Ian wrote an examination. What percent of the maximum marks one should

I'm going to make some assumptions, since I'm not familiar with the terminology (pass marks, maximum marks, etc) used in this problem. Can I safely assume that "total marks of the exam" and "maximum marks" mean the same thing? If so, here's how I'd solve.

Starting out, there seem to be three unknowns. There's the number of marks Ian got; let's call that i. The maximum marks; we'll call that m. And the number of marks you need to pass; that's p.

The question asks what percent of the maximum is needed to pass. To answer this, you don't need to know the exact maximum, OR the exact passing mark! You only need to know the value of p/m.

"What is p/m?"

(1) The ratio of pass mark to the marks obtained by Ian in the exam is 3 : 4 and the ratio of marks obtained by Ian and total marks of the exam is 3 : 5.

Let's turn this into math.

p/i = 3/4
i/m = 3/5

If this lets us calculate p/m, it's sufficient.

i = 3/5 (m)

p/ (3/5 (m)) = 3/4

(5/3) (p/m) = 3/4

p/m = 3/4 * 3/5 = 9/20

So, this gives us an answer: 9/20, or 45%. Statement 1 is sufficient.

(2) The total marks of the exam is 100.

This is a good example of a "nice but not necessary" statement. It's the kind of thing you'd want to know in the real world, for sure, and it definitely makes the solution clearer. But by itself, it doesn't give you an answer. And you don't need it in order to find the answer, either, since you're only asked for a percentage and not an exact value.

The correct answer is A.