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

Question

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%

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

acegmat123 · Answer

Ratio of male to female to total= 6:4:10

Total non-finance students= 100-30=70

Since the gender distribution is same. i.e.: 6:4

Male:female of non- finance students = 42:28

Probability = 42/100= 42%

D

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Abhishek009 · Answer

Let no of attendees be 100

Finance = 30 ; Non Finance = 70
Females = 40 ; Males = 60

Total Attendees = Finance Majors + Non Finance Majors

Since, Ratio of Male : Females ( For finance majors and non-finance majors ) is the same , ratio of Males : Females to the total population will also be same...

= 60 ( Males ) * 70 ( Non Finance ) /100

= 42%
  
Hence, answer will be (D)

BrentGMATPrepNow · Answer

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. https://i.imgur.com/pAxxmoQ.png 30% of the students are finance majors (which implies 70% are NOT finance majors) So, 30 students are finance majors and 70 are not. https://i.imgur.com/bADN32Q.png 40% of the students are female (which implies 60% are male) We get: https://i.imgur.com/YN4usQK.png 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: https://i.imgur.com/bth7L94.png 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 . . . https://i.imgur.com/PIurz3x.png . . . we see that 42 of the 100 students meet this criteria. So, the probability = 42/100 = 42% Answer: D Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time. 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.youtube.com/watch?v=jK-tiBrrf04 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 More questions to practice with: EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

fskilnik · Answer

VERY beautiful problem, in which the  Venn diagram  ("overlapping sets") solves the problem nicely.

https://preview.ibb.co/c1Zo1L/17-Oct18-6h.gif

? = {\rm{None}}\,\,\,\,\left( {\,{\rm{in}}\,\,100\,} \right)

The wording in red is clearly presented below and also in the diagram!

{{{\rm{finance}}\,{\rm{majors}}\,\,{\rm{and}}\,\,{\rm{female}}} \over {{\rm{finance}}\,{\rm{majors}}}} = {{{\rm{non - finance}}\,{\rm{majors}}\,\,{\rm{and}}\,\,{\rm{female}}} \over {{\rm{non - finance}}\,{\rm{majors}}}}\,\,\,\, \Rightarrow \,\,\,\,{x \over {30}} = {{40 - x} \over {70}}

{x \over 3} = {{40 - x} \over 7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,7x = 120 - 3x\,\,\,\,\, \Rightarrow \,\,\,\,x = 12

{\rm{finance}}\,{\rm{majors}}\,\,{\rm{or}}\,\,{\rm{female }}\,{\rm{ = }}\,\,30 + 40 - x\,\,\mathop = \limits^{x\, = \,12} \,\,\,58\,\,\,\,\,

? = {\rm{Total}} - 58\,\,\mathop = \limits^{{\rm{Total}}\, = \,100} \,\,\,42\,\,\,\,\,\,\,\left( {42\% } \right)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

GinoRako · Answer

BrentGMATPrepNow

Thank you! Your explaination was the only one that i could understand this question!

Greeting from the Netherlands

BrentGMATPrepNow · Answer

Thanks  GinoRako !
Greeting back from Vancouver Island!

Akshaynandurkar · Answer

lets assume total students = 100
lets assume females in finance = x
then females in non finance = 40-x
and males in finance = 30-x
and males in non finance = 70-(40-x) = 30+x
take the ratio of males to females for both finance and non finance and equate them to get x
(30-x)/x = (30+x)/(40-x)
x = 12
then total males in non finance = 30+x = 42

miag · Answer

If we take total to be 100, 
Number of finance = 30 
Number of females = 40
Number of males = 60

Making the venn diagram for males and not finance 
we need to find the intersection: which is males and not finance = let it be x (say)
Plugging into the ratio we know, in the form of x

female and fin/ male and fin = female non fin/ male non fin
(100 - (60+70-x))/ (60-x) = (70-x)/x
Solving this we get x = 42, which is the answer

Artemov · Answer

Prob of student, who is a finance major = 30% (given); so, Prob of student, who is not a finance major = 70%
Prob of student, who is a female = 40%; so, Prob of student, who is not a female= 60%

Thus, Prob of student, who is neither female nor a finance major = 60% x 70% = 42%

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