Problem Solving

BTGmoderatorDC 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%

OA D

Source: Veritas Prep

See the image below.



Given that the gender distribution for finance majors and non-finance majors is the same,
we have x/(30 - x) = y/(70 - y)

Also, we have x + y = 60.

From x + y = 60 and x/(30 - x) = y/(70 - y), we get y = 42%.

The correct answer: D

Hope this helps!

-Jay
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I thought I'd point out that Jay and Nitink used an approach known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- finance majors or non-finance majors
- female or not female

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

BTGmoderatorDC 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%

OA D

Source: Veritas Prep

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