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If the base score is between 10 and 99, the bonus is equal [#permalink]
02 Jun 2010, 21:05
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Difficulty:
95% (hard)
Question Stats:
43% (02:56) correct
57% (02:12) wrong based on 624 sessions
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.
Re: 700 level question [#permalink]
03 Jun 2010, 05:04
B
Its cuz the percentage only ranges from 17.9% to 20% measured at any point from 80 to 89 (cuz bonus points=16)
in case of statement A . its insufficient. cuz (10/59)*100 is 16.9 which is not greater than 17% while for many other values it is greater than 17% , so it is insufficient.
Re: 700 level question [#permalink]
03 Jun 2010, 05:45
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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.
Given: Score is a two digit number - \(S=10x+y\) (as the score was between 10 and 99); Bonus - \(B=2x\). Question: is \(2x>\frac{17}{100}(10x+y)\)? --> is \(30x>17y\)?
(1) The base score of the test was between 50 and 90 --> \(5\leq{x}\leq{9}\) --> the range of \(30x\) is \(150\leq{30x}\leq{270}\) and the range of \(17y\) is \(0\leq{17y}\leq{153}\) (as \(y\) can be from 0 to 9). Hence \(30x\) may or may not be more than \(17y\). Not sufficient.
(2) Mrs. T added 16 bonus points to the last test she graded --> \(B=2x=16\) --> \(x=8\) --> \(30x=240\). Max value of \(17y=153\) (as max value of \(y\) is 9), hence \(30x\) is more than \(17y\). Sufficient.
Re: check this out! [#permalink]
09 Feb 2011, 22:33
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Let the base score be
10A+B where A is the tens digit of the base score and B is the units digit of the base score.
Bonus = 2A
Question: is [2A/(10A+B)] * 100 > 17? or [2A/(10A+B) > 0.17
Statement 1: Base score is between 50 and 90. Thus A can range from 5 to 8 [Excluding extreme values]
For each range, the ratio will be the least when B is the highest. Thus, we calculate the Bonus/Base Score ratio based on the highest base score possible for a given value of A
A = 5, Bonus = 10 Base Score = 59 Ratio = 10/59 = 0.169 < 0.17
A = 6, Bonus = 12 Base Score = 69 Ratio = 12/69 = 0.173 > 0.17
Thus not sufficient
Statement 2:
Bonus = 16
A = 8
Ratio 2A/(10A+B)
For A = 8 and B = [0, 9]
16/80> 2A/(10A+B) > 16/89 0.2> 2A/(10A+B) > 0.179
Thus the bonus awarded is greater than 17% of base score!
Sufficient
Ans: B _________________
"Wherever you go, go with all your heart" - Confucius
Re: If the base score is between 10 and 99, the bonus is equal [#permalink]
16 Aug 2013, 07:17
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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
Re: If the base score is between 10 and 99, the bonus is equal [#permalink]
04 Oct 2014, 04:44
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