Martha obtained an average score of y in a total of x mandat

[BTGmoderatorAT]

Martha obtained an average score of y in a total of x mandatory papers. She also obtained a score of z in an additional optional paper. Does Martha's average score on all the x + 1 papers exceed her average score on the x mandatory papers by more than 50%?

(1) 3x = y
(2) 2z - 3y = xy

What's the best way to determine which statement is sufficient? Can any experts help?

[Anil42]

Martha obtained an average score of y in a total of x mandatory papers. She also obtained a score of z in an additional optional paper. Does Martha's average score on all the x + 1 papers exceed her average score on the x mandatory papers by more than 50%?

(1) 3x = y
(2) 2z - 3y = xy

What's the best way to determine which statement is sufficient? Can any experts help?

Let's start by rephrasing the question. If her average score is y on x mandatory papers, the sum of those scores would be yx.
If she receives z on the next paper, she'll now have a total sum of yx + z, and because she's completed another paper, she'll now have x + 1 papers. So her new average will be (yx + z)/(x+1). We want to know if this value is more than 50% greater than her original average of y. In other words we want to know if that new average is greater than 1.5y.

Rephrased Question: Is (yx + z)/(x+1) > 1.5y? Let's clean this up.
Multiply both sides by 2--> 2(yx + z)/(x+1) > 3y?
2yx + 2z > 3y *(x+1)?
2yx + 2z > 3yx + 3y?
2z - 3y > yx?

Statement 1: Nothing about z. Not Sufficient

Statement 2: Well, if 2z - 3y = yx, then we know that the answer to our rephrased question is a definitive NO. So statement 2 alone is sufficient. The answer is B.

[GMATGuruNY]

Martha obtained an average score of y in a total of x mandatory papers. She also obtained a score of z in an additional optional paper. Does Martha's average score on all the x + 1 papers exceed her average score on the x mandatory papers by more than 50%?

(1) 3x = y
(2) 2z - 3y = xy

To simplify the algebra, plug in a value for y and solve for x and z.
Let y=2, implying that 2 is the average score for x papers and that the sum of the scores for x papers = (number of papers)(average score) = (x)(2) = 2x.
For the y=2 average to increase by more than 50%, the new average must be greater than 3.
When an additional paper earns a score of z, the new sum = 2x+z, and the new average for the x+1 papers = (new sum)/(new number of papers) = (2x+z)/(x+1).
Since the answer to the question stem will be YES only if the expression in blue is greater than 3, we get:
(2x + z)/(x+1) > 3
2x + z > 3x + 3
z > x + 3.

Question stem, rephrased:
If y=2, is z > x+3?

Statement 1:
No information about z.
INSUFFICIENT.

Statement 2:
Substituting y=2 into 2z - 3y = xy, we get:
2z - (3*2) = 2x
2z - 6 = 2x
z - 3 = x
z = x+3.
Thus, the answer to the question stem is NO.
SUFFICIENT.

The correct answer is B.