Kate took a test and she got a grade between 80% and 95%, inclusive. What is the greatest percent error she could have?

Since the value is between 80% and 95%, so the greatest percent error she could have is (95% - 80%) / 2 = 7.5%

proof

if we take for example 94.9% (the nearest value to 95%), 100% - 94.9% = 5, 4% this is thepossible value of the greatest percent error

if we take for example 80.001 (nearest value to 80%) the greatest error will be 20%, but she got a grade 95% (20% is impossible)

the greatest percent error is (95% - 80%) / 2 = 7.5%