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If the base score is between 10 and 99, the bonus is equal [#permalink]

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02 Jun 2010, 21:05

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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.

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.

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.

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
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink]

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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]

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04 Oct 2014, 04:44

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Re: If the base score is between 10 and 99, the bonus is equal [#permalink]

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19 Jun 2016, 00:52

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