The user-friendly version of this content is available here.
The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.
This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
Patient Joe has repeated his blood tests after 1 year of dieting. To his surprise, the sum of his LDL and HDL levels has increased by 2%. However, while his HDL (good cholesterol) has increased, his LDL (bad cholesterol) has decreased by 4%. If, the year before, his LDL was 1/4 of the sum LDL and HDL, by how much percent has his HDL increased?
Denote his initial LDL level by l and his initial HDL level by h. The initial value of the sum was (l + h). We know that:
After one year of dieting:
where x is the unknown fraction of HDL.
The increase in HDL is of 20%.
The problem can also be solved by setting the unknown total amount of cholesterol to be 100.