M21-26

Question

If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 and that in Southern Lake decreased by 10%, was the salt concentration in Northern Lake higher than that in Southern Lake in 2000?

(1) In 1900, the salt concentration in Southern Lake was 10% higher than in Northern Lake.
 
(2) In 1900, the salt concentration in Southern Lake was 4%.

Bunuel · Answer

Official Solution:

If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 and that in Southern Lake decreased by 10%, was the salt concentration in Northern Lake higher than that in Southern Lake in 2000? 
 
(1) In 1900, the salt concentration in Southern Lake was 10% higher than in Northern Lake.
 
Let's denote the salt concentration in Northern Lake in 1900 as  x . The salt concentration in Southern Lake in 1900 would then be  1.1x . By 2000, the salt concentration in Northern Lake increased to  1.2x , whereas in Southern Lake it decreased to  1.1x * 0.9 = 0.99x . Since  0.99x < 1.2x , the salt concentration in Northern Lake was indeed higher. This statement is sufficient.
 
(2) In 1900, the salt concentration in Southern Lake was 4%.
 
This information does not provide any insight into the concentration in Northern Lake in 1900. Hence, it's not sufficient.

Answer: A

eddyki · Answer

just wondering:

when we look at statement (1):
the salt concentration could be 1 but it could be also 0,11 in the one lake and 0,01 in the other lake. which would lead to 0,099 > 0,012 ...
so statement 1 should not be sufficient.

where I go wrong?

Bunuel · Answer

Year ---- Northern Lake ---- Southern Lake 
1900 -------- x -------------------- 1.1x
2000 ---- 1.2x -------------------- 0.9*1.1x = 0.99x

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

cosmiclatte · Answer

@ Bunuel ,

While I came to nearly the exact reasoning as the explanation, and I selected the correct answer, when it comes to the concentration of Southern Lake in 2000 can you say that the concentration, based on statement A, will always be the concentration of the Northern Lake in 1900? To clarify, since the question stem says that Southern Lake decreased by 10% from 1900 to 2000 and statement A says that Southern Lake was 10% higher than Northern Lake in 1900, then if you were to select any positive value, whatever concentration selected for Southern Lake in 1900, you know that Northern Lake is 10% less. Therefore, because Northern Lake is already 10% less than Southern Lake in 1900 and Southern Lake decreased by 10% from 1900 to 2000, the concentration of Southern Lake in 2000 is the concentration of Northern Lake in 1900. Is that line of thinking correct? If it is, then can I conclude that the concentration of Northern Lake is greater than Southern Lake in 2000 just from knowing that the concentration of Southern Lake in 2000 is the concentration of Northern Lake in 1900, which let's say is 'x' like the explanation, and the concentration of Northern Lake in 2000 is 1.2x? If this line of thinking is incorrect, any helpful insight as to why this does not work would be appreciated. I don't want to commit the wrong approach/line of thinking to future questions like this.

Thanks

M21-26

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