Data Sufficiency

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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