In a given finance lecture, 30% of the students are finance

If the distribution of gender for finance majors and non-finance majors is the same, then 40% of finance majors are female and 40% of non-finance majors are female. This simplifies the problem dramatically.

So if 30% of the students are finance majors, this means that 70% are NOT finance majors. Then, if 40% of those non-finance majors are female, 60% of those non-finance majors are NOT female. So if we take 60% of 70%, we'll get the total number of students that are NOT finance majors and NOT female. 0.6*0.7=0.42, so 42% is our answer.

The double matrix is a great tool, but it isn't always necessary or the best way to get to the answer — try to use logic to interpret the question first, then decide whether or not it's the best method to solve.

vinni.k wrote:In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%

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 is the probability that the student is neither female nor a finance major?
In other words, what is the probability that the student is a male non-finance major?
Once we simplify the boxes . . .

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

Answer: D

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent