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D.S Problem Solution need help

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D.S Problem Solution need help

by mchaubey » Fri Apr 02, 2010 2:58 pm
I came across this problem, i have the solution for it but its kind of confusing can some one help??


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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Source: — Data Sufficiency |
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by vineetbatra » Fri Apr 02, 2010 3:36 pm
I will go with D. But it took me 3.5 minutes to solve.

Statement 1 tells us that score was between 50-90. So I find 17% of these 2, i.e. 8.5 and 15.3, but their bonus will be 5*2 = 10 and 9*2 =18

Both these guys have bonus > 17% so suff

statement 2 tells that bonus is 16, so the tens digit of the base score is 8. so 17% of 80 = 13.6, even 17% of 89 is less than 16.

Is there an easier way to solve this?
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by suryapal » Fri Apr 02, 2010 5:22 pm
my answer is B

statement 1 : insufficient
take 50 as a score then according to question bonus will be 10 , then bonus will be (10/50)*100=20% i.e. greater than 17% of the score but if we take 59 then bonus will be 10 but , 17% of the 59 is 10.03 i.e bonus is less than 17% of the score

so statement give both yes and no as answer so it is insufficient

statement 2: sufficient
according to statement score is between 80 and 89 and the bonus is 16
is 80 is score than bonus is 20% of the score
if we take 89 as a score than its 17% is 15.13 which is less than 16. i.e the bonus is greater than 17% of the score

so answer is B
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by eaakbari » Sat Apr 03, 2010 12:30 am
St 1
Take 17% of 50
8.5 < 10
but 17% of 90 is greater. Hence Insuff

St 2
If she added 16 points, that tens digit is 8 and he scored in 80's
17% of 80 and 17% of 90 are both under 16

Hence B
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by mchaubey » Mon Apr 05, 2010 4:11 pm
For a given tens digit, the greater the units digit, the smaller a percentage the bonus will represent. For instance, if the student scored 10 points, his 2-point bonus would be 20% of his base score. On the other hand, if the student scored 19 points, his 2-point bonus would be about 11% of his base score.

Statement (1): The smallest percentage increases will come from the least tens digit
with the greatest units digit; the greatest percentage increase will
come from a units digit of zero. Just check 59 for the least, and any multiple of 10 for the greatest. Or, if some of this didn't occur to you, just check the extreme tens (5 and 9) with the extreme units (0 and 9)


If the base score was 90, then the bonus would have been 18 points. Since 18/90 = .2, the bonus was 20% of the base score. If the base score was 59, however, the bonus would have been 10 points. Since 10/59 equals approximately 16.9%, the bonus would not have been higher than 17%; NOT sufficient.

Statement (2): Since the bonus was 16 points, the base score must have been between 80 and 89. Then, the base score was at most 89, which means that the bonus must have been at least 16/89, which is approximately 17.97%; SUFFICIENT.
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