shekar123 wrote:

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?

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

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

Alternative solution :

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

if base score 51 then Bonus score :10

17% of 51 = 8.67 so Bonus score is more than 17% of base Score.

if base score is 59 then also Bonus score :10

17% of 59 = 10.03 here bonus is not greater then 17% of base score

Hence two cases insufficient

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

if Bonus is 16 then Base score must be between 80 and 89

17% of 80=13.60 , So Bonus is more than 17% of base score

17% of 89 = 15.13, Here also Bonus is more than 17 % of base score

if Base score is between 80-89 bonus score 16, will always be more than 17% of base core

Hence B is sufficient.

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- Stne