If a is a positive integer, what is the value of 75 percent of b/a ?

Knowing that ‘a’ is a positive integer, we need to find the value of 75 percent of the fraction b/a i.e. \(\frac{3}{4}\)th of the fraction \(\frac{b}{a}\). To do this, we need data about ‘a’ and ‘b’ OR at least some information about the relationship between the two. Any information that gives us these will be sufficient.

From statement I alone, we get a = 2 but we do not have any information about b. Hence, we can only rewrite the expression as \(\frac{3}{4}\)th of \(\frac{b}{2}\) which yields us another expression i.e. \(\frac{3b}{8}\); we still need the value of b to find a value for this expression.
Statement I alone is insufficient. Answer options A and D can be ruled out, possible answer options are B, C or E.

From statement II alone, b =4a. Substituting this value in the given expression,

\(\frac{3}{4}\)th of b / a = ¾ * (\(\frac{4a}{a}\)) = ¾ * (4) = 3. We get a unique value for the expression. Statement II alone is sufficient.
The correct answer option is B.

After you have interpreted statement I alone and arrived at the conclusion that data about ‘b’ will help you solve the question, if you see statement II alone, some of you may fall for the trap that statement II is needed with statement I to solve the question since statement II gives the value of b. Answer option C is the trap answer here, IMO.

But, remember that in DS questions, you have to test the individual statements alone. Also remember that you are trying to find the value of an expression and not only the individual values of a and b, so do not focus on finding the individual values all the time; instead be aware and alert about information that might help you solve the expression itself.

Hope that helps!