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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.