If the salt concentration in Northern Lake

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If the salt concentration in Northern Lake

by NandishSS » Wed Jan 24, 2018 6:58 pm
If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?


(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake

(2) In 1900 the salt concentration in Southern Lake was 4%

OA: A

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by DrMaths » Thu Jan 25, 2018 6:56 am
If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?

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

1900 N : S
2000 1.2N : 0.9S

(1) S = 1.1N, so in 2000 1.2N:1.1*0.9N = 1.2:0.99 SUFFICIENT
(2) INSUFFICIENT as there is nothing to relate N to S

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by ceilidh.erickson » Thu Jan 25, 2018 4:38 pm
NandishSS wrote:If the salt concentration in Northern Lake increased by 20% from 1900 to 2000 while that in Southern Lake decreased by 10%, is in 2000, the salt concentration in Northern Lake higher than that in Southern Lake?


(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake

(2) In 1900 the salt concentration in Southern Lake was 4%

OA: A
To expand on DrMaths...

If we take:
N = northern lake salt concentration in 1900
S = southern lake salt concentration in 1900,

then 1.2N = northern lake salt concentration in 2000
and 0.9S = southern lake salt concentration in 1900.

The question is asking - the salt concentration in Northern Lake higher than that in Southern Lake in 2000? -->
1.2N > 0.9S ?
Multiply by 10: 12N > 9S ?
Cross-divide: N/S > 9/12 ? ---> N/S > 3/4 ?
(we're allowed to divide by the variable S because salt concentrations must be positive.

Target question: N/S > 3/4 ?

(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake
translate:
S = 1.1N
N/S ---> N/(1.1N) = 10/11
We have an exact value for the ratio N/S, so that's sufficient to answer our target question.

(2) In 1900 the salt concentration in Southern Lake was 4%
S = 0.4
If we try to plug that into the target question --->
N/0.4 > 3/4 ?
We have no idea, because we still don't know what the value of N is.

The answer is A.

Here's a good rule of thumb: if a DS question asks for a PROPORTION, you usually don't need a value (in this case, a value for the salt concentration level) to answer the question.
Ceilidh Erickson
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Harvard Graduate School of Education

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by NandishSS » Tue Jan 30, 2018 7:16 am
HI Experts,

Can you pls help me with plugging numbers

Thanks
Nandish

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by ceilidh.erickson » Tue Jan 30, 2018 2:37 pm
NandishSS wrote:HI Experts,

Can you pls help me with plugging numbers

Thanks
Nandish
Picking numbers would work well here. Don't worry about picking realistic salinity concentrations - just pick easy number to work with!

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

(1) In 1900 the salt concentration in Southern Lake was 10% higher than that in Northern Lake


Case 1:
Northern: 1900 = 50% salt --> 2000 = 60% salt
Southern: 1900 = 55% salt --> 2000 = 49.5% salt
Yes, Northern is higher

Case 2:
Northern: 1900 = 10% salt --> 2000 = 12% salt
Southern: 1900 = 11% salt --> 2000 = 9.9% salt
Yes, Northern is higher

We can see that regardless of what numbers we pick, Northern will always be increasing to more than Southern's starting point, and Southern will be decreasing. Therefore, we have sufficient information to show that Northern's salt concentration is higher.

(2) In 1900 the salt concentration in Southern Lake was 4%

Case 1:
Northern: 1900 = 50% salt --> 2000 = 60% salt
Southern: 1900 = 4% salt --> 2000 = 3.6% salt
Yes, Northern is higher

Case 2:
Northern: 1900 = 1% salt --> 2000 = 1.2% salt
Southern: 1900 = 4% salt --> 2000 = 3.6% salt
No, Northern is NOT higher

Insufficient. We got different results when we tested different cases here.

The answer is A.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education