MI3 wrote:Q. The average score of x number of exams is y. When an additional exam of score z is added in, does the average score of the exams increase by 50%?
(1) 3x = y (2) 2z - 3y = xy
Please opine on how to resolve the above problem.
Here's an approach that requires very little algebra.
Statement 1: 3x = y.
No information about z.
Insufficient.
Statement 2: 2z - 3y = xy.
2z = 3y + xy.
Let x=2, y=4.
Sum of the 2 scores = number*average = 2*4 = 8.
2z = 3*4 + 2*4 = 20, so z = 10.
With z included, average of the 3 scores = (8+10)/3 = 6.
Percent increase from 4 to 6 = 50%.
Let x=7, y=10.
Sum of the 7 scores = number*average = 7*10 = 70.
2z = 3*10 + 7*10 = 100, so z = 50.
With z included, average of the 8 scores = (70+50)/8 = 15.
Percent increase from 10 to 15 = 50%.
Since in each case the average increases by 50% -- and the 2 cases employ very different numbers -- sufficient.
The correct answer is
B.
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