Extreme numbers ? I have done it using the following approach and could solve it in less than a minute. Let me know if this solution looks O.K to you, else give me a shout,I will try to follow an another approach.

When Mrs. T's students answer the bonus question correctly, she awards a bonus. If the base score is between 10 and 99, the bonus is equal to 2 times the tens digit in the base score. The last test Mrs. T scored was between 10 and 99, and the student answered the bonus question correctly. Was the bonus given greater than 17% of the base score?

Say, the base score is of the form (10*a)+b , then bonus = 2*a; So, the rephrased question is

Is (2a/((10*a)+b)) > 17/100 ?

(1) The base score of the test was between 50 and 90.

Say the base score is in the 50's, So a = 5 here. =>(2a/((10*a)+b)) = 10/(50+b);
Is 10/(50+b) > 0.17 ? Taking the least and highest values of b and dividing the numerator with (50+b), you get 10/50 = 0.2(Where b =0), 10/59 = 0.16x(Where b =9); Hence Insufficient (You need not check the rest)

(2) Mrs. T added 16 bonus points to the last test she graded.

=> 2a = 16 => a = 8; => (2a/((10*a)+b)) = 16/(80+b);
Is 16/(80+b) > 0.17 ? Taking the least and highest values of b and dividing the numerator with (80+b), you get 16/80 = 0.2 (Where b =0) and 16/89 = 0.17x; So,16/(80+b)>17% Hence sufficient to answer the question.

Option [spoiler]B[/spoiler]