vaibhav101 wrote:the average score of X number of exams is Y. when an additional exam score Z is added in, does the average score of the exams increase by 50%?
1) 3x=y
2) 2z-3y=xy
Current average = y
=> Sum of X scores = xy
Sum of scores (x + 1) after the addition of new score z = xy + z
=> New average = (xy + z)/(x + 1)
Question: Is (xy + z)/(x + 1) = y + 50% of y = 1.5y?
So, we need to determine whether (xy + z)/(x + 1) = 1.5y.
Let's take each statement one by one.
1) 3x = y
There is no information about z. Insufficient.
2) 2z - 3y = xy
Let's manipulate (xy + z)/(x + 1) = 1.5y to see if it reurns statement 2.
(xy + z)/(x + 1) = 1.5y
xy + z = 1.5xy + 1.5y
z = 0.5xy + 1.5y
2z = xy + 3y; multiplying the eqn by 2
=> 2z - 3y = xy. Sufficient
The correct answer:
B
Hope this helps!
-Jay
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