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.
Let T = the tens digit of the base score and U = the units digit of the base score.
Base score = 10T + U.
Bonus = 2T.
If the bonus is greater than 17% of the base score:
2T > .17(10T + U)
.3T > .17U
T > (17U)/30.
Question rephrased: Is T > (17U)/30?
Statement 1: The base score of the test was between 50 and 90.
If the base score = 51:
5 > (17*1)/30
5 > 17/30.
YES.
If the base score = 59:
5 > (17*9)/30
5 > (17*3)/10
5 > 5.1.
NO.
Since in the first case the answer is YES, and in the second case the answer is NO, INSUFFICIENT.
Statement 2: Mrs. T added 16 bonus points to the last test she graded.
2T = 16.
T = 8.
Thus, the base score can be any value between 80 and 89, inclusive.
The greatest possible value of U is 9:
8 > (17*9)/30
8 > 5.1
YES.
Since 8 is greater than the maximum possible value of (17U)/30, SUFFICIENT.
The correct answer is
B.
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