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by DanaJ » Tue Nov 30, 2010 1:55 pm
Source: Veritas Prep

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%

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by shovan85 » Wed Dec 01, 2010 2:16 am
DanaJ wrote:Source: Veritas Prep

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%

Experts: only Veritas Prep experts, please!
IMO D

Draw a box diagram as shown below. The 4 parameters here are Female, Male, Finance major, Non Finance major.

As it is in percentage take the total as 100. (Shown in Yellow)

30% of the students are finance majors (shown in Yellow) and 40% of the students are female (shown in Yellow)

Thus, remaining total Non finance students 70%(shown in Orange) and 60% of the students are male (shown in Orange).

Say female non finance be x then female finance will be 40-x
Say male non finance be y then female finance will be 60-y

Now question says The gender distribution for finance majors and non-finance majors is the same.

Thus x/(40-x) = y/(60-y) ...(1)

and we know x+y = 70 then x = 70-y.

Put 70-y at the place of x in eqn(1) thus solving we get y = 42 (shown red)

Now see what is y? It is the student neither female nor a finance major.

Thus 42/100 = 42%
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by jaymw » Wed Dec 01, 2010 7:06 am
The key to solving this is the following sentence:

The gender distribution for finance majors and non-finance majors is the same

We know that 40% of the total students are female. That means 40% of the finance majors are female and 40% of the non-finance majors are female.

Therefore, 60% of all non-finance majors are male. We have 70% of total students who are non-finance majors. Thus, the percent of male non-finance majors (what the questions asks you for) is 60%*70%=42%

Hope this was helpful.
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by David@VeritasPrep » Fri Dec 03, 2010 3:53 am
OA is D.

Both examples above give you the techniques to solve this problem.

Because the numbers are fairly straightforward I would use the method discussed by Jaymw. If the problem had variables in the answer choices we would need to solve this more in the way mentioned by Shovan.

Thanks guys!

Solution: To make the calculations easier, let's assume that there are 100 students in the lecture (100 is usually a good number for percent problems without concrete numbers). Of those 100 students, 30 are finance majors and 40 are female. Of the 70 non-finance majors, we know that 60 percent of them are male and 40 percent are female. Since we are looking for male non-finance majors, the total number of students is 60 percent of 70, or 42. Thus, our probability is 42% that the student called on will be male and a non-finance major.
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by thp510 » Fri Dec 17, 2010 3:02 am
David@VeritasPrep wrote:OA is D.

Solution: To make the calculations easier, let's assume that there are 100 students in the lecture (100 is usually a good number for percent problems without concrete numbers). Of those 100 students, 30 are finance majors and 40 are female.
Of the 70 non-finance majors, we know that 60 percent of them are male and 40 percent are female. Since we are looking for male non-finance majors, the total number of students is 60 percent of 70, or 42. Thus, our probability is 42% that the student called on will be male and a non-finance major.

David

Is their a simple way to explain how "The gender distribution for finance majors and non-finance majors is the same." allows you to automatically say that "Of the 70 non-finance majors, we know that 60 percent of them are male and 40 percent are female"?
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by Zerks87 » Thu Dec 30, 2010 10:10 am
I like David's explanation. I figured it out a little differently. Instead of taking 60% of 70. My thinking was:

You have 30% finance majors and, therefore, 70% non-finance majors or 7/10 of student are NOT finance majors

You have 40% females in the class and, therefore, 60% males or 6/10.

Since these two are independent events, you can multiple the two probabilities together, so:

(6/10)*(7/10) = 42/100 or 42%, D

If an expert could tell me whether my reasoning is sound, it would be appreciated.
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by anshumishra » Thu Dec 30, 2010 10:45 am
Zerks87 wrote:I like David's explanation. I figured it out a little differently. Instead of taking 60% of 70. My thinking was:

You have 30% finance majors and, therefore, 70% non-finance majors or 7/10 of student are NOT finance majors

You have 40% females in the class and, therefore, 60% males or 6/10.

Since these two are independent events, you can multiple the two probabilities together, so:

(6/10)*(7/10) = 42/100 or 42%, D

If an expert could tell me whether my reasoning is sound, it would be appreciated.
IMO, That works ! Nice approach !
Thanks
Anshu

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by del@btg » Wed Apr 27, 2011 9:54 pm
Brilliant!!!
jaymw wrote:The key to solving this is the following sentence:

The gender distribution for finance majors and non-finance majors is the same

We know that 40% of the total students are female. That means 40% of the finance majors are female and 40% of the non-finance majors are female.

Therefore, 60% of all non-finance majors are male. We have 70% of total students who are non-finance majors. Thus, the percent of male non-finance majors (what the questions asks you for) is 60%*70%=42%

Hope this was helpful.
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by sugmomo » Wed Apr 27, 2011 10:13 pm
Good Problem.Thanks for sharing.

Any idea under which range will this problem be listed ?
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by dtweah » Thu Apr 28, 2011 6:05 am
jaymw wrote:The key to solving this is the following sentence:

The gender distribution for finance majors and non-finance majors is the same

We know that 40% of the total students are female. That means 40% of the finance majors are female and 40% of the non-finance majors are female.

Therefore, 60% of all non-finance majors are male. We have 70% of total students who are non-finance majors. Thus, the percent of male non-finance majors (what the questions asks you for) is 60%*70%=42%

Hope this was helpful.
If the difficulty of a problem lies in language ambiguity, GMAT is Probably NOT Going to ask the question. How can the 'gender distribution for finance majors and non-finance majors is the same' mean that 40% of the finance majors are female and 40% of the non-finance majors are female? Since when gender meant ONLY FEMALE?
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by jaymw » Thu Apr 28, 2011 8:30 pm
dtweah wrote:
jaymw wrote:The key to solving this is the following sentence:

The gender distribution for finance majors and non-finance majors is the same

We know that 40% of the total students are female. That means 40% of the finance majors are female and 40% of the non-finance majors are female.

Therefore, 60% of all non-finance majors are male. We have 70% of total students who are non-finance majors. Thus, the percent of male non-finance majors (what the questions asks you for) is 60%*70%=42%

Hope this was helpful.
If the difficulty of a problem lies in language ambiguity, GMAT is Probably NOT Going to ask the question. How can the 'gender distribution for finance majors and non-finance majors is the same' mean that 40% of the finance majors are female and 40% of the non-finance majors are female? Since when gender meant ONLY FEMALE?
How do you think that sentence is ambiguous, i.e. what other way is there to interpret it? Gender distribution describes how the two genders are distributed, i.e. male/female-ratio or male/whole population-ratio or female/male ratio or female/whole population-ratio. If one of these ratios is the same in 2 events, then all the other ratios will be the same as well!

Gender does not mean "only female", of course, but once you know that 40% of a certain population are female, it is pretty clear what the remaining 60% are.
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by edvhou812 » Fri Apr 29, 2011 6:57 pm
This question is a Probability problem that asks for condition 1 AND condition 2. Formula: A*B

Finance majors are 30%
Hence non-finance majors are 70% (7/10)
Females are 40%
Hence males are 60% (6/10)

The probability of randomly picking a male that is not a finance major is: 6/10*7/10 = 42/100 => 42%
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by force5 » Fri Apr 29, 2011 10:40 pm
nice question... can i request another one...
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by factor26 » Thu May 26, 2011 2:25 pm
Hi

Can anyone explain the sentence "the gender distrinution for finance majors and non finance majors is the same."

The same as what? ... I actually just reread this again, gender distribution is referring to male and female (naturally) and
Each class of student finance or not. It just seems a little tricky here can someone better explain this?
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by edvhou812 » Thu May 26, 2011 6:57 pm
factor26 wrote:Hi

Can anyone explain the sentence "the gender distrinution for finance majors and non finance majors is the same."

The same as what? ... I actually just reread this again, gender distribution is referring to male and female (naturally) and
Each class of student finance or not. It just seems a little tricky here can someone better explain this?
The ratio between males and females among the majors is the same. For example: If there are 100 non-finance majors, 50 would be male and 50 would be female.
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