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.