Of the students in a certain school, 65 percent are enrolled in an art

Let us suppose the following,
Total students = x,
People enrolled in only art class = a,
People enrolled in only music class = c,
People enrolled in both art and music class = b

From prompt we know,
a+b = 0.65x, --- (1)
c+b = 0.70x --- (2)

we need to find b as a percent of x

Statement 1: 25 percent of the students are enrolled in only a music class.

Okay, so we are given,
c = 0.25x --- (3)

From (2) and (3), we can easily find b.

Hence sufficient

Statement 2: The ratio of the number of students who are enrolled in both an art class and a music class to the number of students who are enrolled in neither an art class nor a music class is 9 to 2.

On translating this into variables we get,

\(\frac{b}{x-(a+b+c)} = \frac{9}{2}\)
Adding and removing the variable 'b' ,
\(\frac{b}{x-((a+b)+(b+c)-b)} = \frac{9}{2}\) --- (4)
From (1), (2) and (4), we get
\(\frac{b}{x-(0.65x+0.75x - b)} = \frac{9}{2}\)
\(\frac{b}{x - 1.35x + b} = \frac{9}{2}\)
\(\frac{b}{- 0.35x + b} = \frac{9}{2}\)

From this we should be able to take out 'b' as a percent of 'x'.

Hence sufficient

Answer = D