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percentage & Number theory

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percentage & Number theory

by raunakrajan » Tue Jul 06, 2010 12:50 pm
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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by khondkar » Tue Jul 06, 2010 1:40 pm
raunakrajan 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.
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by jeremy8 » Tue Jul 06, 2010 4:07 pm
I think the answer is B).

Statement 1 tells us that the score is between 50 and 90. Taking two extremes, 50 and 59, we see that the bonus on 50 would be 10, which is 20% of 50, so the bonus would be greater than 17% of the base score.

59 would still yield a bonus of 10 on the base score, but 0.17*59 is actually 10.03, so the bonus would not be greater than 17% of the base score, hence INSUFFICIENT, since we can prove both scenarii possible.

Statement 2 basically tells us that the last score was between 80 and 89 included (tens digit 8, times 2), so again we test for extremes.
In the case of 80, 16 points is again 20% of the base score, which is greater than 17% of 80.
In the case of 89, 0.17*89=15.13, so again the bonus is greater than 17% of the base score.

This is enough information to determine that the bonus is greater than 17% of the base score, hence SUFFICIENT, or B).

When the GMAT asks for "is x greater than" kind of questions, it's usually good to test extremes.
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by Rahul@gurome » Tue Jul 06, 2010 10:45 pm
Let us assume the base score = 10x + y
Then bonus = 2x
The main question becomes is 2x > 17% of (10x + y) or 0.3x > 0.17y?

(1) 50 < 10x + y < 90. We know that 0 ≤ y ≤ 9 or 0 ≤ 0.17y ≤ 1.53...range of y
So, 5 < x < 9 or 1.5 < 0.3x < 2.7....range of x
From the range of x and y we can say that 0.3x may or may not be greater than 0.17y
So, (1) is NOT SUFFICIENT.

(2) Bonus = 2x = 16, which means x = 8
So, 0.3x = 0.3(8) = 2.4
Since y is the units digit of the base score so y can take the values from 0 to 9. The maximum value of 0.17y = 0.17(9) = 1.53
We can see that 2.4 > 1.53, so 0.3x > 0.17y
So, (2) is SUFFICIENT.

The correct answer is (B).
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