Data Sufficiency

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.