OG p.236 #156 Bad question?

[OneTwoThreeFour]

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]

[towerSpider]

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

[towerSpider]

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

[towerSpider]

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.

[OneTwoThreeFour]

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.

[Jeff@TargetTestPrep]

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