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Intern  Joined: 27 Sep 2009
Posts: 39
If the base score is between 10 and 99, the bonus is equal  [#permalink]

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38 00:00

Difficulty:   95% (hard)

Question Stats: 42% (02:51) correct 58% (02:43) wrong based on 810 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59075

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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.

Hope it's clear.
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Director  V
Joined: 27 May 2012
Posts: 935
Re: If the base score is between 10 and 99, the bonus is equal  [#permalink]

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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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- Stne
##### General Discussion
Intern  Joined: 31 May 2010
Posts: 4

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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.
Director  Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 787
Location: India
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40 GPA: 3.5
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3
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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Director  Status: -=Given to Fly=-
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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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Director  Status: -=Given to Fly=-
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GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40 GPA: 3.5
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Bunuel Rocks _________________
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Joined: 02 Sep 2009
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Re: If the base score is between 10 and 99, the bonus is equal  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Manager  Joined: 14 Nov 2011
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Re: If the base score is between 10 and 99, the bonus is equal  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
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Re: If the base score is between 10 and 99, the bonus is equal  [#permalink]

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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]

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________ Re: If the base score is between 10 and 99, the bonus is equal   [#permalink] 05 Sep 2019, 23:21
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