In a given finance lecture, 30% of the students are finance majors, and 40% of the students

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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%

Answer: D
Source: Veritas Prep

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BTGModeratorVI wrote:
Sat Jun 27, 2020 6:43 am
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%

Answer: D
Source: Veritas Prep
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.
Image

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

40% of the students are female
We get:
Image

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:
Image

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 . . .
Image
. . . 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
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BTGModeratorVI wrote:
Sat Jun 27, 2020 6:43 am
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%

Answer: D
Solution:

We see that the problem is asking for the percentage of students who are male and non-finance majors. We can let the number of students at the lecture be 100. Thus, 30 students are finance majors and 70 are non-finance majors. Furthermore, 40 students are female, and 60 are male.

We can let x and y be the number of female and male students who are finance majors, respectively. So we can create the equations:

x + y = 30

and

x/y = (40 - x)/(60 - y)

Since y = 30 - x, we have:

x/(30 - x) = (40 - x)/(60 - (30 - x))

x/(30 - x) = (40 - x)/(30 + x)

x(30 + x) = (30 - x)(40 - x)

30x + x^2 = 1200 - 70x + x^2

100x = 1200

x = 12

So we have 12 female finance majors, which means there are 30 - 12 = 18 male finance majors, and therefore, there are 60 - 18 = 42 male students who are not finance majors.

Alternate Solution:

We see that the problem is asking for the percentage of students who are male and non-finance majors. We can let the number of students at the lecture be 100. Thus 30 students are finance majors and 70 are non-finance majors. Furthermore, 40 students are female and 60 are male.

Since the gender distribution is the same for both finance and non-finance majors is the same, 40% of both finance and non-finance majors is female and 60% of both finance and non-finance majors is male. Thus, of the 70 non-finance majors, 70*(0.6) = 42 are male. Since we assumed that there were 100 students in the class, the probability that a randomly chosen student turns out to be a non-finance major male is 42/100 = 42%.

Answer: D

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