rohanchowdhary wrote:

Hi All

I am stuck in this DS question.

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

Average of x mandatory papers is y and average of x+1 papers is \(\frac{xy+z}{x+1}\)

The question is whether -

\(\frac{\frac{xy+z}{x+1} - y}{y} > 0.5\) ==> \(\frac{xy+z}{x+1} - y > 0.5y\) ==> \(\frac{xy+z}{x+1} > \frac{3}{2}y\) ==> 2xy + 2z > 3xy +3y ==> 2z - 3y > xy

1) There is no information on z. Insufficient.

2) 2z – 3y = xy

==> 2z – 3y is not greater than xy

==> Martha’s average score on all the x+ 1 papers

does not exceed her average score on the x mandatory papers by more than 50%

This statement is sufficient as we have a definite answer.

Answer is B.