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OG p.236 #156 Bad question?

Expert replies
by OneTwoThreeFour » Sun Feb 06, 2011 12:23 pm
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%

[spoiler] The correct answer is D. The solution is that since 5% is sodium chloride, thus 500 gallons are sodium chloride and 9500 gallons are water. If 2,500 gallons of water were evaporated, then it would be 10,000- 2,500 =7500. And 500/ 7500 is about 6.667%.
BUT:
The question is saying 2,500 gallons of WATER evaporated, not sodium chloride! (Plus sodium chloride is a salt compound and I don't think it evaporates anyway.) So shouldn't it be 9500 -2,500 and then 500/7000 = 7.14%? Thankfully, D is still the closest answer. But, I would certainly be very unhappy if this appeared on the real test and the options for the answer choices include 6.67% and 7.14%. [/spoiler]
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Source: — Problem Solving |

by towerSpider » Sun Feb 06, 2011 1:33 pm
OneTwoThreeFour wrote: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%
lets says it's 40 gallons (with 5% (2) nacl). so 10 removed so we have 30 gallons with 2 gallons nacl so:

2/30 * 100 = 2/3 * 10 = D
People are not prisoners of fate, but prisoners of their own mind.
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by towerSpider » Sun Feb 06, 2011 1:51 pm
OneTwoThreeFour wrote: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%

[spoiler] The correct answer is D. The solution is that since 5% is sodium chloride, thus 500 gallons are sodium chloride and 9500 gallons are water. If 2,500 gallons of water were evaporated, then it would be 10,000- 2,500 =7500. And 500/ 7500 is about 6.667%.
BUT:
The question is saying 2,500 gallons of WATER evaporated, not sodium chloride! (Plus sodium chloride is a salt compound and I don't think it evaporates anyway.) So shouldn't it be 9500 -2,500 and then 500/7000 = 7.14%? Thankfully, D is still the closest answer. But, I would certainly be very unhappy if this appeared on the real test and the options for the answer choices include 6.67% and 7.14%. [/spoiler]
5% of 10000 = 500 (amount of nacl)
2500 g ran away:
500 nacl still in 7500:

500/7500 * 100 = 500 / 75
= 100 / 15
= 20 / 3
= D
People are not prisoners of fate, but prisoners of their own mind.
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by towerSpider » Sun Feb 06, 2011 2:03 pm
OneTwoThreeFour wrote: The question is saying 2,500 gallons of WATER evaporated, not sodium chloride! (Plus sodium chloride is a salt compound and I don't think it evaporates anyway.) So shouldn't it be 9500 -2,500 and then 500/7000 = 7.14%? Thankfully, D is still the closest answer. But, I would certainly be very unhappy if this appeared on the real test and the options for the answer choices include 6.67% and 7.14%.
no. you see if you have only red and yellow cups in bag. r are red and y are yellow. what's PERCENTAGE OF RED OF ALL THE CUPS IN BAG?

then you would do:

r/(r+y) * 100 .... do you see? you put EVERYTHING IN DENOMINATOR! in your case you put amount of water but NOT amount of nacl.
People are not prisoners of fate, but prisoners of their own mind.
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by OneTwoThreeFour » Sun Feb 06, 2011 2:21 pm
Thanks, I see what I did wrong. Forgot to include the 500 in the denominator. I still disagree with the steps in OG though, it really should be 9500 - 2500 = 7000. Then it should be 500 / (7000 + 500). By having 10,000 straight up subtracting 2500 means that we are not taking into consideration that water and nacl are two separate entities. To each his or her own, I guess this is just how my brain works.
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by Jeff@TargetTestPrep » Thu Jun 28, 2018 5:16 pm
OneTwoThreeFour wrote: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%
Originally, there are 0.05 x 10,000 = 500 gallons of sodium chloride. Since 2,500 gallons of water evaporate, the solution remains is 7,500 gallons; thus, the percentage of sodium chloride in the solution is:

500/7,500 = 5/75 = 1/15 ≈ 0.0667 = 6.67%

Answer: D

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