.

$$\frac{10000}{7500} * 5$$

$$= \frac{20}{3}$$

= 6.67%

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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  22 Jul 2014, 18:34
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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.
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  23 Jul 2014, 01:32
Expert's post
Enael wrote:
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.

What contradiction do you see between you solution and mine?
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  23 Jul 2014, 08:27
Bunuel wrote:
Enael wrote:
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.

What contradiction do you see between you solution and mine?

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
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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  24 Jan 2015, 08:24
How do you convert 1/15 to decimals quickly during the test?

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Re: A tank contains 10,000 gallons of a solution that is 5 [#permalink]  24 Jan 2015, 10:41
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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.

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Re: A tank contains 10,000 gallons of a solution that is 5   [#permalink] 24 Jan 2015, 10:41
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