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If the base score is between 10 and 99, the bonus is equal

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shekar123
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If the base score is between 10 and 99, the bonus is equal [#permalink] New post   02 Jun 2010, 22:05
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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.
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Re: 700 level question [#permalink] New post   03 Jun 2010, 06:45
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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.

Answer: B.

Hope it's clear.
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink] New post   16 Aug 2013, 08:17
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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

Hence B is sufficient.
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soumyaterala
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Re: 700 level question [#permalink] New post   03 Jun 2010, 06:04
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.
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Re: check this out! [#permalink] New post   09 Feb 2011, 23:33
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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
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Re: check this out! [#permalink] New post   09 Feb 2011, 23:34
I don't think actual GMAT Questions will involve division with primes as large as 59

Where do you get these questions from dude? :D
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Re: 700 level question [#permalink] New post   10 Feb 2011, 03:16
Bunuel Rocks :)

Please don't read my crappy explanation :D
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink] New post   31 May 2013, 05:43
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If the base score is between 10 and 99, the bonus is equal [#permalink] New post   03 Jun 2013, 19:00
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


Hi Bunnel,

Thanks for this initiative.
However I miss the source of these questions and an idea about how 'GMAT like' these questions are.

Will be great help if you added those informations as well.
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink] New post   04 Jun 2013, 03:32
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cumulonimbus wrote:
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


Hi Bunnel,

Thanks for this initiative.
However I miss the source of these questions and an idea about how 'GMAT like' these questions are.

Will be great help if you added those informations as well.


All bumped questions are GMAT-like. As for the source, if it's not given in the tags, then it's not known.
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink] New post   24 Aug 2023, 12:27
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Re: If the base score is between 10 and 99, the bonus is equal [#permalink]
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