aditiniyer wrote:The average 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% ?
A) 3x = y
B) 2z-3y = xy
Statement 1:
No information about z.
INSUFFICIENT.
Statement 2:
Case 1: x=1 and y=1, implying that 1 exam has an average score of 1
Sum of the scores = (number of exams)(average score) = 1*1 = 1.
Plugging x=1 and y=1 into 2z-3y = xy, we get:
2z - 3*1 = 1*1
2z = 4
z = 2.
When the additional exam with a score of 2 is included, the new average for the resulting 2 exams = (old sum + z)/2 = (1 + 2)/2 = 1.5.
Since the average increases from 1 to 1.5, it increases by exactly 50%.
Case 2: x=3 and y=2, implying that 3 exams have an average score of 2
Sum of the scores = (number of exams)(average score) = 3*2 = 6.
Plugging x=3 and y=2 into 2z-3y = xy, we get:
2z - 3*2 = 3*2
2z = 12
z = 6.
When the additional exam with a score of 6 is included, the new average for the resulting 4 exams = (old sum + z)/4 = (6 + 6)/4 = 3.
Since the average increases from 2 to 3, it increases by exactly 50%.
The two cases above illustrate that -- for any positive values x and y -- the average will increase by exactly 50%.
SUFFICIENT.
The correct answer is
B.
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