This question can be solved using the Double Matrix method.

Note: This technique can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- Major (Finance or Non-Finance)
- Gender (Female or Male)

Since we're dealing with percents all the way through to the answer choices, let's make things easy on ourselves and say that there are 100 students in the lecture.
So, here's the setup.


30% of the students are finance majors
So, 30 students are finance majors and 70 are not.


40% of the students are female
We get:


The gender distribution for finance majors and non-finance majors is the same.
In other words, there's a 40/60 female/male split among the finance majors and among the non-finance majors.
We get:


What percent of the students are neither female nor a finance major?
In other words, what percent of students are male non-finance majors?
Once we simplify the boxes . . .

. . . we see that 42 of the 100 students meet this criteria.
42/100 = 42%

Answer:

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