melguy wrote:Please help me with the problem . Thanks

Statement 1:

1/3 = Spanish
1/4 = French

i.e. 7/12 are language students and hence 5/12 must be band students, considering there is no overlap.

Statement 2:

1/8 take Latin so 7/8 must be band student.

Since we don't know the total number languages offered at this school, we can't even determine the fraction of students who are language students. And even if we could determine the fraction of students who are language students, statement 2 does not help us determine the fraction
of band students.
Answer: E

Melguy, I just wanted to address two of your conclusions regarding statement 1.
Even though 1/3 of students take Spanish and 1/4 take French, we can't conclude that 7/12 are language students.
To begin, there might be other languages available (like Latin, and perhaps others).
Also, we can't even conclude that 7/12 of students take Spanish OR French, because it's possible that there is some overlap (i.e., students taking more than 1 language).
For example, let's say there are 12 students, and students A,B,C an D all take Spanish (so 1/3 take Spanish). If A,B and C also take French (so 1/4 take French), then 4/12 of students take Spanish OR French.

The other thing I wanted to point out is this: 7/12 are language students and hence 5/12 must be band students, considering there is no overlap.
If it were the case that 7/12 are language students, all we can conclude is that 5/12 are NOT language students. We can't make any conclusions about the band students from this information.

Cheers,
Brent