Data Sufficiency

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.

1) Tells you that 17% of the bonus value is anywhere between 8.5 and 15.3. If the tens digit is 8 or 9, then the answer is YES, otherwise NO. INSUFF

2) Tells you that the tens digit is 8, but it could be between 17% of 18 and 17% of 98. INSUFF.

Put together, we know that the know that 17% of base score is < 16, which is the bonus points offered.

OA is B

rijul007 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.

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.